,,transcrib]s ,,note3 ,! pla9 text v]sion ( ?is ebook includes ma!matical =mulas 9 ,te,x notation4 ,^! =mulas are enclos$ betwe5 doll> signs4 ,! ,,html v]sion includes ! same =mulas r5d]$ 9 _! orig9al =m4 ,,e9/e9',s ,,!ories ,,( ,,relativity ,,& ,,gravitation ,a ,,selection ,,( ,,mat]ial ,,f ,,! ,,essays ,,submitt$ ,,9 ,,! ,,competition ,,= ,,! ,,eug5e ,,higg9s ,,prize ,,( #e1jjj ,,compil$ ,,& ,,edit$1 ,,& ,,introductory ,,matt] ,,suppli$ ,,by ,j4 ,,malcolm ,,bird1 ,associate ,editor1 ,sci5tific ,am]ican ,,new ,,york ,,sci5tific ,,am]ican ,,publi%+ ,,co41 ,,munn ,,co4 #aiba ,,preface ,! ob/acles :i* ! layman f9ds to und]/&+ ,e9/e9's relativity !ories lie n s mu* 9 ! inh]5t difficulty ( ^! !ories !mselves z 9 ! difficulty ( prep>+ ! m9d = _! reception4 ,! !ory is no m difficult ?an any sci5tific developm5t ( comp>able dep?2 x is n s difficult z "s ( ^!4 ,b x is a fact t = a dec5t und]/&+ ( x1 a l>ge backgr\nd ( sci5tific k & sci5tific habit ( ?\ght is ess5tial4 ,! bulk ( ! writ]s :o h attempt$ to expla9 ,e9/e9 to ! g5]al read] h n realiz$ ! great gulf :i* lies betwe5 ! m5tal processes ( ! tra9$ ma!matician & ^? ( ! man 9 ! /reet4 ,!y h n p]ceiv$ t ! lay read] mu/ be p]sonally conduct$ = a long di/ance f ! ve/ibule ( ! temple ( sci5ce be=e he comes to ,e9/e91 & t he _c by any possibility make ?is j\rney unaid$4 ,! result has be5 to pit*=k ! read] into ! intricacies ( ! subject )\t adequate prep>ation4 ,! pres5t volume avoids ?is mi/ake ) ! utmo/ c>e4 ,x avoids x1 9 fact1 ) su* delib]ation z to make x 9 ord] to say a ^w 9 explanation ( :at w at fir/ glance seem an extraord9>y arrangem5t ( mat]ial4 ,x 0 to be expect$1 d\btless1 t ?is book w\ld op5 ) a brief /atem5t ( ! g5esis & ! outcome ( ! ,e9/e9 ,prize ,essay ,conte/ = ! #e1jjj prize (f]$ by ,mr4 ,eug5e ,higg9s4 ,x 0 d\btless to be expect$ t1 aft] ?is _h be5 dismiss$1 ! w9n+ essay w\ld be giv5 ! po/ ( honor 9 advance ( all o!r mat]ial be>+ actually on ! ,e9/e9 !ories4 ,:5 ! read] obs]ves t ?is has n be5 done1 he w by all means expect a ^w ( explanation2 & x is ma9ly = ! purpose ( giv+ ?is t we make ^! introductory rem>ks4 ,! essays submitt$ 9 ! conte/1 & 9 p>ticul> ! comm5ts ( a few disappo9t$ read]s ^u ,mr4 ,bolton's prize essay1 make q pla9 :at might h be5 anticipat$--t 9 ! small compass ( #c1jjj words x is n possible bo? to prep>e ! read]'s m9d = a discussion ( ,relativity & to give a discussion t %all be adequate4 ,mr4 ,bolton himself1 9 reply+ to a prote/ t he _h n done all ?is1 has us$ ! ^w miracle--we ?9k x a well-advis$ "o4 ,no miracle 0 expect$ z a result ( ! conte/1 & none has be5 a*iev$4 ,b 9 aw>d+ ! prize1 ! ,judges _h to decide :e!r x 0 ! be/ prelim9>y exposition or ! be/ discussion t 0 want$4 ,!y decid$1 & rightly we believe1 t ! aw>d %\ld g to an actual /atem5t ( :at ! ,e9/e9 !ories are & :at !y d1 r ?an to a m]e introduction1 h[ev] well conceiv$ & well execut$ ! latt] might be4 ,nev]!less1 we %\ld be clos+ our eyes to a v obvi\s fact if we did n recognize t1 )\t some?+ 9 ! way ( prep>ation1 ! g5]al read] is n go+ to pursue ,mr4 ,bolton's essay1 or any o!r essay on ?is subject1 ) pr(it4 ,x is 9 ord] ! m =cefully to hold out inducem5ts to him to subject himself to ?is prep>ation t we place at ! head ( ! book ! *apt]s design$ to give x to him4 ,*apt] ,,ii4 is int5d$ s to br+ ! m9d ( ! read] into contact ) c]ta9 philosophical problems pres5t$ to u by our exp]i5ces ) ! ext]nal _w & our ef=ts to le>n ! facts ab\t x1 t he may approa* ! subject ( relativity ) an appreciation ( ! place x occupies z a phase ( human ?\ght & a pill> ( ! sci5tific /ructure4 ,until ! read] is aw>e ( ! exi/5ce ( ^! problems & ! directions tak5 by ! ef=ts1 successful & unsuccessful1 to unravel !m1 he is n equipp$ to compreh5d ! doctr9e ( relativity at all2 he is 9 mu* ! same case z a *ild ^: education _h rea*$ only ! prim] /age1 if ask$ to read ! ma/]pieces ( lit]ature4 ,he lacks n alone ! vocabul>y1 b equally ! m5tal backgr\nd on :i* ! vocabul>y is bas$4 ,x w be not$ t 9 ?is & ! *apt]s imm$iately foll[+ x1 ! ,editor has suppli$ mat]ial freely4 ,! obvi\s int]pretation is t satisfactory mat]ial cov]+ ! desir$ gr\nd 0 n f\nd 9 any ( ! essays2 = we are sure ! scope & numb] ( ! cr$it$ exc]pts w make x cle> t all contributions 7 adequately scrut9iz$ 9 se>* ( available passages4 ,?is inadequacy ( ! compet+ essays has be5 sev]ely comm5t$ ^u by sev]al correspond5ts1 & ! inf]5ce drawn t z a :ole ! (f]+s 7 n up to ! m>k4 ,su* a viewpo9t is :olly unju/ to ! conte/ants4 ,! essays :i* paid s]i\s att5tion to ! bus9ess ( pav+ ! way to relativity necess>ily did s at ! exp5se ( complet5ess 9 ! lat] p>agraphs :]e specific explanation ( ! ,e9/e9 !ories 0 9 ord]4 ,mr4 ,law1 ^: essay 0 by all means ! be/ ( ^? t gave mu* space to introductory rem>ks1 f\nd himself left ) only #fjj words 9 :i* to tell :at x 0 t he _h be5 introduc+4 ,! majority ( ! conte/ants appe> to h fac$ ! same "q z to subject matt] :i* ! ,judges fac$1 & to h rea*$ ! same decision4 ,!y accord+ly devot$ _! att5tion t[>d ! prize1 r ?an t[>d ! production ( an essay t w\ld be/ supplem5t t ( ! w9n]4 ,x is = ?is v reason t1 9 ^! prelim9>y *apt]s1 s l>ge a proportion ( ! mat]ial has _h to be suppli$ by ! ,editor2 & ?is v circum/ance is a tribute to ! good judgm5t ( ! competitors1 r ?an gr\nd = criticism ( _! "w4 ,! g5]al introduction ( ,*apt] ,,ii4 out ( ! way1 ,*apt]s ,,iii4 & ,,iv4 take up ! bus9ess ( lead+ ! read] into ! actual subject ( relativity4 ,! subject is "h develop$ 9 :at may be call$ ! hi/orical ord]--! ord] 9 :i* x took =m 9 ,e9/e9's own m9d4 ,bo? 9 & outside ! conte/ ( :i* ?is book is ! outcome1 a majority ( ^? :o h writt5 on relativity h foll[$ ?is ord]1 :i* is inde$ a v natural "o & "o well calculat$ to give to ! r surpris+ assumptions ( relativity a reasonabl5ess :i* !y might well appe> to ! lay m9d to lack if laid d[n m arbitr>ily4 ,9 ^! two *apt]s no ef=t is made to c>ry ! argum5t beyond ! =mulation ( ! ,special ,pr9ciple ( ! relativity ( uni=m motion1 b ?is pr9ciple is develop$ 9 consid]ably m detail ?an w\ld be ! case if x 7 left entirely to ! compet+ essayi/s4 ,! reason = ?is is aga9 t we are deal+ ) a phase ( ! subject :i* is ( subord9ate importance s f> z a complete /atem5t ( ! ,g5]al ,!ory ( ,relativity is conc]n$1 b :i* is ( ! greate/ significance 9 connection ) ! ef=t ( ! layman to acquire ! prop] prelim9>y ori5tation t[>d ! l>g] subject4 ,*apt] ,v4 goes back aga9 to g5]al gr\nd4 ,among ! ideas :i* ! compet+ essayi/s 7 =c$ to introduce into _! text on a lib]al scale is t ( non-,euclidean geometry4 ,! entire =mulation ( ! ,g5]al ,!ory ( ,relativity is 9 fact an ex]cise 9 ?is4 ,! essayi/s--good1 bad & indiff]5t alike--7 q unanim\s 9 _! decision t ?is 0 "o ?+ :i* ! read] w\ld h to assume ! responsibility ( acquir+ = himself4 ,c]ta9ly !y 7 ju/ifi$ 9 ?is2 = ! ,editor has be5 able to expla9 :at non-,euclidean geometry is only by us+ up consid]ably m space ?an ! conte/ants _h = an entire essay4 ,no ef=t has be5 made to set =? any ( ! details ( any ( ! v>i\s non-,euclidean geometries2 x has simply be5 ! aim to draw ! divid+ l9e betwe5 ,euclidean & non-,euclidean1 & to make ! exi/5ce ( ! latt] appe> reasonable1 s t :5 ! essayi/s come to talk ab\t x ! read] w n feel hopelessly at sea4 ,9 o!r words1 ?is is ano!r case ( provid+ ! m5tal backgr\nd1 b on su* a scale t x has seem$ necess>y to give a sep>ate *apt] to x4 ,*apt] ,,vi4 completes ! prelim9>y c\rse 9 ! fundam5tals ( relativity by ty+ up toge!r ! f9d+s ( ,*apt] ,v4 & ^? ( ,*apt]s ,,iii4 & ,,iv4 ,x repres5ts m or less ( a la/-m9ute *ange ( plan2 = :ile x _h be5 ! ,editor's int5t f ! beg9n+ to place ! mat]ial ( ,*apt]s ,,ii4-,v4 9 its pres5t position1 8 prelim9>y impression w\ld h be5 t ! "w ( ! pres5t ,*apt] ,,vi4 w\ld be adequately done by ! essayi/s !mselves4 ,8 read+ ( ! essays1 h[ev]1 conv9c$ him t x _h n s be5 done--t ) ! possible exception ( ,mr4 ,francis1 ! essayi/s did n make ei!r a s]i\s or a successful ef=t to %[ ! organic connection betwe5 ! ,special ,!ory ( ,relativity & ! ,m9k[ski space-"t /ructure1 or ! utt] futility ( try+ to reconcile ourselves to ! results ( ! =m] )\t employ+ ! ideas ( ! latt]4 ,s ,*apt] ,,vi4 0 suppli$ to make good ?is defici5cy1 & to complete ! m5tal equipm5t :i* ! read] requires = 8 battle ) ! ,g5]al ,!ory4 ,9 lay+ d[n a set ( g5]al pr9ciples to gov]n ! aw>d ( ! prize1 "o ( ! fir/ ?+s consid]$ by ! ,judges 0 ! relative importance ( ! ,special & ! ,g5]al ,!ories4 ,x 0 _! op9ion t no essay c\ld possibly qualify = ! prize :i* did n v di/9ctly give to ! ,g5]al ,!ory ! c5t] ( ! /age2 & t 9 fact discussion ( ! ,special ,!ory 0 p]t95t only s long z x contribut$1 9 proportion to ! space assign$ x1 to ! attack ^u ! ma9 subject4 ,! same pr9ciple has be5 employ$ 9 select+ essays = complete or sub/antially complete reproduction 9 ?is volume4 ,writ]s :o dealt ) ! ,special ,!ory 9 any o!r s5se ?an z a prelim9>y /ep t[>d ! ,g5]al ,!ory h be5 relegat$ to ! introductory *apt]s1 :]e su* exc]pts f _! "w h be5 us$ z 7 f\nd usable4 ,! di/9ction ( publication "u "n & title is res]v$ = ^? :o wrote consi/5tly & specifically ^u ! l>g] subject--) ! "o exception ( ,dr4 ,russell1 ^: exposition ( ! ,special ,!ory is s f> ! be/ ( ^? submitt$ & at ! same "t s di/9ctive t we h conclud$ x w appe> to bett] advantage by itself ?an z a "p ( ,*apt]s ,,iii4 & ,,iv4 ,foll[+ aft] ,mr4 ,bolton's essay we h tri$ to arrange ! v>i\s contributions1 n at all 9 any ord] ( m]it1 b 9 ! ord] t w make connect$ read+ ( ! book mo/ ne>ly possible & pr(itable4 ,ea* essay %\ld be made easi] ( read+ by ! exam9ation ( ^? prec$+ x2 at ! same "t ea*1 by ! *oice ( gr\nd cov]$ & by ! emphasis on po9ts n br\ght out %>ply by its pr$ecessors1 %\ld ?r[ new light ^u ^! pr$ecessors4 ,! read] w f9d t no two ( ! essays giv5 ?us 9 full duplicate or ev5 come close to duplicat+ "o ano!r4 ,!y h ( c\rse be5 select$ ) ?is 9 view2 ea* repres5ts ! be/ ( sev]al essays ( sub/antially ! same "*4 ,n all ( !m require comm5t "h1 b conc]n+ "s ( !m a ^w may well be said4 ,mr4 ,francis1 we believe1 has succe$$ 9 pack+ m sub/ance into 8 #c1jjj words ?an any o!r competitor4 ,mr4 ,elliot has come clos] ?an anybody else to really expla9+ relativity 9 t]ms famili> to ev]ybody1 )\t ask+ ! read] to enl>ge 8 vocabul>y & ) a m9imum dem& s f> z enl>g+ 8 m5tal outlook is conc]n$4 ,7 x n = c]ta9 conspicu\s defects1 8 essay w\ld probably h tak5 ! prize4 ,9 ju/ice to ! ,judges1 we %\ld /ate t we h tak5 ! lib]ty ( elim9at+ ,mr4 ,elliot's conclud+ p>agraph1 :i* 0 ! mo/ objectionable feature ( 8 essay4 ,dr4 ,du%man *ose = 8 title ! "o :i* we adopt$ = ?is book4 ,x became necess>y1 !re=e1 = u to f9d a new title = 8 essay2 aside f ?is in/ance1 ! ma9 titles appe>+ at ! heads ( ! v>i\s complete essays are ^? ( ! au?ors4 ,! subtitles h 9 practically e in/ance be5 suppli$ editorially4 ,dr4 ,pick]+ submitt$ two essays1 "o writt5 f ! viewpo9t ( ! physici/1 ! o!r f t ( ! a/ronom]4 ,to make ea* complete1 he naturally f\nd x necess>y to duplicate betwe5 !m c]ta9 introductory & g5]al mat]ial4 ,we h run ! two essays toge!r into a s+le n>rative1 ) ! elim9ation ( ?is duplicat$ mat]ial2 aside f ?is blue-p5cil+ no alt]ation has be5 made 9 ,dr4 ,pick]+'s text4 ,?is text h[ev] s]v$ z ! basis ( blue-p5cil+ t ( sev]al o!r conte/ants1 z indicat$ 9 ! foot notes4 ,= ! read] :o is qualifi$ or :o c qualify to und]/& x1 ,dr4 ,murnaghan's essay is p]haps ! mo/ illum9at+ ( all4 ,ev5 ! read] :o does n und]/& x all w realize t its au?or br+s to ! subject a fre%ness ( viewpo9t & an orig9ality ( treatm5t :i* are r lack+ 9 "s ( ! publi%$ essays1 & :i* x w readily be und]/ood 7 conspicu\sly lack+ 9 a good _m ( ! unpubli%$ ones4 ,dr4 ,murnaghan ( all ! competitors has come close/ to mak+ a contribution to sci5ce z well z to ! semi-popul> lit]ature ( sci5ce4 ,9 ! composite *apt]s1 ! brackets foll[$ by ref]5ce numb]s h be5 us$ z ! mo/ practicable means ( id5tify+ ! v>i\s individual contributions4 ,we believe t ?is "p ( ! text c be read )\t all[+ ! frequ5t occurr5ce ( ^! symbols to di/ract ! eye4 ,z to ! ref]5ces !mselves1 ! a/]isk m>ks ! contributions ( ! ,editor4 ,! numb]s are ^? atta*$ to ! essays 9 ord] ( & at ! "t ( _! receipt2 x has be5 m conv5i5t to use ^! ?an to assign consecutive numb]s to ! quot$ essays4 ,! sev]al numb]s id5tify passages f ! essays ( ! foll[+ conte/ants3 #aj3 ,fr$]ick ,w4 ,%urlock1 ,d]by1 ,engl&4 #ah3 ,l4 ,l4 ,:yte1 ,cambridge1 ,engl&4 #bd3 ,pr(4 ,moritz ,s*lick1 ,univ]sity ( ,ro/ock1 ,g]many4 #cj3 ,c4 ,e4 ,rose1 ,m4,e41 ,little ,rock1 ,ark4 #cc3 ,h4 ,g>telmann1 ,brem51 ,g]many4 #ce3 ,pr(4 ,joseph ,s4 ,ames1 ,johns ,hopk9s ,univ]sity1 ,baltimore4 #dg3 ,james ,o4 ,g4 ,gibbons1 ,ea/ ,orange4 ,n4 ,j4 #hb3 ,*>les ,h4 ,burr1 ,philadelphia4 #aja3 ,l4 ,f4 ,h4 de ,miffonis4 ,b4,a41 ,c4,e41 ,ottawa1 ,canada4 #ajb3 ,*>les ,a4 ,brunn1 ,kansas ,city4 #ajf3 ,j4 ,elias ,fries1 ,fell[ ,a4,i4,e4,e41 ,birm+ham1 ,ala4 #aad3 ,dean ,w4 ,p4 ,graham1 ,syracuse ,univ]sity1 ,syracuse1 ,n4 ,y4 #aae3 ,rev4 ,george ,?omas ,manley1 ,london4 #aaf3 ,pr(4 ,j4 ,a4 ,s*\t51 ,delft1 ,ne!rl&s4 #aba3 ,elwyn ,f4 ,burrill1 ,b]keley1 ,cal4 #abe3 ,doro?y ,burr1 ,bryn ,mawr1 ,pa4 #acj3 ,c4 ,w4 ,kanolt1 ,bureau ( ,/&>ds1 ,wa%+ton4 #ace3 ,rob]t ,/ev5son1 ,new ,york4 #aci3 ,leopold ,s*ors*1 ,new ,york4 #ada3 ,dr4 ,m4 ,c4 ,mott-,smi?1 ,los ,angeles1 ,calif4 #adg3 ,edw>d ,a4 ,cl>ke1 ,columbus1 ,o4 #adi3 ,edw>d ,a4 ,p>tridge1 ,philadelphia4 #aej3 ,col4 ,john ,millis1 ,u4 ,s4 ,a41 ,*icago4 #aeb3 ,george ,f4 ,m>/ell]1 ,detroit4 #aef3 ,d4 ,b4 ,hall1 ,c9c9nati4 #afe3 ,francis ,f>quh>1 ,york1 ,pa4 #agh3 ,dr4 ,george de ,bo!zat1 ,dayton1 ,o4 #agi3 ,pr(essor ,a4 ,e4 ,caswell1 ,univ]sity ( ,oregon1 ,eug5e1 ,ore4 #ahb3 ,c4 ,e4 ,dimick1 ,new ,london1 ,conn4 #ahf3 ,e>l ,r4 ,evans1 ,wa%+ton1 ,d4 ,c4 #ahh3 ,norman ,e4 ,gilb]t1 ,d>tm\? ,college1 ,hanov]1 ,n4 ,h4 #aib3 ,a4 d',abro4 ,new ,york4 #aid3 ,l4 ,m4 ,alex&]1 ,c9c9nati4 #aig3 ,k5ne? ,w4 ,re$1 ,ea/ ,clevel&1 ,o4 #aih3 ,pr(4 ,e4 ,n4 da ,c4 ,&rade1 ,ordnance ,college1 ,woolwi*1 ,engl&4 #baf3 ,pr(essor ,&rew ,h4 ,patt]son1 ,univ]sity ( ,nor? ,c>ol9a1 ,*apel ,hill1 ,n4 ,c4 #bbj3 ,pr(4 ,ar?ur ,gordon ,web/]1 ,cl>k ,college1 ,worce/]1 ,mass4 #bba3 ,walt] van ,b4 ,rob]ts1 ,pr9ceton ,univ]sity1 ,n4 ,j4 #bbc3 ,paul ,m4 ,bat*eld]1 ,au/91 ,tex4 #bbg3 ,pr(4 ,r4 ,w4 ,wood1 ,johns ,hopk9s ,univ]sity1 ,baltimore4 #bbi3 ,e4 ,p4 ,fairbairn1 ,m4,c41 ,b4,sc41 ,glasg[4 #bca3 ,r4 ,f4 ,deimel1 ,hobok51 ,n4 ,j4 #bcb3 ,lieut4 ,w4 ,m>k ,angus1 ,u4 ,s4 ,n41 ,philadelphia4 #bce3 ,edw>d ,adams ,ri*>dson1 ,kansas ,city4 #bfc3 ,pr(4 ,william ,b5jam9 ,smi?1 ,tulane ,univ]sity1 ,new ,orleans4 #bfd3 ,james ,rice1 ,univ]sity ( ,london1 ,london4 #bfg3 ,william ,hemm5way ,pratt1 ,lynn1 ,mass4 #bgb3 ,r4 ,bruce ,l9dsay1 ,new ,b$=d1 ,mass4 #bhc3 ,frank ,e4 ,law1 ,montclair1 ,n4 ,j4 ,9 addition to ! specific cr$it giv5 by ^! ref]5ces = specifically quot$ passages1 ! ,editor feels t he ought to ackn[l$ge 8 g5]al indebt$ness to ! compet+ essayi/s1 collectively1 = ! _m ideas :i* he has tak5 away f _! text to clo! 9 8 own words4 ,?is does n mean t ! ,editor has und]tak5 g5]ally to improve ^u ! language ( ! competitors1 b m]ely t ! read+ ( all _! essays has giv5 him _m ideas ( su* complex orig9 t he c\ld n assign cr$it if he w\ld4 ,,table ,,( ,,cont5ts ,i4--,! ,e9/e9 #e1jjj ,prize3 ,h[ ! ,conte/ ,came to be ,held1 & ,"s ( ! ,details ( ,its ,conduct4 ,by ! ,editor #a ,,ii4--,! ,_w--,& ,u3 ,an ,introductory ,discussion ( ! ,philosophy ( ,relativity1 & ( ! ,me*anism ( our ,contact ) ,"t & ,space4 ,by v>i\s contributors & ! ,editor #ai ,,iii4--,! ,relativity ( ,uni=m ,motion3 ,classical ,ideas on ! ,subject2 ! ,e!r & ! ,app>5t ,possibility ( ,absolute ,motion2 ! ,mi*elson-,morley ,exp]im5t & ! ,f9al ,negation ( ?is possibility4 ,by v>i\s contributors & ! ,editor #dg ,,iv4--,! ,special ,!ory ( ,relativity3 ,:at ,e9/e9's ,/udy ( ,uni=m ,motion ,tells ,u ,ab\t ,"t & ,space & ! ,nature ( ! ,ext]nal ,reality4 ,by v>i\s contributors & ! ,editor #gf ,v4--,t ,p>allel ,po/ulate3 ,mod]n ,geometric ,me?ods2 ! ,divid+ ,l9e ,betwe5 ,euclidean & ,non-,euclidean2 & ! ,significance ( ! ,latt]4 ,by ! ,editor #aaa ,,vi4--,! ,space-,"t ,cont9uum3 ,m9k[ski's ,_w ( ,ev5ts1 & ! ,way 9 ,:i* ,x ,fits ,into ,e9/e9's ,/ructure4 ,by ! ,editor & a few contributors #ada ,,vii4--,relativity3 ,! ,w9n+ ,essay 9 ! ,conte/ = ! ,eug5e ,higg9s #e1jjj ,prize4 ,by ,lyndon ,bolton1 ,briti% ,pat5t ,(fice1 ,london #afi ,,viii4--,! ,new ,concepts ( ,"t & ,space3 ,! ,essay 9 ,behalf ( ,:i* ! ,greate/ ,numb] ( ,diss5t+ ,op9ions ,h ,be5 ,record$4 ,by ,montgom]y ,francis1 ,new ,york #aha ,,ix4--,! ,pr9ciple ( ,relativity3 ,a ,/atem5t ( ,:at x is ,all ,ab\t1 9 ,ideas ( ,"o ,syllable4 ,by ,hugh ,elliot1 ,*islehur/1 ,k5t1 ,engl& #aie ,x4--,space1 ,"t & ,gravitation3 ,an ,outl9e ( ,e9/e9's ,!ory ( ,g5]al ,relativity4 ,by ,w4 de ,sitt]1 ,univ]sity ( ,leyd5 #bjf ,,xi4--,! ,pr9ciple ( ,g5]al ,relativity3 ,h[ ,e9/e91 to a ,degree ,nev] ,be=e ,equall$1 ,isolates ! ,ext]nal ,reality f ! ,obs]v]'s ,contribution4 ,by ,e4 ,t4 ,bell1 ,univ]sity ( ,seattle #bah ,,xii4--,=ce ,vs4 ,geometry3 ,h[ ,e9/e9 ,has ,sub/itut$ ! ,second = ! ,fir/ 9 ,connection ) ! ,cause ( ,gravitation4 ,by ,saul ,du%man1 ,s*5ectady #bcj ,,xiii4--,an ,introduction to ,relativity3 ,a ,treatm5t 9 :i* ! ,ma!matical ,connections ( ,e9/e9's ,"w are ,br\ght ,out ,m ,/rongly & ,m ,successfully ?an ,usual 9 a ,popul> ,explanation4 ,by ,h>old ,t4 ,davis1 ,univ]sity ( ,wiscons9 #bdj ,,xiv4--,new ,concepts = ,old3 ,:at ! ,_w ,looks ,l ,aft] ,e9/e9 ,has ,_h ,8 ,way ) ,x4 ,by ,john ,g4 ,mc,hardy1 ,comm&] ,r4 ,n41 ,london #bea ,,xv4--,! ,new ,_w3 ,a ,univ]se 9 ,:i* ,geometry ,takes ! ,place ( ,physics1 & ,curvature t ( ,=ce4 ,by ,george ,fr$]ick ,hem5s1 ,m4,c41 ,b4,sc41 ,london #bfe ,,xvi4--,! ,que/ ( ! ,absolute3 ,mod]n ,developm5ts 9 ,!oretical ,physics1 & ! ,climax ,suppli$ by ,e9/e94 ,by ,dr4 ,francis ,d4 ,murnaghan1 ,johns ,hopk9s ,univ]sity1 ,baltimore #bgf ,,xvii4--,! ,physical ,side ( ,relativity3 ,! ,imm$iate ,contacts betwe5 ,e9/e9's ,!ories & ,curr5t ,physics & ,a/ronomy4 ,by ,pr(essor ,william ,h4 ,pick]+1 ,h>v>d ,college ,obs]vatory1 ,m&eville1 ,jamaica #bhg ,,xviii4--,! ,practical ,significance ( ,relativity3 ,! ,be/ ,discussion ( ! ,special ,!ory ,among ,all ! ,compet+ ,essays4 ,by ,pr(4 ,h5ry ,norris ,russell1 ,pr9ceton ,univ]sity #cjf ,,xix4--,e9/e9's ,!ory ( ,relativity3 ,a ,simple ,explanation ( ,8 ,po/ulates & ,_! ,consequ5ces4 ,by ,t4 ,royds1 ,kodaikanal ,obs]vatory1 ,india #cah ,,xx4--,e9/e9's ,!ory ( ,gravitation3 ,! ,discussion ( ! ,g5]al ,!ory & ,its ,mo/ ,important ,application1 f ! ,essay by ,pr(4 ,w4 ,f4 ,g4 ,swann1 ,univ]sity ( ,m9nesota1 ,m9neapolis #cbg ,,xxi4--,! ,equival5ce ,hypo!sis3 ,! ,discussion ( ,?is1 ,) ,its ,difficulties & ! ,mann] 9 ,:i* ,e9/e9 ,has ,resolv$ ,!m1 f ! ,essay by ,pr(4 ,e4 ,n4 da ,c4 ,&rade1 ,ordnance ,college1 ,woolwi*1 ,engl& #ccd ,,xxii4--,! ,g5]al ,!ory3 ,fragm5ts ( ,p>ticul> ,m]it on ,?is ,phase ( ! ,subject4 ,by ,v>i\s ,contributors #cch ,i4 ,,! ,,e9/e9 #e1jjj ,,prize ,,h[ ,,! ,,conte/ ,,came ,,to ,,be ,,held1 ,,& ,,"s ,,( ,,! ,,details ,,( ,,its ,,conduct ,,by ,,! ,,editor ,9 ,janu>y1 #aiji1 an anonym\s donor :o 0 int]e/$ 9 ! spread ( correct sci5tific ideas (f]$ ?r\gh ! ,sci5tific ,am]ican a prize ( #ejj = ! be/ essay expla9+1 9 simple non-te*nical language1 t p>adise ( ma!maticians & bugaboo ( pla9 ord9>y folk--! f\r? dim5sion4 ,_m essays 7 submitt$ 9 ?is competition1 & 9 addition to t ( ! w9n] "s tw5ty 7 adjudg$ wor?y ( ultimate publication4 ,x 0 felt t ! competition _h add$ di/9ctly to ! popul> und]/&+ ( ?is significant subject2 t x _h done mu* to cle> up popul> misconception ( j :at ! ma!matician means :5 he talks ( f\r or ev5 m dim5sions2 & t x _h !re=e be5 z successful z x 0 unusual 9 "*4 ,9 ,novemb]1 #aiai1 ! _w 0 />tl$ by ! ann\ncem5t f ,london t exam9ation ( ! photographs tak5 dur+ ! total sol> eclipse ( ,may #bi? _h be5 conclud$1 & t pr$ictions bas$ ^u ! ,e9/e9 !ories ( relativity _h be5 v]ifi$4 ,9 ! reaction f ! long surfeit ( w> news an item ( ?is sort 0 a ?or\ghly j\rnali/ic "o4 ,long cable dispat*es 7 c>ri$ 9 ! news columns all ov] ! _w2 ,e9/e9 & 8 !ories 7 giv5 a prom95t place on ! front pages day aft] day2 lead+ sci5ti/s 9 great numb] 7 call$ ^u to tell ! public ?r\gh ! reportorial m$ium j :at ! excitem5t 0 all ab\t1 j 9 :at way ! classical sci5tific /ructure _h be5 ov]?r[n4 ,in/ead ( be+ a m]e n9e days' wond]1 ! ,e9/e9 !ories held _! place 9 ! public m9d4 ,! m s]i\s p]iodicals devot$ space to !m4 ,fir/ & la/1 a v notable gr\p ( sci5tific m5 attempt$ to expla9 to ! g5]al read] ! scope & cont5t ( ,e9/e9's sy/em4 ,^! ef=ts1 well consid]$ z !y 71 c\ld be no m ?an p>tially successful on acc\nt ( ! v radical "* ( ! revisions :i* ! relativity doctr9e dem&s 9 our fundam5tal concepts4 ,su* revisions _c be made 9 a day2 ! av]age p]son has n ! viewpo9t ( ! ma!matician :i* p]mits a sudd5 & complete ex*ange ( "o set ( fundam5tals = ano!r4 ,b ! :ole subject _h caught ! popul> att5tion s /rongly1 t ev5 complete initial failure to discov] :at x 0 all ab\t did n disc\rage ! g5]al read] f pursu+ ! matt] ) det]m9ation to come to "s und]/&+ ( :at _h happ5$ to ,newton & ,newtonian me*anics4 ,,! ,,donor ,,& ,,! ,,prize ,9 ,may1 #aibj1 ,mr4 ,eug5e ,higg9s1 an ,am]ican citiz5 long resid5t 9 ,p>is1 a lib]al patron ( ! arts & sci5ces1 & a lifelong fri5d ( ! ,sci5tific ,am]ican & its proprietors1 sugge/$ t ! success ( ! ,f\r? ,dim5sion ,prize ,conte/ ( #aiaj _h be5 s great t x might be desirable to (f] ano!r prize 9 simil> fa%ion = ! be/ popul> essay on ! ,e9/e9 !ories4 ,he /at$ t if 9 ! op9ion ( ! ,sci5tific ,am]ican ^! !ories 7 ( suffici5t importance1 & ! probability ( gett+ a good numb] ( m]itori\s essays 7 suffici5tly great1 & ! public ne$ & desire = enlight5m5t 7 suffici5tly pres5t1 he w\ld feel incl9$ to (f] su* a prize1 leav+ ! conduct ( ! conte/ to ! ,sci5tific ,am]ican z 9 ! =m] ev5t4 ,x 0 ! judgm5t ( ! editors ( ! ,sci5tific ,am]ican t all ^! provisos %\ld be met ) an affirmative1 & t ,mr4 ,higg9s accord+ly c\ld ) propriety be enc\rag$ to (f] ! prize4 ,9 8 prelim9>y lett] ,mr4 ,higg9s _h sugge/$ t 9 view ( ! app>5t great] importance ( ! subject to be propos$ = discussion by ! conte/ants ( #aibj1 ! prize (f]$ %\ld probably be m lib]al ?an 9 ! =m] in/ance4 ,?is view met ) ! approval ( ! editors z well2 b !y 7 totally unprep>$ = ! receipt1 late 9 ,june1 ( a cablegram f ,mr4 ,higg9s /at+ t he _h decid$ to g ahead ) ! matt]1 & t he 0 =w>d+ a draft = #e1jjj to repres5t ! am\nt ( ! prize4 ,su* a sum1 exce$+ any aw>d op5 to a pr(essional man ) ! s+le exception ( ! ,nobel ,prize1 = :i* he _c specifically compete1 fairly took ! brea? ( ! ,editors1 & made x imm$iately cle> t ! conte/ w\ld attract ! wide/ att5tion1 & t x %\ld score ! mo/ conspicu\s success4 ,x also made x cle> t ! h&l+ ( ! conte/ w\ld be a m s]i\s matt] ?an _h be5 anticipat$4 ,9 spite ( ! fact t x w\ld n = "s "t be possible to ann\nce ! id5tity ( ! ,judges1 x 0 felt t ! prospective conte/ants %\ld h e opportunity = ext5sive prep>ation2 s ! conte/ 0 ann\nc$1 & ! rules gov]n+ x pr9t$ z f> z !y c\ld be det]m9$ on su* %ort %rift1 9 ! ,sci5tific ,am]ican = ,july #aj1 #aibj4 ,sev]al po9ts ( ambiguity _h to be cle>$ up aft] ?is initial publication4 ,9 p>ticul>1 x _h be5 ,mr4 ,higg9s' sugge/ion t 9 ! v probable ev5t ( ! ,judges' inability to agree ^u ! w9n+ essay1 ! prize might1 at _! discretion1 be divid$ betwe5 ! contributors ( ! be/ two essays4 ,?is condition 0 actually pr9t$ 9 ! fir/ ann\ncem5t1 b ! ,po/ ,(fice ,dep>tm5t insi/$ ^u its )drawal1 on ! gr\nd t ) x 9 =ce ! conte/ant w\ld n "k :e!r he 7 compet+ = #e1jjj or = #b1ejj1 & t ?is w\ld introduce ! elem5t ( *ance :i* alone 0 necess>y1 "u ! ,f$]al /atutes1 to make ! conte/ a lott]y4 ,s ?is provision 0 replac$ by "o to ! effect t 9 ! ev5t ! ,judges 7 n able to agree1 ! ,e9/e9 ,editor %\ld ca/ ! decid+ vote betwe5 ! essays respectively favor$ by !m4 ,! ann\ncem5t attract$ ! wide/ att5tion1 & 0 copi$ 9 newspap]s & magaz9es all ov] ! _w4 ,inquiries p\r$ 9 f all qu>t]s1 & ! ,e9/e9 ,editor f\nd x almo/ impossible to keep himself suppli$ ) pro(s ( ! conditions & rules to mail 9 response to ^! inquiries4 ,x 0 imm$iately cle> t !re 0 go+ to be a l>ge numb] ( essays submitt$1 & t _m di/+ui%$ names w\ld be li/$ among ! competitors4 ,,! ,,judges ,9 ! ,sci5tific ,am]ican = ,septemb] #ah1 ann\ncem5t 0 c>ri$ 9 ! foll[+ words3 ,we are assur$ ) complete c]ta9ty t ! competition = ! five-?\s&-doll> prize w be v ke51 & t _m essays w be submitt$ :i*1 if !y bore ! names ( _! au?ors1 w\ld pass any:]e z au?oritative /atem5ts4 ,! judges w confront a task ( extraord9>y difficulty 9 ! ef=t to det]m9e :i* ( ^! ef=ts is ! be/2 & we believe ! difficulties are su* t multiplication ( judges w\ld m]ely multiply ! ob/acles to an agreem5t4 ,x is altoge!r likely t ! initial impressions ( two or ?ree or five judges w\ld incl9e t[>d two or ?ree or five essays1 & t any f9al decision w\ld be atta9able only aft] mu* consultation & discussion4 ,x seems to u t by mak+ ! committee z small z possible :ile /ill pres]v+ ! necess>y feature t its decision repres5t a cons5sus1 we %all simplify bo? ! m5tal & ! physical problem ( com+ to an agreem5t4 ,we believe t ! aw>d %\ld if possible repres5t a unanim\s decision1 )\t any m9ority report1 & t su* a requirem5t is f> m likely to be met among two m5 ?an among ?ree or five4 ,at ! same "t1 ! br++ toge!r ( two m5 & ! details ( g5]al adm9i/ration ( _! "w toge!r are f> simpl] ?an if !re 7 ?ree or five4 ,s we h f9ally decid$ to h b two judges1 & 9 ?is we h ! endorsem5t ( all ! compet5t op9ion t we h consult$4 ,! g5tlem5 :o h cons5t$ to act z ,judges are ,pr(essors ,leigh ,page & ,edw9 ,plimpton ,adams1 ( ! dep>tm5ts ( physics ( ,yale & ,pr9ceton ,univ]sities1 respectively4 ,bo? are ( ! y\ng] g5]ation ( physici/s t has paid special att5tion to ^? phases ( ma!matics & physics involv$ 9 ! ,e9/e9 !ories1 & bo? h paid special att5tion to ^! !ories !mselves4 ,we are gratifi$ to be able to put =w>d z ,judges two m5 s em95tly qualifi$ to act4 ,we feel t we may "h appropriately quote ,pr(essor ,page1 :o says 9 8 acceptance3 ',z ! l>ge prize (f]s a great inducem5t1 ,i _h ?\ght ( ent]+ ! conte/4 ,h[ev] ,i realize t n _m p 9 ?is c\ntry h made a consid]able /udy ( ,e9/e9's !ory1 & if all :o h %\ld ent] ! conte/1 x w\ld be difficult to secure suitable ,judges4' ,)\t any desire to put ! g5tleman 9 ! position ( plead+ = himself1 we ?9k ?is sugge/s v well ! ext5t to :i* ! ,sci5tific ,am]ican1 ! conte/ants1 & ! public at l>ge1 are indebt$ to ,pr(essors ,page & ,adams = _! will+ness to s]ve 9 ! difficult capacity ( ,judges4 ,x might appropriately h be5 add$ to ?is ann\ncem5t t x 0 altoge!r to ! cr$it ( sci5ce & ! sci5tific _s t ! fir/ two g5tlem5 approa*$ ) ! invitation to act z ,judges 7 will+ to =ego _! prospects z conte/ants 9 ord] ?us to contribute to ! success ( ! conte/4 ,,?ree ,,?\s& ,,words ,( ! conditions1 ! "o :i* evok$ mo/ comm5t 0 t /at+ ! ^w limit4 ,?is limit 0 decid$ ^u aft] ! mo/ c>eful discussion ( ! possibilities ( ! situation4 ,x 0 n imag9$ = a mom5t t any conte/ant w\ld succe$ 9 gett+ )9 #c1jjj words a complete discussion ( all aspects ( ! ,special & ! ,g5]al ,!ories ( ,relativity4 ,x 0 h[ev] felt t = popul> read+ a s+le essay %\ld n be mu* if any long] ?an ?is4 ,moreov]1 ,i w say q frankly t we %\ld nev] h enc\rag$ ,mr4 ,higg9s to (f] su* a prize if we _h suppos$ t ! w9n+ essay 0 ! only ?+ ( value t w\ld come f ! conte/1 or if we _h n expect$ to f9d 9 _m ( ! o!r essays mat]ial :i* w\ld be altoge!r des]v+ ( ! light4 ,f ! beg9n+ we _h 9 view ! pres5t volume1 & ! sev]e re/riction 9 l5g? 0 delib]ately impos$ = ! purpose ( =c+ e conte/ant to /ick to :at he consid]$ ! mo/ significant viewpo9ts1 & to give 8 be/ skill to display+ ! !ories ( ,e9/e9 to ! utmo/ advantage f ^! viewpo9ts4 ,we felt t div]g5t viewpo9ts w\ld be m advantage\sly treat$ 9 ?is mann] ?an if we gave ea* conte/ant en\gh space to discuss ! subject f all sides2 & t ! aw>d ( ! prize to ! essay :i*1 among o!r requirem5ts1 seem$ to ! ,judges to embody ! be/ *oice ( mat]ial1 w\ld greatly simplify ! work+ ( ! conte/ )\t effect+ any inju/ice aga9/ ^? conte/ants :o display$ ) equal skill less happily *os5 mat]ial4 ,p]haps on ?is po9t ,i may aga9 quote ) pr(it ! editorial page ( ! ,sci5tific ,am]ican3 ,an essay ( ?ree ?\s& words is n long en\gh to lose a read] m ?an once2 if x does lose him x is a failure1 & if x doesn't x is a competitor t w g into ! f9al elim9ation trials = ! prize4 ,if we c pres5t1 z a result ( ! conte/1 six or a doz5 essays ( ?is l5g? t w n lose ! lay read] at all1 we %all h produc$ some?+ amply wor? ! exp5diture ( ,mr4 ,higg9s' money & our "t4 ,= su* a numb] ( essays ( su* "* w ( necessity pres5t _m diff]5t aspects ( ! ,e9/e9 !ories1 & 9 _m diff]5t ways1 & 9 do+ s w contribute greatly to ! popul> enlight5m5t4 ,really ! significant "p ( :at has already appe>$ is n ! "p t is intelligible1 b r ! "p t1 be+ un9telligible1 ca/s ! %ad[ ( d\bt & suspicion on ! :ole4 ,! successful competitor = ! prize & 8 close conte/ants w h writt5 essays t1 )\t any claim to complet5ess1 w emphasize :at seems to ea* au?or ! big out/&+ feature2 & e "o ( !m w be intelligible4 ,toge!r !y w 9 all probability be reasonably complete1 & w reta9 ! individual *>act]i/ic ( intelligibility4 ,!y w approa* ! v>i\s p>ts ( ! field f v>i\s directions--we c\ld fill ?is page ) sugge/ions z to h[ ! "o item ( ! f\r-dim5sional "* ( ,e9/e9's "t-space might be set =? = ! g5]al read]4 ,& :5 a man mu/ say 9 ?ree ?\s& words z mu* z he c ( :at em95t sci5ti/s h said 9 :ole volumes--well1 ! result 9 "s cases w be %e] failure1 & 9 o!rs a product ( ! fir/ wat]4 ,! be/ ( ! essays w %9e ?r\gh intellig5t selection ( :at is to be said1 & brilliant success 9 say+ x4 ,x is to get a gr\p ( essays ( ?is "*1 n to get ! s+le essay :i* w e>n ! palm1 t ! prize is (f]$4 ,,! ,,compet+ ,,essays ,at all times aft] ! fir/ ann\ncem5t ! ,e9/e9 ,editor _h a heavy correspond5ce2 b ! fir/ real evid5ce t ! conte/ 0 "u way came ) ! arrival ( ! fir/ essay1 :i* w&]$ into our (fice 9 ! middle ( ,septemb]4 ,ab\t a week lat] !y began to filt] 9 at ! rate ( "o or two p] day--mo/ly f =eign conte/ants :o 7 tak+ no *ances on ! mails4 ,heavy returns did n comm5ce until ab\t t5 days be=e ! clos+ date4 ,! great avalan*e1 h[ev]1 0 res]v$ = ! morn+ ( ,monday1 ,novemb] #a/4 ,"h we _h ! b5efit ( ?ree days' mail2 !re 7 ab\t #abj essays4 ,among ^? :i* 7 ?r[n out on ! gr\nd ( lat5ess ! honors %\ld no d\bt g to ! man :o mail$ 8 (f]+ 9 ,! ,hague on ,octob] #ca/4 ,essays 7 receiv$ 9 great] quantity f ,g]many ?an f any o!r =eign c\ntry1 d\btless because ( ! /agg]+ value ( #e1jjj :5 conv]t$ into m>ks at late #aibj rates4 ,engl& /ood next on ! li/2 & "o or m essays 7 receiv$ f ,au/ria1 ,cze*oslovakia1 ,jugoslavia1 ,france1 ,switz]l&1 ! ,ne!rl&s1 ,d5m>k1 ,italy1 ,*ile1 ,cuba1 ,mexico1 ,india1 ,jamaica1 ,s\? ,africa & ! ,fiji ,isl&s4 ,canada1 ( c\rse1 contribut$ h] fair %>e2 & few ( our own /ates 7 miss+ on ! roll-call4 ,! g5]al level ( ,engli% composition among ! essays f non-,engli%-speak+ s\rces 0 ab\t :at might h be5 expect$4 ,a man may h a ?or\gh utilit>ian k ( a =eign tongue1 b :5 he attempts int5sive lit]>y competition ) a man :o 0 br\ght up 9 t tongue he is at a disadvantage4 ,we read ,fr5* & ,g]man ) ease & ,spani% & ,italian )\t too mu* difficulty1 ourselves2 we %\ld nev] und]take s]i\s writ+ 9 any ( ^! languages4 ,n _m ( ! =eign contributions1 ( c\rse1 7 z ludicr\s z ! "o we quote to "s ext5t 9 our conclud+ *apt]1 b mo/ ( !m 7 di/9ctly bel[ p> z lit]>y compositions4 ,drs4 ,de ,sitt] & ,s*lick 7 ! notable exceptions to ?is2 bo? %[$ ! ability to compete on a foot+ ( absolute equality ) ! be/ ( ! native product4 ,we d>e say x 0 a =egone conclusion t _m essays %\ld h be5 ov] ! limit1 & t a few %\ld h be5 ov] x to ! po9t ( absurdity4 ,! w9n+ essay conta9s #b1iai words1 plus or m9us a reasonable all[ance = error 9 c\nt+2 t x %\ld come s f> f be+ on ! ragg$ edge %\ld be suffici5t answ] to ^? :o prote/$ aga9/ ! sev]ity ( ! limitation4 ,"o inquir]1 by ! way1 want$ to "k if #c1jjj words 0 n a mispr9t = #cj1jjj4 ,ano!r conte/ant sugge/$ t in/ead ( disqualify+ any essay t 0 ov] ! l9e1 we amputate ! sup]flu\s words at ! end4 ,?is 0 a plausible en\gh sugge/ion1 s9ce any essay able to compete aft] su* amputation mu/ necess>ily h be5 "o ( extreme wor?2 b =tunately we did n h to decide :e!r we %\ld foll[ ! s*eme4 ,p]haps tw5ty ( ! essays submitt$ 7 s s]i\sly 9 excess ( ! limit t x 0 n ev5 necess>y to c\nt _! words 9 detail2 mo/ ( ^! (f5d]s ran to #c1ejj words or !reab\ts1 & "o--a good "o1 too1 f :i* we use a good deal ( mat]ial 9 ?is volume--actually _h #d1gjj4 ,on ! o!r extreme 7 a few competitors :o seem$ to ?9k t ! %orte/ essay 0 necess>ily ! be/1 & :o tri$ to dismiss ! subject ) #ejj or #a1jjj words4 ,by a curi\s trick ( *ance !re 7 submitt$ 9 competition = ! prize exactly #cjj essays4 ,( c\rse a few ( ^! did n require s]i\s consid]ation--?is is inevitable 9 a conte/ ( su* magnitude4 ,b aft] exclud+ all ! essays t 7 admitt$ly n ab\t ! ,e9/e9 !ories at all1 & all ^? ^: ,engli% 0 s execrable z to make !m q out ( ! "q1 & all ^? :i* took ! subject s lightly z n to write reasonably close to ! limit ( #c1jjj words1 & all ^? :i* 7 giv5 ov] to explanation ( ! mann] 9 :i* ,e9/e9's !ories v]ify ^? ( ! writ]1 & all ^? 9 :i* ! writ] attempt$ to sub/itute 8 own cosmic s*eme = ,e9/e9's--aft] all ?is1 !re rema9$ "s #bge essays :i* 7 s]i\s ef=ts to expla9 9 simple t]ms ! nature & cont5t & consequ5ces ( ,special & ,g5]al ,relativity4 ,,look+ ,,= ,,! ,,w9n] ,! ,e9/e9 ,editor 0 9 suffici5tly close t\* ) ! details ( ! adjudication ( ! essays to h e realization ( ! difficulty ( ?is "w4 ,! calib] ( ! essays submitt$ 0 on ! :ole high4 ,!re 7 _m :i* w\ld h be5 well wor?y ( ! prize 9 ! abs5ce ( o!rs t 7 di/9ctly bett]--_m :i* x 0 n possible to elim9ate on ! gr\nd ( specific faults1 & :i* c\ld only be adjudg$ n ! be/ by detail$ comp>ison ) specific o!r essays4 ,x 0 ?is detail$ comp>ison :i* took "t1 & :i* s delay$ ! aw>d t we 7 n able to publi% ! w9n+ essay any soon] ?an ,febru>y #e?4 ,especially difficult 0 ?is process ( elim9ation aft] ! numb] ( surviv+ essays _h be5 r$uc$ to tw5ty or less4 ,! advantages ( plan possess$ by "o essay _h to be weigh$ aga9/ ^? ( execution exhibit$ 9 ano!r4 ,a c]ta9 essay _h to be critically comp>$ ) ano!r s l x 9 plan t ! two might h be5 writt5 f a common outl9e1 & at ! same "t ) a ?ird z unlike x 9 scope & cont5t z day & night4 ,& all ! "t !re 0 pres5t 9 ! backgr\nd ! consci\sness t a prize ( #e1jjj hung ^u ! decision to be rea*$4 ,= anyone :o reg>ds ?is z an easy task we h no worse wi% ?an t he may "s day h to attack a simil> "o4 ,we _h anticipat$ t ! bulk ( ! sup]ior essays w\ld be among ^? receiv$ dur+ ! la/ day or two ( ! conte/2 = we felt t ! m5 be/ equipp$ to attack ! subject w\ld be ! mo/ impress$ ) its s]i\sness4 ,"h we 7 q (f ! track4 ,! sev5te5 essays :i* )/ood mo/ /ubbornly ! ,judges' ef=ts at elim9ation 71 9 ord] ( receipt1 numb]s #h1 #ah1 #bh1 #dj1 #da1 #dc1 #ib1 #ie1 #ig1 #acj1 #aha1 #aid1 #aih1 #bbc1 #bfg1 #bgj1 #bge3 a fairly ev5 di/ribution4 ,! w9n] 0 ! #ibnd essay receiv$4 ,! ,judges held _! f9al meet+ 9 ! editorial (fice on ,janu>y #ah1 #aiba4 ,! f\r essays :i* 7 be=e ! committee at ! />t ( ! session 7 spe$ily cut to ?ree1 & !n to two2 & aft] an all-day session ! ,judges f\nd !mselves consci5ti\sly able to agree on "o ( ^! z ! be/4 ,?is unanimity 0 especially gratify+1 ! m s s9ce x by no means 0 to be confid5tly expect$1 on a priori gr\nds1 t x w\ld be possible ( atta9m5t4 ,ev5 ! ,e9/e9 ,editor1 :o might h be5 call$ ^u = a f9al decision b wasn't1 c h>dly be class$ z a diss5t]2 = ) "s slight m5tal res]vations 9 favor ( ! essay by ,mr4 ,francis :i* did n ent] ! ,judges' f9al discussion at all1 & :i* he r suspects appeals m to 8 p]sonal ta/e ?an to 8 s\nde/ judgm5t1 he is entirely 9 accord ) ! v]dict r5d]$4 ,! fact t ! prize w5t to ,engl& 0 no surprise to ^? acqua9t$ ) ! hi/ory ( ,e9/e9's !ories4 ,! ,special ,!ory1 promulgat$ fifte5 ye>s ago1 receiv$ its fair %>e ( att5tion f ma!maticians all ov] ! _w1 & is d\btless z well kn[n & z fully appreciat$ "h z else:]e4 ,b x has nev] be5 elevat$ to a position ( any great importance 9 ma!matical !ory1 simply because ( itself1 9 ! abs5ce ( its ext5sion to ! g5]al case1 x des]ves little importance4 ,x is m]ely an int]e/+ bit ( ab/ract speculation4 ,! ,g5]al ,!ory 0 put out by ,e9/e9 9 f9i%$ =m dur+ ! w>4 ,ow+ to ! sci5tific moratorium1 8 pap]1 & h5ce a cle> und]/&+ ( ! new me?ods & results & ( ! sweep+ consequ5ces if ! ,g5]al ,!ory %\ld prevail1 did n atta9 g5]al circulation outside ,g]many until "s "t 9 #aiah or ev5 lat]4 ,_h x n be5 = ,edd+ton x is d\btful t ! ,briti% a/ronom]s w\ld h realiz$ t ! eclipse exp$itions 7 ( p>ticul> consequ5ce4 ,!re=e at ! "t ( ^! exp$itions1 & ev5 z late z ! ,novemb] ann\ncem5t ( ! f9d+s1 ! g5]al body ( sci5tific m5 9 ,am]ica _h n adequately realiz$ ! imm5se di/9ction betwe5 ! ,special & ! ,g5]al ,!ories1 _h n adequately appreciat$ t ! latt] l$ to di/9ctive consequ5ces ( any import1 & we fe> 9 _m cases _h n ev5 realiz$ explicitly t ! deflection ( light & ! behavior ( ,m]cury 7 matt]s /rictly ( ! ,g5]al & 9 no s5se ( ! ,special ,!ory4 ,c]ta9ly :5 ! ,am]ican newspap]s 7 se>*+ frantically = somebody to int]pret to _! public ! great /ir made by ! ,briti% ann\ncem5t t ,e9/e9's pr$ictions _h be5 v]ifi$1 !y f\nd no "o to d ?is dec5tly2 nor 7 our magaz9es mu* m successful 9 spite ( ! great] "t !y _h to devote to ! se>*4 ,9 a ^w1 !re is n ! slighte/ room = d\bt t ,am]ican sci5ce 0 9 l>ge measure caught asleep at ! swit*--p]haps = no reason )9 its control2 & t ,am]ican writ]s 7 9 no su* favorable case to write conv9c+ly on ! subject z 7 _! ,briti% & cont95tal contempor>ies4 ,s x 0 q 9 accord ) :at might h be5 expect$ to f9d1 on op5+ ! id5tify+ envelopes1 t n alone ! w9n+ essay1 b its two mo/ imm$iate rivals1 come f memb]s ( t s*ool ( ,briti% ?\ght :i* _h be5 9 contact ) ! ,e9/e9 !ories 9 _! entirety = two ye>s long] ?an ! av]age ,am]ican ( equal compet5ce4 ,?is rip] famili>ity ) ! subject 0 b\nd to yield rip] fruit4 ,inde$1 _h x n be5 = ! h&icap ( writ+ 9 a /range language1 x is reasonable to assume t ! sci5ti/s ( ,g]many w\ld h made a %[+ sup]ior to t ( ei!r ,am]icans or ,briti%--& = ! same reason t ,brita9 %[$ to bett] advantage ?an ,am]ica4 ,,! ,,w9n] ,,( ,,! ,,prize ,mr4 ,bolton1 ! w9n] ( ! big prize1 we suppose may fairly be ref]r$ to z unkn[n 9 a /rict sci5tific s5se4 ,inde$1 at ! "t ( ! publication ( 8 essay 9 ! ,sci5tific ,am]ican no?+ c\ld be le>n$ ab\t him on ! ,am]ican side ( ! wat] beyond ! b>e facts t he 0 n a "y man1 & t he _h = a good _m ye>s occupi$ a position ( rank 9 ! ,briti% ,pat5t ,(fice4 7,x w be recall$ t ,e9/e9 himself 0 9 ! ,swiss ,pat5t ,(fice = "s "t47 ,9 response to ! reque/ ( ! ,sci5tific ,am]ican = a brief biographical sket* t w\ld s]ve to introduce him bett] to our read]s1 ,mr4 ,bolton suppli$ su* a concise & app>5tly su* a *>act]i/ic /atem5t t we c d no bett] ?an quote x v]batim4 ,i 0 born 9 ,dubl9 9 #ahfj1 b ,i h liv$ 9 ,engl& s9ce #ahfi4 ,my family belong$ to ! l&$ g5try class1 b ,i owe no?+ to weal? or position4 ,i 0 9 fact put ?r\gh s*ool & college on an income :i* a workman w\ld despise n[adays4 ,aft] att5d+ sundry small s*ools1 ,i ent]$ ,clifton ,college 9 #ahgc4 ,my c>e] !re 0 *eck]$1 b x end$ well4 ,i 0 always fairly good at natural sci5ce & v fond ( all sorts ( me*anical ?+s4 ,i 0 an hone/ work] b no use at classics1 & z ,i did practically no?+ else = ! fir/ f\r ye>s at ,clifton1 ,i came to consid] myself some?+ ( a dunce4 ,b a big public s*ool is a little _w4 ,ev]yone gets an opportunity1 (t5 seem+ly by accid5t1 & x is up to him to take x4 ,m9e did n come till ,i 0 ne>ly #ag4 ,z ,i 0 int5d$ = ! eng9e]+ pr(ession1 ,i 0 s5t to ! milit>y side ( ! s*ool 9 ord] to le>n "s ma!matics1 at :i* subject ,i 0 !n consid]$ v weak4 ,?is 0 c]ta9ly true1 z at t "t ,i b>ely knew h[ to solve a quadratic1 ,i 0 only ab\t halfway ?r\gh ! ?ird book ( ,euclid1 & ,i knew no trigonometry4 ,b ! tea*+ 0 inspir+1 & ,i took readily to ma!matics4 ,"o day x came out t ,i _h be5 mak+ q a good />t ) ! diff]5tial calculus on my own )\t tell+ anybody4 ,aft] t all 0 well4 ,i left ,clifton 9 #ahhj ) a ,s*ool ,exhibition & a ma!matical s*ol>%ip at ,cl>e ,college1 ,cambridge4 ,aft] tak+ my degree 9 #ahhc z a ,wrangl]1 ,i taught sci5ce & ma!matics at ,well+ton ,college1 b ,i 0 attract$ by :at ,i _h he>d ( ! ,pat5t ,(fice & ,i ent]$ x ?r\gh op5 competition 9 #ahhe4 ,dur+ my (ficial c>e] ,i h be5 "o ( ! ,comptroll]'s private secret>ies & ,i am n[ a ,s5ior ,exam9]4 ,dur+ ! w> ,i 0 atta*$ to ! ,inv5tions ,dep>tm5t ( ! ,m9i/ry ( ,munitions1 :]e my "w relat$ ma9ly to anti-aircraft gunn]y4 ,i h contribut$1 & am /ill contribut+ to (ficial publications on ! subject4 ,i h writt5 a fair numb] ( essays on v>i\s subjects1 ev5 on lit]ature1 b my only extra-(ficial publications relate to /]eoscopic photography4 ,i read a pap] on ?is subject be=e ! ,royal ,photographic ,society 9 #aijc :i* 0 favorably notic$ by ,dr4 von ,rohr ( ,messrs4 ,zeiss ( ,j5a4 ,i h also writt5 9 ! ,amateur ,photograph]4 ,i h be5 fairly successful at a?letics1 & ,i am a memb] ( ! ,le&] ,club4 ,t ,mr4 ,bolton did n take ! prize ?r\gh default ( s]i\s competition %\ld be pla9 to any read] :o exam9es ! text f compet+ essays :i* is to be f\nd 9 ?is volume4 ,! ref]5ce li/ ( ^! competitors1 too1 supplem5t$ by ! names t appe> at ! heads ( complete essays1 %[s a notable array ( di/+ui%$ p]sonalities1 & ,i c\ld m5tion p]haps a doz5 m v well kn[n m5 ( sci5ce ^: excell5t essays h seem$ a trifle too advanc$ = our imm$iate use1 b to :om ,i am "u a good deal ( obligation = "s ( ! ideas :i* ,i h attempt$ to clo! 9 my own language4 ,be=e leav+ ! subject1 we wi% to say "h a ^w ( appreciation = ! mann] 9 :i* ! ,judges h dis*>g$ _! duties4 ,! read] w h difficulty 9 realiz+ :at x means to read su* a numb] ( essays on su* a subject4 ,we 7 =tunate beyond all expectation 9 f9d+ ,judges :o comb9$ a ?or\gh sci5tific grasp ( ! ma!matical & physical & philosophical aspects ( ! matt] ) an extremely human viewpo9t :i* preclud$ any possibility ( an aw>d to an essay t 0 n prop]ly a popul> discussion1 & ) a will+ness to g to meet ea* o!r's op9ions t is r>e1 ev5 among ^? ) less gr\nd = confid5ce 9 _! own views ?an is possess$ by ,drs4 ,page & ,adams4 ,,ii4 ,,! ,,_w--,,& ,,u ,an ,introductory ,discussion ( ! ,philosophy ( ,relativity1 & ( ! ,me*anism ( ,our ,contact ) ,"t & ,space ,,by ,,v>i\s ,,contributors ,,& ,,! ,,editor ,f a "t beyond ! dawn ( hi/ory1 mank9d has be5 seek+ to expla9 ! univ]se4 ,at fir/ ! ef=t did n conc]n itself fur!r probably ?an to make a supposition z to :at 7 ! causes ( ! v>i\s ph5om5a pres5t$ to ! s5ses4 ,z k increas$1 fir/ by obs]vation & lat] by exp]im5t also1 ! ideas z to ^! causes pass$ progressively ?r\gh ?ree /ages--! !ological 7! causes 7 ?\ght to be spirits or gods72 ! metaphysical 7! causes 7 ?\ght 9 ?is second>y or int]m$iate /age to be "s inh]5t1 animat+1 en]giz+ pr9ciples72 & ! sci5tific 7! causes 7 f9ally ?\ght ( z simply me*anical1 *emical1 & magneto-electrical attractions & repulsions1 qualities or *>act]i/ics ( matt] itself1 or ( ! ?+ ( :i* matt] is itself compos$47 ,) increase ( k1 & along ) ! inquiry z to ! nature ( causes1 !re arose an inquiry also z to :at reality 04 ,:at 0 ! ess5tial nature ( ! /uff ( :i* ! univ]se 0 made1 :at 0 matt]1 :at 7 ?+s 9 !mselves1 :at 7 ! n\m5a 7! realities71 ly+ back ( ! ph5om5a 7! appe>ances78 ,gradually ideas expla9+ motion1 =ce1 & en]gy 7 develop$4 ,at ! same "t inquiry 0 made z to ! nature ( man1 ! work+ ( 8 m9d1 ! nature ( ?\ght1 ! relation ( 8 concepts 7ideas7 to 8 p]ceptions 7k ga9$ ?r\gh ! s5se7 & ! relations ( bo? to ! n\m5a 7realities74#bhc ,! g5]al direction tak5 by ?is inquiry has be5 t ( a conflict betwe5 two s*ools ( ?\ght :i* we may *>act]ize z ^? ( absolutism & ( relativism499 ,! anci5t ,greek philosoph]s believ$ t !y c\ld tap a s\rce ( k pure & absolute by sitt+ d[n 9 a *air & reason+ ab\t ! nature ( "t & space1 & ! me*anism ( ! physical _w4#bba ,!y ma9ta9$ t ! m9d holds 9 its own "r c]ta9 concepts ?an :i* no?+ is m fundam5tal4 ,!y consid]$ x prop] to conceive ( "t & space & matt] & ! o!r ?+s pres5t$ to _! s5ses by ! _w z hav+ a real exi/5ce 9 ! m9d1 reg>dless ( :e!r any ext]nal reality c\ld be id5tifi$ ) ! concept z ultimately put =?4 ,!y c\ld ev5 dispute ) significance ! qualities :i* 7 to be ascrib$ to ?is ab/ract conceptual "t & space & matt]4 ,all ?is 0 done )\t ref]5ce to ! ext]nal reality1 (t5 9 defiance ( t reality4 ,! m9d c\ld picture ! _w z x ought to be2 if ! recalcitrant facts refus$ to fit into ! picture1 s mu* ! worse = !m4 ,we all h he>d ! tale ( h[ g5]ation aft] g5]ation ( ,greek philosoph]s disput$ le>n$ly :y & h[ x 0 t a live fi% c\ld be add$ to a brimm+ pail ( wat] )\t rais+ ! level ( ! fluid or increas+ ! weight2 until "o day "s common p]son conceiv$ ! tr\blesome idea ( try+ x out exp]im5tally to le>n :e!r x 7 s--& f\nd t x 0 n4 ,true or false1 ! anecdote admirably illu/rates ! subord9ate place :i* ! ext]nals held 9 ! absoluti/ sy/em ( ,greek ?\ght499 ,"u ?is sy/em a s+le obs]v] is compet5t to exam9e a s+le ph5om5on1 & to write d[n ! absolute law ( nature by ref]r+ ! results to 8 innate ideas ( absolute qualities & /ates4 ,! root ( ! ^w absolute signifies tak+ away1 & 9 its philosophical s5se ! ^w implies ! ability ( ! m9d to subtract away ! prop]ties or qualities f ?+s1 & to consid] ^! ab/ract qualities deta*$ f ! ?+s2 = example1 to take away ! coldness f ice1 & to consid] pure or ab/ract coldness ap>t f any?+ t is cold2 or to take away motion f a mov+ body1 & to consid] pure motion ap>t f any?+ t moves4 ,?is assum$ p[] is bas$ ^u ! ,socratic !ory ( innate ideas4 ,accord+ to ?is !ory ! m9d is end[$ by nature ) ! absolute ideas ( h>dness1 coldness1 r\ndness1 equality1 motion1 & all o!r absolute qualities & /ates1 & s does n h to le>n !m4 ,?us a ,socratic philosoph] c\ld discuss pure or absolute be+1 absolute space & absolute "t4#aba ,,gett+ ,,away ,,f ,,! ,,greek ,,ideas ,?is ,greek mode ( ?\ght p]si/$ into ! late ,middle ,ages1 at :i* "t x 0 /ill altoge!r 9 ord] to dispose ( a tr\blesome fact ( ! ext]nal _w by quot+ ,ari/otle aga9/ x4 ,dur+ ! ,r5aissance1 :i* intellectually at lea/ m>ks ! transition f anci5t to mod]n1 !re came into be+ ano!r type ( absolutism1 equally extreme1 equally arbitr>y1 equally unju/ifi$4 ,! revolt aga9/ ! m5tal slav]y to ,greek ideas c>ri$ ! p5dulum too f> to ! o!r side1 & e>ly mod]n sci5ce z a consequ5ce is disfigur$ by :at we mu/ n[ recognize z gross mat]ialism4 ,! human m9d 0 relegat$ to ! position ( a m]e innoc5t by/&]4 ,! ext]nal reality 0 ev]y?+1 & aside f 8 function z a record] ! obs]v] did n 9 ! lea/ matt]4 ,! :ole aim ( sci5ce 0 to isolate & classify ! elusive ext]nal fact4 ,! rle ( ! obs]v] 0 9 e possible way m9imiz$4 ,x 0 ( c\rse 8 duty to get ! facts "r1 b s f> z any contribution to ^! 0 conc]n$ he did n c\nt--he 0 def9itely disqualifi$4 ,he really play$ ! "p ( an intrud]2 f 8 position outside ! ph5om5a he 0 se>*+ = ! absolute tru? ab\t ^! ph5om5a4 ,! only diff]5ce betwe5 8 viewpo9t & t ( ,ari/otle 0 t ! latt] look$ entirely inside himself = ! elusive tru?1 :ile ! classical sci5ti/1 z we call him n[1 look$ = x entirely outside himself4 ,let me illu/rate ! diff]5ce betwe5 ! two viewpo9ts :i* ,i h discuss$1 & ! ?ird "o :i* ,i am ab\t to outl9e1 by ano!r concrete in/ance4 ,! ,greeks1 & ! m$ievals z well1 7 fond ( discuss+ a "q :i* embodies ! :ole ( :at ,i h be5 say+4 ,?is "q involv$1 on ! "p ( "o :o attempt$ to answ] x1 a *oice betwe5 ! obs]v] & ! ext]nal _w z ! seat ( reality4 ,x 0 put 9 _m =ms2 a famili> "o is ! foll[+3 ,if ! w9d blew d[n a great tree at a "t & place :]e !re 0 no consci\s be+ to he>1 w\ld !re be any noise8 ,! ,greek _h to answ] ?is "q 9 ! negative because to him ! noise 0 entirely a ph5om5on ( ! li/5]4 ,! classical sci5ti/ _h to answ] x 9 ! affirmative because to him ! noise 0 entirely a ph5om5on ( ! tree & ! air & ! gr\nd4 ,today we answ] x 9 ! negative1 b = a v diff]5t reason f t :i* sway$ ! ,greek4 ,we believe t ! noise is a jo9t ph5om5on ( ! obs]v] & ! ext]nals1 s t 9 ! abs5ce ( ei!r x mu/ fail to take exi/5ce4 ,we believe !re are s\nd waves produc$1 & all t2 b :at ( x8 ,!re is no noise 9 ! pres5ce ( ! fall+ tree & ! abs5ce ( ! obs]v]1 any m ?an !re w\ld be 9 ! pres5ce ( ! obs]v] & ! abs5ce ( ! tree & ! w9d2 ! noise1 a jo9t ph5om5on ( ! obs]v] & ! ext]nals1 exi/s only 9 _! jo9t pres5ce4 ,,relativism ,,& ,,reality ,?is is ! viewpo9t ( relativism4 ,! /atue is gold5 = "o obs]v] & silv] to ! o!r4 ,! sun is ris+ "h & sett+ 9 ano!r "p ( ! _w4 ,x is ra9+ "h & cle> 9 ,*icago4 ,! obs]v] 9 ,delft he>s ! bomb>dm5t ( ,antw]p & ! obs]v] 9 ,london does n4 ,if !y 7 to be consi/5t1 bo? ! ,greek & ! m$ieval-mod]n absoluti/ w\ld h to dispute :e!r ! /atue 7 really gold5 or silv]1 :e!r ! sun 7 really ris+ or sett+1 :e!r ! wea!r 7 really fair or f\l1 :e!r ! bomb>dm5t 7 really accompani$ by l\d noises or n2 & on ea* ( ^! que/ions !y w\ld h to come to an agreem5t or confess _! me?ods inadequate4 ,b to ! relativi/ ! answ] is simple--:e!r ?is or t be true dep5ds ^u ! obs]v]4 ,9 simple cases we und]/& ?is full well1 z we h always realiz$ x4 ,9 less simple cases we recognize x less easily or n at all1 s t "s ( our ?\ght is absoluti/ 9 its t5d5cies :ile ! re/ is relativi/ic4 ,e9/e9 is ! fir/ ev] to realize ?is fully--or if n ?is1 !n ! fir/ ev] to realize x s fully z to be mov$ t[>d a /udi$ ef=t to free human ?\ght f ! mixture ( relativism & absolutism & make x consi/5tly ! "o or ! o!r4 ,?is br+s x ab\t t ! obs]v$ fact occupies a position ( unexpect$ significance4 ,= :5 we discuss matt]s ( physical sci5ce "u a /rictly relativi/ic philosophy1 we mu/ put away z metaphysical ev]y?+ t smacks ( a reality p>tly conceal$ beh9d our obs]vations4 ,we mu/ focus att5tion ^u ! reports ( our s5ses & ( ! in/rum5ts t supplem5t !m4 ,^! obs]vations1 :i* jo9 our p]ceptions to _! ext]nal objects1 af=d u our only objective manife/ations2 !m we mu/ accept z f9al--subject always to su* correction z m ref9$ obs]vations may sugge/4 ,! "q :e!r a true l5g? or area or mass or velocity or duration or temp]ature exi/s back ( ! num]ical det]m9ation1 or 9 ! pres5ce ( a det]m9ation t is subject to correction1 or 9 ! abs5ce ( any det]m9ation at all1 is a metaphysical "o & "o t ! physici/ mu/ n ask4 ,l5g?1 area1 mass1 velocity1 duration1 temp]ature--none ( ^! has any mean+ o!r ?an ! numb] obta9$ by measurem5t499 ,if sev]al diff]5t det]m9ations are *eck$ ov] & no error c be f\nd 9 any ( !m1 ! fault mu/ lie n ) ! obs]v]s b ) ! object1 :i* we mu/ conclude pres5ts diff]5t values to diff]5t obs]v]s4#cc ,we are aft] all accu/om$ to ?is viewpo9t2 we d n dem& t ,pittsburgh %all pres5t ! same di/ance f ,new ,york & f ,philadelphia1 or t ! ,new ,york] & ! ,philadelphian come to any agreem5t z to ! real di/ance ( ,pittsburgh4 ,! di/ance ( ,pittsburgh dep5ds ^u ! position ( ! obs]v]4 ,nor d we dem& t ! man :o locates ! magnetic pole 9 "o spot 9 #aijj & 9 ano!r 9 #aiba come to a decision z to :]e x really is2 we accept 8 /atem5t t its position dep5ds ^u ! "t ( ! obs]vation4 ,:at ?is really means is t ! di/ance to ,pittsburgh & ! position ( ! magnetic pole are jo9t prop]ties ( ! obs]v] & ! obs]v$--relations betwe5 !m1 z we might put x4 ,?is is obvi\s en\gh 9 ! case ( ! di/ance ( ,pittsburgh2 x is h>dly s obvi\s 9 ! case ( ! position ( ! magnetic pole1 v>y+ ) ! lapse ( "t4 ,b if we reflect t ! obs]vation ( #aijj & t ( #aiba 7 bo? valid1 & bo? repres5t$ ! true position ( ! pole = ! obs]v] ( ! date 9 "q1 we mu/ see t ?is is ! only explanation t %[s u ! way out4 ,i d n wi% to speak too def9itely ( ! ,e9/e9 !ories 9 ^! introductory rem>ks1 & s %all refra9 f m5tion+ explicitly 9 ?is place ! situation :i* !y br+ up & ^u :i* :at ,i h j said has direct be>+4 ,x w be recogniz$ :5 x arises4 ,:at mu/ be po9t$ out "h1 h[ev]1 is t we are putt+ ! ?+ :i* ! sci5ti/ calls ! obs]v$ value on a foot+ ( va/ly great] consequ5ce ?an we %\ld h be5 will+ (fh& to conc$e to x4 ,s f> z any s+le obs]v] is conc]n$1 8 own be/ obs]v$ values are !mselves ! ext]nal _w2 he _c prop]ly g beh9d ! conditions surr\nd+ 8 obs]vations & speak ( a real ext]nal _w beyond ^! obs]vations4 ,any _w :i* he may ?9k ( z s exi/+ is purely a conceptual _w1 "o :i* = "s reason he inf]s to exi/ beh9d ! deceptive obs]vations4 ,provid$ he makes ?is res]vation he is q privileg$ to speculate ab\t ?is conceal$ _w1 to be/[ ^u x any *>act]i/ics t he pleases2 b x c h no real exi/5ce = him until he becomes able to obs]ve x4 ,! only reality he kn[s is ! "o he c directly obs]ve4 ,,laws ,,( ,,nature ,! obs]vations :i* we h be5 discuss+1 & :i* we h be5 try+ to end[ ) *>act]i/ics ( reality :i* !y are frequ5tly n realiz$ to possess1 are ! raw mat]ial ( physical sci5ce4 ,! f9i%$ product is ! result ( br++ toge!r a l>ge numb] ( ^! obs]vations499 ,! :ole und]ly+ ?\ght beh9d ! mak+ ( obs]vations1 9 fact1 is to correlate z _m z possible ( !m1 to obta9 "s g5]alization1 & f9ally to express ?is 9 "s simple ma!matical =m4 ,?is =mulation is !n call$ a law ( nature4#ce ,mu* confusion exi/s because ( a misund]/&+ 9 ! lay m9d ( :at is meant by a law ( nature4 ,x is p]haps n a well *os5 t]m4 ,"o is accu/om$ to associate ! ^w law ) ! idea ( necessity or compulsion4 ,9 ! realm ( nature ! t]m c>ries no su* mean+4 ,! laws ( nature are man's imp]fect attempts to expla9 natural ph5om5a2 !y are n inh]5t 9 matt] & ! univ]se1 n an iron b> ( necessity runn+ ?r\gh worlds1 sy/ems & suns4 ,laws ( nature are little m ?an work+ hypo!ses1 subject to *ange or alt]ation or enl>gem5t or ev5 ab&onm5t1 z man's vision wid5s & deep5s4 ,no sanctity atta*es to !m1 & if any "o1 or all1 ( !m fail to acc\nt = any "p1 or all1 ( ! ph5om5a ( ! univ]se1 !n x or !y mu/ be supplem5t$ or ab&on$4#ajb ,! te/ ( "o ( ^! laws is t x c be %[n to include all ! relat$ ph5om5a hi!rto kn[n & t x enables u to pr$ict new ph5om5a :i* c !n be v]ifi$4 ,if new facts are discov]$ t are n 9 agreem5t ) "o ( ^! g5]aliz$ /atem5ts1 ! assumptions on :i* ! latt] is bas$ are exam9$1 ^? :i* are n 9 accordance ) ! new facts are giv5 up1 & ! /atem5t is modifi$ s z to include ! new facts4#aj ,& if "o rememb]s t ! laws ( physics 7 =m]ly bas$ on a range ( obs]vations mu* n>r[] ?an at pres5t available1 x seems natural t 9 ! light ( ?is wid5+ k "o law or ano!r may be se5 to be n>r[ & insuffici5t4 ,new !ories & laws d n necess>ily disprove old ones1 b expla9 c]ta9 discrepancies 9 !m & p5etrate m deeply into _! und]ly+ pr9ciples1 !reby broad5+ our ideas ( ! univ]se4 ,to foll[ ! new reason+ we mu/ rid ourselves ( ! prejudice beh9d ! old1 n because x is wrong b because x is insuffici5t4 ,! univ]se w n be di/ort$ to fit our rules1 b w tea* u ! rules ( exi/5ce4#abe ,always1 h[ev]1 we mu/ gu>d aga9/ ! too easy error ( attribut+ to ^! rules any?+ l absolute tru?499 ,! mod]n sci5ti/ has atta9$ a v bus9ess-l po9t ( view t[>d 8 laws ( nature4 ,to him a law is fundam5tally no?+ b a %ort-h& way ( express+ ! results ( a l>ge numb] ( exp]im5ts 9 a s+le /atem5t4 ,& x is important to rememb] t ?is m]e %ort5+ ( ! description ( a lot ( div]se occurr5ces is by no means any real explanation ( h[ & :y !y happ5$4 ,9 o!r words1 ! aim ( sci5ce is n ultimately to expla9 b only to discov] ! relations t hold good among physical quantities & to embody all ^! relations 9 z few & z simple physical laws z possible4#bba ,?is is inh]5tly ! me?od ( relativism499 ,"u x a set ( ph5om5a is obs]v$4 ,!re are two or _m obs]v]s1 & !y write d[n _! sev]al f9d+s4 ,^! are review$ by a f9al obs]v] or judge1 :o /ra9s out ! bias due to ! diff]5t viewpo9ts ( ! orig9al obs]v]s4 ,he !n writes d[n1 n any absolute law ( nature gov]n+ ! obs]v$ ph5om5a1 b a law z g5]al z possible express+ _! int]relations4#aba ,& ?r\gh ?is proc$ure mod]n sci5ce & philosophy reveal ) increas+ emphasis t we sup]impose our human qualities on ext]nal nature to su* an ext5t t#ajf we h at once ! /ronge/ practical ju/ification1 9 addition to ! argum5ts ( reason1 = our insi/5ce t ! contact betwe5 objective & subjective repres5t$ by ! obs]vation is ! only ?+ :i* we %all ev] be able to recognize z real4 ,we may indulge 9 ab/ract metaphysical speculation to our he>t's cont5t1 if we be metaphysically incl9$2 we may n attempt to impose ! dicta ( metaphysics ^u ! physical sci5ti/499 ,,concepts ,,& ,,realities ,f ! inquiry & criticism :i* h gone on = c5turies has em]g$ ! foll[+ pres5t-day attitude ( m9d t[>d ! sum total ( our k4 ,! conceptual univ]se 9 our m9ds 9 "s my/]i\s way p>allels ! real univ]se1 b is totally unlike x4 ,our conceptions 7ideas7 ( matt]1 molecules1 atoms1 corpuscles1 electrons1 ! e!r1 motion1 =ce1 en]gy1 space1 & "t /& 9 ! same or simil> relation to reality z ! x's & y's ( ! ma!matician d to ! entities ( 8 problem4 ,matt]1 molecules1 atoms1 corpuscles1 electrons1 ! e!r1 motion1 =ce1 en]gy1 space1 & "t d n exi/ actually & really z we conceive !m1 nor d !y h actually & really ! qualities & *>act]i/ics ) :i* we end[ !m4 ,! concepts are simply repres5tations ( ?+s outside ourselves2 ?+s :i*1 :ile real1 h an ess5tial nature n kn[n to u4 ,matt]1 molecules1 atoms1 corpuscles1 electrons1 ! e!r1 motion1 =ce1 en]gy1 space & "t are m]ely devices1 symbols1 :i* enable u to reason ab\t reality4 ,!y are p>ts ( a conceptual me*anism 9 our m9ds :i* op]ates1 or enables our m9ds to op]ate1 9 ! same sequ5ce ( ev5ts z ! sequ5ce ( ph5om5a 9 ! ext]nal univ]se1 s t :5 we p]ceive by our s5ses a gr\p ( ph5om5a 9 ! ext]nal univ]se1 we c reason out :at result w fl[ f ! int]action ( ! realities involv$1 & ?us pr$ict :at ! situation w be at a giv5 /age 9 ! sequ5ce4 ,b :ile our conceptual univ]se has ?us a me*anical aspect1 we d n reg>d ! real univ]se z me*anical 9 its nature4#bhc ,?is may be illu/rat$ by a little /ory4 ,ent]+ 8 fri5d's h\se1 a g5tleman is seiz$ unaw>es f beh9d4 ,he turns 8 head b sees no?+4 ,8 hat & coat are remov$ & deposit$ 9 _! prop] places by "s invisible ag5t1 seats & tables & refre%m5ts appe> 9 due "t :]e !y are requir$1 all )\t any app>5t cause4 ,! visitor %iv]s ) horror & asks 8 ho/ = an explanation4 ,he is !n told t ! ideas ord] & regul>ity are at "w1 & t x is !y :o acquit !mselves s well ( _! tasks4 ,^! ideas _c be se5 nor felt nor seiz$ nor weigh$2 !y reveal _! exi/5ce only by _! ?\ghtful c>e = ! welf>e ( mank9d4 ,i ?9k ! gue/1 com+ home1 w relate t 8 fri5d's h\se is haunt$4 ,! gho/s may be k9d1 b5evol5t1 ev5 useful2 yet gho/s !y are4 ,n[ 9 ,newtonian me*anics1 absolute space & absolute "t & =ce & in]tia & all ! o!r app>atus1 altoge!r imp]ceptible1 appe>+ only at ! prop] "t to make possible a prop] build+ up ( ! !ory1 play ! same my/]i\s "p z ! ideas ord] & regul>ity 9 my /ory4 ,classical me*anics is haunt$4#aaf ,z a matt] ( fact1 we realize ?is & d n all[ ourselves to be impos$ ^u ) reg>d to ! true nature ( ^! ag5cies499 ,we use a me*ani/ic t]m9ology & a me*ani/ic mode ( reason+ only because we h f\nd by exp]i5ce t !y facilitate our reason+4 ,!y are ! tools :i* we f9d produce results4 ,!y are adapt$ to our m9ds1 b p]haps x w\ld be bett] to say t our m9ds are s con/ruct$ z to r5d] our conceptual univ]se necess>ily me*anical 9 its aspect 9 ord] t our m9ds may reason at all4 ,two ?+s anti!tic are involv$--subject 7our p]ceiv+ m9d :i* builds up concepts7 & object 7! ext]nal reality72 & hav+ nei!r complete nor absolute k ( ei!r1 we _c affirm :i* is m truly to be said to be me*ani/ic 9 its nature1 ?\gh we may suspect t really nei!r is4 ,we no long] ?9k ( cause & effect z dictat$ by inh]5t necessity1 we simply reg>d !m z sequ5ces 9 ! r\t9e ( our s5se-impressions ( ph5om5a4 ,9 a ^w1 we h at l5g? grasp$ ! idea t our notions ( reality1 at pres5t at lea/1 :atev] !y may become ultimately1 are n absolute1 b simply relative4 ,we see1 too1 t we d n expla9 ! univ]se1 b only describe our p]ceptions ( its cont5ts4 ,! s-call$ laws ( nature are simply /atem5ts ( =mul :i* resume or sum up ! relation%ips & sequ5ces ( ph5om5a4 ,our ef=t is con/antly to f9d =mul :i* w describe ! wide/ possible range ( ph5om5a4 ,z our k increases1 t is1 z we p]ceive new ph5om5a1 our laws or =mul break d[n1 t is1 !y fail to af=d a description 9 brief t]ms ( all ( our p]ceptions4 ,x is n t ! old laws are untrue1 b simply t !y are n compreh5sive en\gh to include all ( our p]ceptions4 ,! old laws are (t5 p>ticul> or limit+ in/ances ( ! new laws4#bhc ,f :at we h said ( ! reality ( obs]vations x foll[s t we mu/ support t s*ool ( psy*ology1 & ! p>allel s*ool ( philosophy1 :i* hold t concepts orig9ate 9 p]ceptions4 ,b ?is does n impose s /rong a re/riction ^u conceptions z might appe>4 ,! elem5ts ( all our concepts d come to u f outside2 we manufacture no?+ out ( :ole clo?4 ,b :5 p]ception has suppli$ a suffici5t volume ( raw mat]ial1 we may gr\p its elem5ts 9 ways =eign to actual occurr5ce 9 ! p]ceptual _w1 & 9 s do+ get conceptual results s entirely diff]5t f :at we h consci\sly p]ceiv$ t we are /rongly tempt$ to look ^u !m z hav+ c]ta9ly be5 manufactur$ 9 our m9ds )\t ref]5ce to ! ext]nals4 ,( ev5 m significance is our ability to ab/ract f concrete objects & concrete incid5ts ! ess5tial features :i* make !m alike & diff]5t4 ,b unlike ! ,greeks1 we see t our concept ( coldness is n some?+ ) :i* we 7 end[$ f ! beg9n+1 b m]ely an ab/raction f concrete exp]i5ces ) concrete objects t h be5 cold4 ,,! ,,concepts ,,( ,,space ,,& ,,"t ,:5 we h =m$ ! ab/ract ideas ( coldness & w>m?1 & h _h exp]i5ce indicat+ t ! occurr5ce ( ^! prop]ties v>ies 9 degree1 we are 9 a position to =m ! second>y ab/ract notion cov]$ by ! ^w temp]ature4 ,:5 we h =m$ ! ab/ract ideas ( size & position & sep>ation1 we are simil>ly 9 a position to =m a second>y ab/raction to :i* we give ! "n space4 ,n q s easy to trace to its def9ite s\rce b none ! less cle>ly an ab/raction bas$ on exp]i5ce1 is our idea ( :at we call "t4 ,none ( u are deceiv$ z to ! reality ( ^! ab/ractions499 ,we d n reg>d space z real 9 ! s5se t we reg>d a *air z real2 x is m]ely an ab/ract idea conv5i5t = ! location ( mat]ial objects l ! *air4#aih ,nor d we reg>d "t z real 9 ?is s5se4 ,?+s occupy space1 ev5ts occupy "t2 space & "t !mselves we realize are immat]ial & unreal2 space does n exi/ & "t does n happ5 9 ! same s5se t mat]ial objects exi/ & ev5ts occur4 ,b we f9d x absolutely necess>y to h1 among ! m5tal ma*9]y m5tion$ above z ! app>atus by aid ( :i* we keep track ( ! ext]nal _w1 ^! vessels = t _w to exi/ 9 & move 94 ,space & "t1 !n1 are concepts499 ,x is n /range1 h[ev]1 t :5 confront$ ) ! va/ & bewild]+ complexity ( ! univ]se & ! difficulty ( keep+ sep>ate & di/9ct 9 our m9ds our p]ceptions & conceptions1 we %\ld at times & z respects c]ta9 ?+s project our conceptions illegitimately into ! p]petual univ]se & mi/ake !m = p]ceptions4 ,! mo/ notable example p]haps ( ?is projection has occurr$ 9 ! v case ( space & "t1 mo/ fundam5tal ( all ( our concepts4 ,we got to ?9k ( ^! z absolute1 z indep5d5t ( ea* o!r & ( all o!r ?+s1 & z always exi/+ & cont9u+ to exi/ :e!r or n we or any?+ else exi/$--space z a ?ree-dim5sional1 uni=m cont9uum1 hav+ ! same prop]ties 9 all directions2 "t z a "o-dim5sional1 irrev]sible cont9uum1 fl[+ 9 "o direction4 ,x is difficult to get back to ! idea t space & "t s describ$ & def9$ are concepts m]ely1 = ! idea ( _! absolute exi/5ce is +ra9$ 9 u z ! result probably ( long ance/ral exp]i5ce4#bhc ,newton's def9itions ( c\rse repres5t ! classical idea ( "t & space4 ,he tells u t absolute1 true & ma!matical "t fl[s 9 virtue ( its own nature1 uni=mly & )\t ref]5ce to any ext]nal object2 & t absolute space1 by virtue ( its own nature & )\t ref]5ce to any ext]nal object1 always rema9s ! same & is immovable4 ,( c\rse f mod]n /&po9ts x is absurd to call ei!r ( ^! pron\ncem5ts a def9ition2 b !y repres5t ab\t z well z any words c ! ideas :i* ,newton _h ab\t "t & space1 & !y make x cle> en\gh t he reg>d$ bo? z hav+ real exi/5ce 9 ! ext]nal _w4 ,if space & "t are to be ! vessels ( our univ]se1 & if ! only ?+ t really matt]s is measur$ results1 x is pla9 en\gh t we mu/ h1 f ! v beg9n+1 means ( measur+ space & "t4 ,:e!r we believe space & "t to h real exi/5ce or n1 x is obvi\s t we c measure nei!r directly4 ,we %all h to measure space by measur+ f "o mat]ial object to ano!r2 we %all h to measure "t by "s simil> conv5tion bas$ on ev5ts4 ,we %all lat] h some?+ fur!r to say ab\t ! measurem5t ( "t2 = ! pres5t we ne$ only po9t out t99 ,newtonian "t is measur$ indep5d5tly ( space2 & ! exi/5ce is presuppos$ ( a suitable timekeep]4#aj ,! space ( ,galileo & ,newton 0 conceiv$ ( z empty1 except 9 s f> z c]ta9 p>ts ( x 7 occupi$ by matt]4 ,positions ( bodies 9 ?is space 7 9 g5]al det]m9$ by ref]5ce to#bhc a coord9ate sy/em ( "s k9d4 ,?is is aga9 some?+ t dem&s a c]ta9 am\nt ( discussion4 ,,! ,,ref]5ce ,,frame ,,= ,,space ,! ma!matician1 foll[+ ! lead ( ! great ,fr5* all-ar\nd g5ius1 ,desc>tes1 %[s u v cle>ly h[ to set up1 = ! measurem5t ( space1 ! framework kn[n z ! ,c>tesian coord9ate sy/em4 ,! p]son ( mo/ ord9>y ma!matical atta9m5ts w realize t to locate a po9t 9 a plane we mu/ h two measurem5ts2 & we c\ld probably %[ ?is p]son1 )\t too s]i\s difficulty1 t we c locate a po9t 9 any surface by two measurem5ts4 ,an example ( ?is is ! location ( po9ts on ! e>?'s surface by means ( _! latitude & longitude4 ,x is equally cle> t if we add a ?ird dim5sion & attempt to locate po9ts 9 space1 we mu/ add a ?ird measurem5t4 ,9 ! case ( po9ts on ! e>?'s surface1 ?is might be ! elevation above sea level1 :i* w\ld def9e ! po9t n z "p ( ! sph]ical surface ( ! e>? b z "p ( ! solid sph]e4 ,or we may fall back on ,dr4 ,slosson's sugge/ion t 9 ord] to def9e completely ! position ( 8 laboratory1 we mu/ make a /atem5t ab\t ,broadway1 & "o ab\t #aaf? ,/reet1 & "o tell+ h[ _m flights ( /airs !re are to climb4 ,9 any ev5t1 x %\ld be cle> en\gh t ! complete def9ition ( a po9t 9 space calls = ?ree measurem5ts4 ,! ma!matician =mulates all ?is ) ! utmo/ precision4 ,he asks u to99 pick out any po9t :atev] 9 space & call x ,o4 ,we !n draw or conceive to be drawn ?r\gh ?is po9t ?ree mutually p]p5dicul> l9es call$ coord9ate axes1 :i* we may designate ,,ox1 ,,oy & ,,oz1 respectively4 ,f9ally1 we consid] ! ?ree planes also mutually p]p5dicul> l ! two walls & ! floor ( a room t meet 9 "o common corn]1 :i* are =m$ by ! l9es ,,ox & ,,oy1 ,,oy & ,,oz1 & ,,oz & ,,ox1 respectively4 ,^! ?ree planes are call$ coord9ate planes4 ,& !n any o!r po9t ,p 9 space c be repres5t$ ) respect to ,o by its p]p5dicul> di/ances f ea* ( ! ?ree coord9ate planes--! di/ances x1 y1 z 9 ! figure4 ,^! quantities are call$ ! coord9ates ( ! po9t4#bgb ,to ! layman !re seems some?+ altoge!r naive 9 ?is notion ( ! sci5ti/'s sett+ up ! ?ree sides ( a box 9 space & us+ !m z ! basis ( all 8 "w4 ,! layman someh[ feels t :ile x is p]fectly all "r = him to tell u t he lives at #ajfe 7"o coord9ate7 #aef? ,/reet 7two coord9ates7 on ! ?ird floor 7?ree coord9ates71 x is r trivial bus9ess = ! s]i\s-m9d$ sci5ti/ to consid] ! up-&-d[n1 ! =w>d-&-back1 ! "r-&-left ( e po9t ) :i* he has occasion to deal4 ,!re seems to ! layman some?+ p>ticul>ly inane & fooli% & altoge!r pu]ile ab\t a set ( coord9ate axes1 & y simply c't make him believe t ! s]i\s-m9d$ sci5ti/ has to monkey ) any su* funny bus9ess4 ,he c't be induc$ to take ?is coord9ate-axis bus9ess s]i\sly4 ,nev]!less1 ! fact is t ! sci5ti/ takes x ) ! utmo/ s]i\sness4 ,x is necess>y = him to def9e ! positions ( po9ts2 & he does d x by means ( a set ( coord9ate axes4 ,! sci5ti/1 h[ev]1 is n int]e/$ 9 po9ts ( empty space4 ,! po9t is to him m]ely "p aga9 ( ! conceptual ma*9]y :i* he uses 9 8 ef=t to run along ) ! ext]nal _w4 ,he kn[s !re are no real po9ts1 b x suits 8 conv5i5ce to keep track ( c]ta9 ?+s t are real by repres5t+ !m z po9ts4 ,b ^! ?+s are 9 practically e in/ance mat]ial bodies2 & 9 practically e in/ance1 in/ead ( /ay+ put 9 "o spot1 !y insi/ ^u mov+ ab\t ?r\gh space4 ,! sci5ti/ has to use 8 coord9ate sy/em1 n m]ely to def9e a s+le position ( su* a po9t1 b to keep track ( ! pa? ov] :i* x moves & to def9e its position 9 t pa? at giv5 mom5ts4 ,,"t ,,& ,,! ,,coord9ate ,,sy/em ,?is introduces ! concept ( "t into intimate relation%ip ) ! spatial coord9ate sy/em4 ,& at once we feel ! lack ( a concrete1 visualiz$ f\r? dim5sion499 ,if we want to fix objects 9 ! floor alone1 ! edge ( ! room runn+ t[>d ! ceil+ w\ld become unnecess>y & c\ld be dropp$ f our coord9ate sy/em4 ,t is1 we ne$ only two coord9ates to fix ! position ( a po9t 9 a plane4 ,suppose in/ead ( disc>d+ ! ?ird coord9ate1 we use x to repres5t units ( "t4 ,x !n enables u to record ! "t x took a mov+ po9t 9 ! floor to pass f position to position4 ,c]ta9 po9ts 9 ! room w\ld be v]tically above ! correspond+ po9ts occupi$ by ! mov+ po9t 9 its pa? across ! floor2 & ! v]tical height above ! floor ( su* po9ts corresponds to a value ( ! "t-coord9ate :i* indicates ! "t x took ! po9t to move f position to position4#aeb ,j z ! pa? ( ! po9t across ! floor is a cont9u\s curve 7= ! ma!matician1 x %\ld be und]/ood1 ?is t]m curve includes ! /raight l9e1 z a special case 9 :i* ! curvature happ5s to be z]o72 s ! s]ies ( po9ts above ^! 9 ! room =ms a cont9u\s curve :i* records = u1 n m]ely ! pa? ( ! po9t across ! floor1 b 9 addition ! "t ( its arrival at ea* ( its successive positions4 ,9 ! algebraic "w connect$ ) su* a problem1 ! ?ird coord9ate behaves exactly ! same1 reg>dless ( :e!r we consid] x to repres5t "t or a ?ird spatial dim5sion2 we _c ev5 tell f ! algebra :at x does repres5t4 ,:5 we come to ! m g5]al case ( a po9t mov+ freely ?r\gh space1 we h b ?ree coord9ates at our disposal2 !re is n a f\r? "o by aid ( :i* we c actually diagram its "t-space record4 ,nev]!less1 we c write d[n ! num]ical & algebraic relations betwe5 its ?ree space-coord9ates & ! "t :i* x takes to pass f "o position to ano!r2 & by ?is means we c make all necess>y calculations4 ,its motion is completely def9$ ) reg>d bo? to space & to "t4 ,we are v apt to call att5tion to ! fact t if we did h at our disposal a f\r?1 space-coord9ate1 we c\ld use x to repres5t ! "t graphically1 z be=e1 & actually con/ruct a geometric picture ( ! pa? ( our mov+ po9t ) reg>d to space & "t4 ,& on ?is acc\nt we are v apt to speak z ?\gh ! "t measurem5ts con/itut$ a f\r? coord9ate1 reg>dless ( any "q ( our ability to con/ruct a picture ( ?is coord9ate4 ,! arrival ( a po9t 9 a giv5 position con/itutes an ev5t2 & ?is ev5t is completely def9$ by means ( f\r coord9ates--?ree 9 space1 :i* we c picture on our coord9ate axes1 & "o 9 "t :i* we _c4 ,! set ( coord9ate axes 9 space1 toge!r ) ! z]o po9t f :i* we measure "t1 con/itute :at we call a frame ( ref]5ce4 ,if we are n go+ to pay any att5tion to "t1 we c ?9k ( ! space coord9ate sy/em alone z con/itut+ our ref]5ce frame4 ,?is expression appe>s freely ?r\gh\t ! subsequ5t text1 & always ) "o or ! o!r ( ^! int]pretations4 ,we see1 !n1 h[ we c keep track ( a mov+ po9t by keep+ track ( ! successive positions :i* x occupies 9 our ref]5ce frame499 ,n[ we h impli$ t ^! coord9ate axes are fix$ 9 space2 b !re is no?+ to prev5t u f suppos+ t !y move4#bgb ,if !y d1 !y c>ry ) !m all _! po9ts2 & any motion ( ^! po9ts :i* we may speak ab\t w be m]ely motion ) ref]5ce to ! coord9ate sy/em4 ,if we f9d some?+ outside our coord9ate sy/em t is n mov+1 ! motion ( po9ts 9 our sy/em ) reg>d to ^? outside x w be a comb9ation ( _! motion ) reg>d to our coord9ate axes & t ( ^! axes ) reg>d to ! ext]nal po9ts4 ,?is w be a great nuisance2 & x repres5ts a /ate ( affairs :i* we %all try to avoid4 ,we %all avoid x1 if at all1 by select+ a coord9ate sy/em ) ref]5ce to :i* we1 ourselves1 are n mov+2 "o :i* p>takes ( any motion :i* we may h4 ,or p]haps we %all sometimes wi% to rev]se ! process1 9 /udy+ ! behavior ( "s gr\p ( bodies1 & seek a set ( axes :i* is at re/ ) respect to ^! bodies2 "o :i* p>takes ( any motion !y may h4 ,,! ,,*oice ,,( ,a ,,coord9ate ,,frame ,all ?is emphasizes ! fact t our coord9ate axes are n pick$ out = u 9 advance by nature1 & set d[n 9 "s "o p>ticul> spot4 ,we select !m = ourselves1 & we select !m 9 ! mo/ conv5i5t way4 ,b diff]5t obs]v]s1 or p]haps ! same obs]v] /udy+ diff]5t problems1 w f9d x advantage\s to utilize diff]5t coord9ate sy/ems499 ,! a/ronom] has f\nd x possible1 & highly conv5i5t1 to select a coord9ate frame su* t ! great majority ( ! />s h1 on ! :ole1 no motion ) respect to x4#bhc ,su* a sy/em w\ld be mo/ unsuit$ = inve/igations conf9$ to ! e>?2 = ^! we naturally select a framework atta*$ to ! e>?1 ) its orig9 ,o at ! e>?'s c5t] if our inve/igation cov]s ! entire globe & at "s m conv5i5t po9t if x does n1 & 9 ei!r ev5t accompany+ ! e>? 9 its rotation & revolution4 ,b su* a framework1 z well z ! "o atta*$ to ! fix$ />s1 w\ld be highly inconv5i5t = an inve/igator ( ! motions ( ! planets2 he w\ld d\btless atta* 8 ref]5ce frame to ! sun4#aja ,9 ?is connection a vital "q sugge/s itself4 ,is ! expression ( natural law indep5d5t ( or dep5d5t ^u ! *oice ( a sy/em ( coord9ates8 ,& to :at ext5t %all we be able to reconcile ! results ( "o obs]v] us+ "o ref]5ce frame1 & a second obs]v] us+ a diff]5t "o8 ,! answ] to ! second "q is obvi\s499 ,true1 if any s]ies ( ev5ts is describ$ us+ two diff]5t sets ( axes1 ! descriptions w be diff]5t1 dep5d+ ^u ! "t sy/em adopt$ & ! relative motion ( ! axes4 ,b if ! connection betwe5 ! ref]5ce sy/ems is kn[n1 x is possible by ma!matical processes to d$uce ! quantities obs]v$ 9 "o sy/em if ^? obs]v$ 9 ! o!r are kn[n4#ce ,?is process ( translat+ ! results ( "o obs]v] into ^? ( ano!r is kn[n z a trans=mation2 & ! ma!matical /atem5t ( ! rule gov]n+ ! trans=mation is call$ ! equation or ! equations 7!re are usually sev]al ( !m7 ( ! trans=mation499 ,trans=mations ( ?is "* con/itute a well-develop$ bran* ( ma!matics4#ce ,:5 we inquire ab\t ! inv>iance ( natural law x is necess>y to be r sure ( j :at we mean by ?is expression4 ,! /atem5t t a giv5 body is mov+ ) a velocity ( #ge miles p] h\r is ( c\rse n a natural law2 x is a m]e num]ical obs]vation4 ,b aside f su* num]ical results1 we h a l>ge numb] ( ma!matical relations :i* give u a m or less g5]al /atem5t ( ! relations t exi/ betwe5 velocities1 accel]ations1 masses1 =ces1 times1 l5g?s1 temp]atures1 pressures1 etc41 etc4 ,!re are "s ( ^! :i* we w\ld be prep>$ to /ate at once z univ]sally valid--di/ance travell$ equals velocity multipli$ by "t1 = in/ance4 ,we d n believe t any conceivable *ange ( ref]5ce sy/ems c\ld br+ ab\t a condition 9 :i* ! product ( velocity & "t1 z measur$ f a c]ta9 framework1 w\ld fail to equal di/ance z measur$ f ?is same framework4 ,!re are o!r relations m or less ( ! same sort :i* we probably believe to be 9 ! same inv>iant category2 !re are o!rs1 p]haps1 ( :i* we might be d\btful2 & presumably !re are /ill o!rs :i* we %\ld suspect ( re/rict$ validity1 hold+ 9 c]ta9 ref]5ce sy/ems only & n 9 o!rs4 ,! "q ( inv>iance ( natural law1 !n1 may turn out to be "o :i* may be answ]$ 9 ! l>ge by a s+le /atem5t2 x may equally turn out to be "o t has to be answ]$ 9 ! small1 by consid]+ p>ticul> laws 9 connection ) p>ticul> trans=mations betwe5 p>ticul> ref]5ce sy/ems4 ,or1 p]haps1 we may f9d ourselves ju/ifi$ 9 tak+ ! /& t an alleg$ law ( nature is truly su* a law only 9 ! ev5t t x is indep5d5t ( ! *ange f "o ref]5ce sy/em to ano!r4 ,9 any ev5t1 ! "q may be =mulat$ z foll[s3 ,obs]v] ,a1 us+ ! ref]5ce sy/em ,r1 measures c]ta9 quantities t1 w1 x1 y1 z4 ,obs]v] ,b1 us+ ! ref]5ce sy/em ,s1 measures ! same items & gets ! values t'1 w'1 x'1 y'1 z'4 ,! appropriate trans=mation equations = calculat+ ! "o set ( values f ! o!r is f\nd4 ,if a ma!matical relation ( any sort is f\nd to exi/ betwe5 ! values t1 w1 x1 y1 z1 w ! same relation exi/ betwe5 ! values t'1 w'1 x'1 y'1 z'8 ,if x does n1 are we ju/ifi$ 9 /ill call+ x a law ( nature8 ,& if x does n1 & we refra9 f call+ x su* a law1 may we expect 9 e case to f9d "s relation t w be inv>iant "u ! trans=mation1 & t may !re=e be recogniz$ z ! natural law connect+ t1 w1 x1 y & z8 ,i h f\nd x advisable to discuss ?is po9t 9 su* detail because "h m ?an 9 any o!r s+le place ! compet+ essayi/s betray unc]ta9ty ( ?\ght & slopp9ess ( expression4 ,x doesn't am\nt to mu* to talk ab\t ! inv>iance ( natural laws & _! p]si/5ce z we pass f "o coord9ate sy/em to ano!r1 unless we are fairly well =tifi$ ) respect to j :at we mean by inv>iance & by natural law4 ,we don't expect ! velocity ( a tra9 to be #fj miles p] h\r alike :5 we measure x ) respect to a signal t[] along ! l9e & ) respect to a mov+ tra9 on ! o!r track4 ,we don't expect ! angul> displacem5t ( ,m>s to *ange z rapidly :5 he is on ! o!r side ( ! sun z :5 he is on our side4 ,b we d1 ,i ?9k1 r expect t 9 any ph5om5on :i* we may obs]ve1 we %all f9d a natural law ( "s sort :i* is dep5d5t = its validity nei!r ^u ! units we employ1 nor ! place f :i* we make our measurem5ts1 nor any?+ else ext]nal to ! ph5om5on itself4 ,we %all see1 lat]1 :e!r ?is expectation is ju/ifi$1 or :e!r x w h to be disc>d$ 9 ! f9al unravell+ ( ! absoluti/ f ! relativi/ic philosophy :i*1 ) ,e9/e91 we are to und]take499 ,,iii ,,! ,,relativity ,,( ,,uni=m ,,motion ,classical ,ideas on ! ,subject2 ! ,e!r & ! ,app>5t ,possibility ( ,absolute ,motion2 ! ,mi*elson-,morley ,exp]im5t & ! ,f9al ,negation ( ,?is ,possibility ,,by ,,v>i\s ,,contributors ,,& ,,! ,,editor ,:5 we speak ( a body z be+ 9 motion1 we mean t ?is body is *ang+ its position 9 space4 ,n[ x is cle> t ! position ( an object c only be det]m9$ ) ref]5ce to o!r objects3 9 ord] to describe ! place ( a mat]ial ?+ we mu/1 = example1 /ate its di/ances f o!r ?+s4 ,if !re 7 no su* bodies ( ref]5ce1 ! words position 9 space w\ld h no def9ite mean+ = u4#bd ,! numb] ( su* ext]nal bodies ( ref]5ce :i* x is necess>y to cite 9 ord] to def9e completely ! position ( a giv5 body 9 space dep5ds ^u ! "* ( ! space dealt )4 ,we h se5 t :5 we visualize ! space ( our exp]i5ce z a surface ( any "*1 two citations are suffici5t2 & t :5 we conceive ( x z surr\nd+ u 9 ?ree dim5sions we require ?ree4 ,x w be realiz$ t ! ma!matician is m]ely meet+ ?is requirem5t :5 he sets up 8 sy/em ( coord9ate axes to s]ve z a ref]5ce frame499 ,:at is true ( place mu/ be true also ( motion1 s9ce ! latt] is no?+ b *ange ( place4 ,9 fact1 x w\ld be impossible to ascribe a /ate ( motion or ( re/ to a body pois$ all alone 9 empty space4 ,:e!r a body is to be reg>d$ z re/+ or z mov+1 & if ! latt] at :at spe$1 dep5ds entirely ^u ! objects to :i* we ref] its positions 9 space4#bd ,z ,e9/e9 sits at 8 desk he appe>s to u to be at re/2 b we "k t he is mov+ ) ! rotation ( ! e>? on its axis1 ) ! e>? 9 its orbit ab\t ! sun1 & ) ! sol> sy/em 9 its pa? ?r\gh space--a complex motion ( :i* ! p>ts or ! :ole c be detect$ only by ref]5ce to appropriately *os5 ones ( ! heav5ly bodies4 ,no me*anical te/ has ev] be5 devis$ :i* w detect ?is motion1#ahb if we res]ve = discussion 9 its prop] place ! ,f\cault p5dulum exp]im5t :i* w reveal ! axial rotation ( our globe499 ,no savage1 if he 7 to /& /ill1 c\ld be conv9c$ t he 0 mov+ ) a v high velocity or 9 fact t he 0 mov+ at all4#cj ,y drop a co9 /raight d[n a %ip's side3 f ! l& its pa? appe>s p>abolic2 to a pol> onlook] x :irls circle-wise2 to dwell]s on ,m>s x d>ts spirally ab\t ! sun2 to a /ell> obs]v] x gyrates ?r\gh ! sky#bfc 9 a pa? ( _m complications4 ,to y x drops 9 a /raight l9e f ! deck to ! sea499 ,yet its v>i\s tracks 9 %ip-space1 sea-space1 e>?-space1 sun-space1 />-space1 are all equally real1#bfc & ! "o :i* w be s+l$ out = att5tion dep5ds entirely ^u ! obs]v]1 & ! objects to :i* he ref]s ! motion499 ,! e>? moves 9 ! sol> sy/em1 :i* is itself approa*+ a di/ant />-clu/]4 ,b we _c say :e!r we are mov+ t[>d ! clu/]1 or ! clu/] t[>d u1#ah or bo?1 or :e!r we are conduct+ a successful /]n *ase ( x1 or x ( u199 unless we h 9 m9d "s ?ird body ) ref]5ce to :i* ! motions ( e>? & />-clu/] are measur$4#ah ,& if we h ?is1 ! measurem5ts made ) ref]5ce to x are ( significance ) reg>d to x1 r ?an ) reg>d to ! e>? & ! />-clu/] alone499 ,we c express all ?is by say+ ,all motions are relative2 !re is no su* ?+ z absolute motion4 ,?is l9e ( argum5t has 9 fact be5 foll[$ by _m natural philosoph]s4 ,b is its result 9 agreem5t ) actual exp]i5ce8 ,is x really impossible to di/+ui% betwe5 re/ & motion ( a body if we d n take into consid]ation its relations to o!r objects8 ,9 fact x c easily be se5 t1 at lea/ 9 _m cases1 no su* di/9ction is possible4 ,,:o ,,is ,,mov+8 ,imag9e y\rself sitt+ 9 a railroad c> ) veil$ w9d[s & runn+ on a p]fectly /raight track ) un*ang+ velocity3 y w\ld f9d x absolutely impossible to asc]ta9 by any me*anical means :e!r ! c> 7 mov+ or n4 ,all me*anical in/rum5ts behave exactly ! same1 :e!r ! c> be /&+ /ill or 9 motion4#bd ,if y drop a ball y w see x fall to ! floor 9 a /raight l9e1 j z ?\gh y _h dropp$ x :ile /&+ on ! /ation plat=m4 ,fur!rmore1 if y drop ! ball f ! same height 9 ! two cases1 & measure ! velocities ) :i* x /rikes ! c> floor & ! /ation plat=m1 or ! times :i* x requires = ! desc5t1 y w f9d ^! id5tical 9 ! two cases4#ahb ,any *anges ( spe$ or ( direction 7z :5 ! c> spe$s up or sl[s d[n or r\nds a curve7 c be detect$ by obs]v+ ! behavior ( bodies 9 ! c>1 )\t app>5t ref]5ce to any outside objects4 ,?is becomes p>ticul>ly obvi\s ) sudd5 irregul>ities ( motion1 :i* manife/ !mselves by %ak+ ev]y?+ 9 ! c>4 ,b a uni=m motion 9 a /raight l9e does n reveal itself by any ph5om5on )9 ! vehicle4#bd ,moreov]1 if we remove ! veil f our w9d[ to ! ext5t t we may obs]ve ! tra9 on ! adjo9+ track1 we %all be able to make no decision z to :e!r we or x be mov+4 ,?is is inde$ an exp]i5ce :i* we h all _h499 ,(t5 :5 seat$ 9 a tra9 ab\t to leave ! /ation1 we h ?\ght ourselves "u way1 only to p]ceive z ! motion becomes no long] uni=m t ano!r tra9 has be5 back+ into ! /ation on ! adjo9+ track4 ,aga91 z we 7 hurri$ on our j\rney1 we h1 rais+ sudd5ly our eyes1 be5 puzzl$ to say :e!r ! pass+ tra9 7 mov+ ) u or aga9/ u or inde$ /&+ /ill2 or m r>ely we h _h ! impression t bo? x & we seem$ to be at re/1 :5 9 tru? bo? 7 mov+ rapidly ) ! same spe$4#hb ,ev5 ?is phrase 9 tru? is a relative "o1 = x arises ?r\gh us+ ! e>? z an absolute ref]5ce body4 ,we are inde$ naive if we _c appreciate t !re is no reason = do+ ?is beyond conv5i5ce1 & t to an obs]v] deta*$ f ! e>? x 7 j z reasonable to say t ! rails are slid+ "u ! tra9 z t ! tra9 is advanc+ along ! rails4 ,"o ( my own mo/ vivid *ildhood recollections is ( ! t]ror ) :i*1 rid+ on a tra9 t pass$ ?r\gh a n>r[ cut1 ,i hid my head 9 ! mat]nal lap to %ut out ! horrid sight ( ! e>? ru%+ pa/ my w9d[4 ,! abs5ce ( a backgr\nd 9 relatively sl[ retrograde motion 0 suffici5t to prev5t my consci\sness f draw+ ! accu/om$ conclusion t aft] all x 0 really ! tra9 t 0 mov+499 ,,me*anical ,,relativity ,s we c enunciate ! foll[+ pr9ciple3 ,:5 a body is 9 uni=m rectil9e> motion relatively to a second body1 !n all ph5om5a take place on ! fir/ 9 exactly ! same mann] z on ! second2 ! physical laws = ! happ5+s on bo? bodies are id5tical4#bd ,& betwe5 a sy/em ( bodies1 no?+ b relative motion may be detect$ by any me*anical means :atev]2 any attempt to discuss absolute motion presupposes a sup]-obs]v] on "s body ext]nal to ! sy/em4 ,ev5 !n1 ! absolute motion is no?+ b motion relative to ?is sup]-obs]v]4 ,by no me*anical means is uni=m /raight-l9e motion ( any o!r ?an relative "* to be detect$4 ,?is is ! ,pr9ciple ( ,me*anical ,relativity4 ,!re is no?+ new 9 ?is4 ,x 0 kn[n to ,galileo1 x 0 kn[n to ,newton1 x has be5 kn[n ev] s9ce4 ,b ! curi\s p]si/5ce ( ! human m9d 9 habits ( ?\ght :i* confuse relativity ) absolutism br\ght ab\t a /ate ( affairs :]e we attempt$ to "k ?is & to ignore x at ! same "t4 ,we %all h to return to ! ma!matical mode ( reason+ to see h[ ?is happ5$4 ,! ma!matician has a way all 8 own ( putt+ ! /atem5t ( relativity :i* we h made4 ,he recalls1 :at we h already se51 t ! obs]v] on ! e>? :o is measur+ 8 absolute motion ) respect to ! e>? has m]ely atta*$ 8 ref]5ce framework to ! e>?2 t ! pass5g] 9 ! tra9 :o measures all motion naively ) respect to 8 tra9 is m]ely c>ry+ 8 coord9ate axes along ) 8 baggage1 in/ead ( leav+ !m on ! solid gr\nd2 t ! a/ronom] :o deals ) ! motion ( ! e>? ab\t ! sun1 or ) t ( ! fix$ />s aga9/ "o ano!r1 does s simply by ! artifice ( hit*+ 8 frame ( ref]5ce to ! sun or to "o ( ! fix$ />s4 ,s ! ma!matician po9ts out t dispute z to :i* ( two bodies is 9 motion comes "r d[n to dispute z to :i* ( two sets ( coord9ate axes is ! bett] "o1 ! m ne>ly natural or absolute4 ,he !re=e phrases ! me*anical pr9ciple ( relativity z foll[s3 ,among all coord9ate sy/ems t are m]ely 9 uni=m /raight-l9e motion to "o ano!r1 no "o occupies any position ( unique natural advantage2 all su* sy/ems are equival5t = ! inve/igation ( natural laws2 all sy/ems lead to ! same laws & ! same results4 ,! ma!matician has ?us remov$ ! /atem5t ( relativity f its intimate association ) ! ext]nal obs]v$ ph5om5a1 & transf]r$ x to ! obs]v] & 8 ref]5ce frame4 ,we mu/ ei!r accept ! pr9ciple ( relativity1 or seek a set ( coord9ate axes t h be5 s+l$ out by nature z an absolute ref]5ce frame4 ,^! axes mu/ be 9 "s way unique1 s t :5 we ref] ph5om5a to !m1 ! laws ( nature take a =m ( exceptional simplicity n atta9$ ?r\gh ref]5ce to ord9>y axes4 ,:]e %all we look = su* a pref]r$ coord9ate sy/em899 ,,! ,,se>* ,,= ,,! ,,absolute ,old] !ory clung to ! belief t !re 0 su* a ?+ z absolute motion 9 space4#aig ,z ! body ( sci5tific law develop$ f ! sixte5? c5tury onw>d1 ! n unnatural hypo!sis crept 91 t ^! laws 7t is to say1 _! ma!matical =mulations r ?an _! v]bal /atem5ts7 w\ld reveal !mselves 9 especially simple =ms1 7 x possible = exp]im5t]s to make _! obs]vations f "s absolute /&po9t2 f an absolutely fix$ position 9 space r ?an f ! mov+ e>?4#bfd ,some:]e a set ( coord9ate axes incapable ( motion 0 to be f\nd1#aig a fix$ set ( axes = measur+ absolute motion2 & = two hundr$ ye>s ! _w ( sci5ce /rove to f9d x1#adg 9 spite ( :at %\ld h be5 assurance t x did n exi/4 ,b ! se>* fail$1 & gradually ! univ]sal applicability ( ! pr9ciple ( relativity1 s f> z x conc]n$ me*anical ph5om5a1 grew into g5]al acceptance499 ,& aft] ! developm5t1 by ! great ma!maticians ( ! eighte5? c5tury1 ( ,newton's laws ( motion into _! mo/ complete ma!matical =m1 x 0 se5 t s f> z ^! laws are conc]n$ ! absoluti/ hypo!sis m5tion$ is q unsupport$4 ,no complication is introduc$ into ,newton's laws if ! obs]v] has to make 8 measurem5ts 9 a frame ( ref]5ce mov+ uni=mly ?r\gh space2 & = measurem5ts 9 a frame l ! e>?1 :i* moves ) *ang+ spe$ & direction ab\t ! sun & rotates on its axis at ! same "t1 ! complication is n ( s decisive a nature z to give u any clue to ! e>?'s absolute motion 9 space4 ,b me*anics1 albeit ! olde/1 is yet only "o ( ! physical sci5ces4 ,! great advance made 9 ! ma!matical =mulation ( optical & electromagnetic !ory dur+ ! n9ete5? c5tury reviv$ ! hope ( discov]+ absolute motion 9 space by means ( ! laws d]iv$ f ?is !ory4#bfd ,newton _h suppos$ light to be a mat]ial emanation1 & if x 7 s1 its passage across empty space f sun & />s to ! e>? rais$ no problem4 ,b aga9/ ,newton's !ory ,huygh5s1 ! ,dut* a/ronom]1 advanc$ ! idea t light 0 a wave motion ( "s sort4 ,dur+ ! ,newtonian p]iod & = _m ye>s aft]1 ! corpuscul> !ory prevail$2 b ev5tually ! tables 7 turn$499 ,m5 made rays ( light int]f]e1 produc+ d>kness 7see page #fa74 ,f ?is1 & f o!r ph5om5a l pol>ization1 !y _h d$uc$ t light 0 a =m ( wave motion simil> to wat] ripples2 = ^! int]f]e1 produc+ level surfaces1 or re9=ce ea* o!r1 produc+ waves ( abnormal height4 ,b if light 7 to be reg>d$ z a =m ( wave motion--& ! ph5om5a c\ld app>5tly be expla9$ on no o!r basis--!n !re mu/ be "s m$ium capable ( und]go+ ?is =m ( motion4#ace ,transmission ( waves across empty space )\t ! aid ( an int]m$i>y mat]ial m$ium w\ld be action at a di/ance1 an idea repugnant to u4 ,trammel$ by our tactual1 wire-pull+ conceptions ( a mat]ial univ]se1 we c\ld n accu/om ourselves to ! idea ( some?+--ev5 s immat]ial a some?+ z a wave--be+ transmitt$ by no?+4 ,we ne$$ a ^w--e!r--to c>ry light if n to %$ x2 j z we ne$ a ^w--in]tia--to c>ry a projectile 9 its flight4#bca ,x 0 necess>y to inve/ ?is m$ium ) prop]ties to acc\nt = ! obs]v$ facts4 ,on ! :ole x 0 reg>d$ z ! p]fect fluid4#bce ,! e!r 0 imag9$ z an all-p]vad+1 impond]able sub/ance fill+ ! va/ empt9ess ?r\gh :i* light rea*es u1 & z well ! int]molecul> spaces ( all matt]4 ,no?+ m 0 kn[n def9itely1 yet ?is mu* s]v$ z a good work+ hypo!sis on ! basis ( :i* ,maxwell 0 enabl$ to pr$ict ! possibility ( radio communication4 ,by its fruits ! e!r hypo!sis ju/ifi$ itself2 b does ! e!r exi/8#bca ,,! ,,e!r ,,& ,,absolute ,,motion ,if x does exi/1 x seems q necess>y1 on m]e philosophical gr\nds1 t x %all be eligible to s]ve z ! long-s\ght ref]5ce frame = absolute motion4 ,surely x does n make s5se to speak ( a homog5e\s m$ium fill+ all space1 suffici5tly mat]ial to s]ve z a means ( communication betwe5 remote worlds1 & 9 ! next brea? to d5y t motion ) respect to ?is m$ium is a concept ( significance499 ,su* a sy/em ( ref]5ce z 0 (f]$ by ! e!r1 coext5sive ) ! entire kn[n region ( ! univ]se1 mu/ necess>ily s]ve = all motions )9 our p]ceptions4#ahf ,! conclusion seems inescapable t motion ) respect to ! e!r ought to be ( a suffici5tly unique "* to /& out above all o!r motion4 ,9 p>ticul>1 we ought to be able to use ! e!r to def9e1 some:]e1 a sy/em ( axes fix$ ) respect to ! e!r1 ! use ( :i* w\ld lead to natural laws ( a uniquely simply description4 ,maxwell's "w add$ fuel to ?is hope499 ,dur+ ! la/ c5tury1 aft] ! units ( electricity _h be5 def9$1 "o set = /atic electrical calculations & "o = electromagnetic calculations1 x 0 f\nd t ! ratio ( ! metric units ( capacity = ! two sy/ems 0 num]ically equal to :at _h already be5 f\nd z ! velocity ) :i* light is transmitt$ ?r\gh ! hypo!tical e!r4 ,"o def9ition ref]s to electricity at re/1 ! o!r to electricity 9 motion4 ,maxwell1 ) little m work+ basis ?an ?is1 und]took to prove t electrical & optical ph5om5a 7 m]ely two aspects ( a common cause1#bce to :i* ! g5]al designation ( electromagnetic waves 0 appli$4 ,maxwell treat$ ?is topic 9 great fullness & ) complete success4 ,9 p>ticul>1 he d]iv$ c]ta9 equations giv+ ! relations betwe5 ! v>i\s electrical quantities involv$ 9 a giv5 ph5om5on4 ,b x 0 f\nd1 extraord9>ily en\gh1 t ^! relations 7 ( su* "* t1 :5 we subject ! quantities involv$ to a *ange ( coord9ate axes1 ! trans=m$ quantities did n pres]ve ^! relations if ! new axes happ5$ to be 9 motion ) respect to ! orig9al ones4 ,?is1 ( c\rse1 0 tak5 to indicate t motion really is absolute :5 we come to deal ) electromagnetic ph5om5a1 & t ! e!r :i* c>ries ! electromagnetic waves really may be look$ to to display ! prop]ties ( an absolute ref]5ce frame4 ,ref]5ce to ! ph5om5on ( ab]ration1 :i* ,dr4 ,pick]+ has discuss$ adequately 9 8 essay & :i* ,i ne$ !re=e m5tion "h only by "n1 indicat$ t ! e!r 0 n dragg$ along by mat]ial bodies ov] & ?r\gh :i* x might pass4 ,x seem$ t x mu/ filt] ?r\gh su* bodies1 presumably via ! molecul> int]/ices1 )\t appreciable opposition4 ,7 ?is n ! case1 we %\ld be 9 "s d\bt z to ! possibility ( obs]v+ ! velocity ?r\gh ! e!r ( mat]ial bodies2 if ! e!r adjac5t to su* bodies is n dragg$ along or ?r[n into eddies1 b /&s /ill :ile ! bodies pass1 !re seems no imag9able reason = any?+ o!r ?an ! complete success ( su* obs]vations4 ,& ( c\rse ^! are ( ! utmo/ importance1 ! mom5t we assign to ! e!r ! rle ( absolute ref]5ce frame4 ,,! ,,e>? ,,& ,,! ,,e!r ,"o body 9 motion ) respect to ! e!r is our e>? itself4 ,we d n "k 9 advance 9 :at direction to expect ?is motion or :at magnitude to anticipate t x w h4 ,b "o ?+ is cle>499 ,9 its motion ar\nd ! sun1 ! e>? has1 at opposite po9ts on its orbit1 a diff]5ce 9 velocity ) respect to ! surr\nd+ m$ium :i* is d\ble its orbital velocity ) respect to ! sun4 ,?is diff]5ce comes to #cg miles p] second4 ,! e>? %\ld !re=e1 at "s "t 9 ! ye>1 %[ a velocity equal to or great] ?an #ah #a_/b miles p] second1 ) ref]5ce to ! univ]sal m$ium4 ,! fam\s ,mi*elson-,morley exp]im5t ( #ahhg 0 c>ri$ out ) ! expectation ( obs]v+ ?is velocity4#bfg ,! e!r1 ( c\rse1 & h5ce velocities ?r\gh x1 _c be obs]v$ directly4 ,b x acts z ! m$ium = ! transmission ( light499 ,if ! velocity ( light ?r\gh ! e!r is ,c & t ( ! e>? ?r\gh ! e!r is v1 !n ! velocity ( light pa/ ! e>?1 s ! argum5t runs1 mu/ v>y f ,c-v to ,cv1 accord+ z ! light is mov+ exactly 9 ! same direction z ! e>?1 or 9 ! opposite direction1#ahb or diagonally across ! e>?'s pa? s z to get ! influ5ce only ( a "p ( ! e>?'s motion4 ,?is ( c\rse assumes t ,c has always ! same value2 an assumption t impresses "o z inh]5tly probable1 & "o t is at ! same "t 9 accord ) ord9>y a/ronomical obs]vation4 ,x is n possible to measure directly ! velocity ( light 7#ahf1ccj miles p] second1 m or less7 ) suffici5t accuracy to give any mean+ to ! v>iation 9 ?is velocity :i* might be effect$ by add+ or subtract+ t ( ! e>? 9 its orbit 7a m]e #ah #a_/b miles p] second74 ,x is1 h[ev]1 possible to play a trick on ! light by s5d+ x back & =? ov] sev]al pa?s1 & comp>+ 7n measur+ absolutely1 b m]ely comp>+7 ) great m9ut5ess ! times consum$ 9 ^! sev]al r\nd trips4 ,a ,,j\rney ,,up/ream ,,& ,,back ,! numb] ( lett]s ! ,sci5tific ,am]ican has receiv$ que/ion+ ! ,mi*elson-,morley exp]im5t indicates t _m p are n acqua9t$ ) ! fundam5tal pr9ciple on :i* x is bas$4 ,s let u look at a simple analog\s case4 ,suppose a swimm] or a r[] make a return trip up/ream & d[n1 cont5d+ ) ! curr5t z he goes up & gett+ its b5efit :5 he comes d[n4 ,obvi\sly1 says snap judgm5t1 s9ce ! two legs ( ! j\rney are equal1 he d]ives exactly z mu* b5efit f ! curr5t :5 he goes ) x z he suff]s h&icap f x :5 he goes aga9/ x2 s ! r\nd trip mu/ take exactly ! same "t z a j\rney ( ! same l5g? 9 /ill wat]1 ! argum5t apply+ equally 9 ! case :]e ! swimm] is a wave ( light 9 ! e!r /ream4 ,b let u look n[ at a num]ical case4 ,a man c r[ 9 /ill wat] at f\r miles p] h\r4 ,he r[s twelve miles up/ream & back1 9 a curr5t ( two miles p] h\r4 ,at a net spe$ ( two miles p] h\r he arrives at 8 turn+ po9t 9 six h\rs4 ,at a net spe$ ( six miles p] h\r he makes ! d[n-/ream leg 9 two h\rs4 ,! elaps$ "t = ! j\rney is eight h\rs2 9 /ill wat] he w\ld r[ ! tw5ty-f\r miles 9 six h\rs4 ,if we 7 to attempt an explanation ( ?is result 9 words we %\ld say t by virtue ( ! v fact t x does delay him1 ! adv]se curr5t prolongs ! "t dur+ :i* x op]ates2 :ile by virtue ( ! v fact t x accel]ates 8 progress1 ! favor+ curr5t %ort5s its v5ue4 ,! c>eless obs]v] realizes t di/ances are equal betwe5 ! two legs ( ! j\rney1 & unconsci\sly assumes t times are equal4 ,if ! j\rney be made directly ) & directly aga9/ ! /ream ( wat] or e!r or :at n1 ret>dation is effect$ to its fulle/ ext5t4 ,if ! c\rse be a diagonal "o1 ret>dation is felt to an ext5t measurable z a compon5t1 & dep5d+ = its exact value ^u ! exact angle ( ! pa?4 ,felt1 h[ev]1 x mu/ always be4 ,"h is :]e we beg9 to get a grip on ! problem ( ! e>? & ! e!r4 ,9 any problem involv+ ! return-trip pr9ciple1 !re w ent] two velocities--t ( ! swimm] & t ( ! m$ium2 & ! "t ( ret>dation4 ,if we "k any two ( ^! items we c calculate ! ?ird4 ,:5 ! swimm] is a ray ( light & ! velocity ( ! m$ium is t ( ! e!r z x fl[s pa/ ! e>?1 we "k ! fir/ ( ^! two2 we hope to obs]ve ! ret>dation s t we may calculate ! second velocity4 ,! app>atus = ! exp]im5t is +5i\s & dem&s description4 ,,! ,,mi*elson-,,morley ,,exp]im5t ,! ma*9e is ( /ructural /eel1 weigh+ #a1ijj p\nds4 ,x has two arms :i* =m a ,greek cross4 ,ea* arm is #ad feet 9 l5g?4 ,! :ole app>atus is float$ 9 a tr\gh conta9+ #hjj p\nds ( m]cury4 ,f\r mirrors are arrang$ on ! end ( ea* arm1 sixte5 9 all1 ) a sev5te5? mirror1 ,m1 set at "o ( ! inside corn]s ( ! cross1 z diagramm$4 ,a s\rce ( light 79 ?is case a calcium flame7 is provid$1 & its rays direct$ by a l5s t[>d ! mirror ,m4 ,"p ( ! light is all[$ to pass /raight ?r\gh ,m to ! opposite arm ( ! cross1 :]e x /rikes mirror #a4 ,x is reflect$ back across ! arm to mirror #b1 !nce to #c1 & s on until x rea*es mirror #h4 ,!nce x is reflect$ back to mirror #g1 to #f1 & s on1 retrac+ its =m] pa?1 & f9ally is caught by ! rev]se side ( ! mirror ,m & is s5t to an obs]v] at ,o4 ,9 retrac+ its pa? ! light sets up an int]f]5ce ph5om5on 7see bel[7 & ! int]f]5ce b&s are visible to ! obs]v]1 :o is provid$ ) a telescope to magnify ! results4 ,a second "p ( ! orig9al light-beam is reflect$ (f at "r angles by ! mirror ,m1 & is pass$ to & fro on ! adjac5t arms ( ! ma*9e1 9 exactly ! same mann] & ov] a simil> pa?1 by means ( ! mirrors ,i1 ,,ii1 ,,iii1 444 ,,viii4 ,?is light f9ally rea*es ! obs]v] at ! telescope1 sett+ up a second set ( int]f]5ce b&s1 p>allel to ! fir/4 ,a ^w n[ ab\t ?is bus9ess ( light int]f]5ce4 ,light is a wave motion4 ,! l5g? ( a wave is b a few million?s ( an in*1 & ! amplitude is correspond+ly m9ute2 b none ! less1 ^! waves behave 9 a ?or\ghly wave-l mann]4 ,9 p>ticul>1 if ! cre/s ( two waves are sup]pos$1 !re is a d\ble effect2 :ile if a cre/ ( "o wave falls ) a tr\gh ( ano!r1 !re is a kill+-(f or int]f]5ce4 ,"u ord9>y circum/ances int]f]5ce ( light waves does n occur4 ,?is is simply because "u ord9>y circum/ances light waves are n pil$ up on "o ano!r4 ,b sometimes ?is pil+ up occurs2 & !n1 j s sure z ! pil$-up waves are 9 ! same phase !y re9=ce "o ano!r1 :ile if !y are 9 opposite phase !y int]f]e4 ,& ! conditions :i* we h outl9$ above1 ) ! telescope & ! mirrors & ! ray ( light retrac+ ! pa? ov] :i* x w5t out1 are conditions "u :i* int]f]5ce does occur4 ,if ! return+ wave is 9 exact phase ) ! outgo+ "o1 ! effect is t ( uni=m d\ble illum9ation2 if x is 9 exactly opposite phase ! effect is t ( complete ext+ui%+ ( ! light1 ! rev]s$ wave exactly cancell+ out ! orig9al "o4 ,if ! two rays are p>tly 9 phase1 !re is p>tial re9=cem5t or p>tial cancell+ out1 accord+ to :e!r !y are ne>ly 9 phase or ne>ly out ( phase4 ,f9ally1 if ! mirrors are n set absolutely p>allel--z mu/ 9 practice be ! case :5 we attempt to measure _! p>allelism 9 t]ms ( ! wave-l5g? ( light--adjac5t p>ts ( ! light ray w v>y 9 ! ext5t to :i* !y are out ( phase1 s9ce !y w h travell$ a fraction ( a wave-l5g? fur!r to get to & f ?is1 t or ! o!r mirror4 ,!re w !n appe> 9 ! telescope alt]nate b&s ( illum9ation & d>kness1 ^: wid? & spac+ dep5d ^u all ! factors ent]+ into ! problem4 ,if x 7 possible = u to make ! app>atus ) su* a degree ( ref9em5t t ! pa? f mirror ,m via mirrors #a1 #b1 #c1 etc41 back ?r\gh ,m & into ! telescope1 7 exactly ! same l5g? z t f flame to telescope by way ( ! mirrors ,i1 ,,ii1 ,,iii1 etc4--exactly ! same to a m>g9 ( error mat]ially less ?an a s+le wave-l5g? ( light--:y1 !n1 ! two sets ( int]f]5ce fr+es w\ld come out exactly sup]pos$ provid$ ! motion ( ! e>? ?r\gh ! e!r turn out to h no influ5ce ^u ! velocity ( light2 or1 if su* influ5ce exi/1 ^! fr+es w\ld be displac$ f "o ano!r to an ext5t measur+ ! influ5ce 9 "q4 ,b our ability to set up ?is complicat$ patt]n ( mirrors at pr$et]m9$ di/ances falls f> %ort ( ! wave-l5g? z a measure ( error4 ,s 9 practice all t we c say is t hav+ once set ! in/rum5t up1 & pass$ a beam ( light ?r\gh x1 !re w be produc$ two sets ( p>allel int]f]5ce fr+es4 ,^! sets w fail ( sup]position--ea* fr+e ( "o set w be remov$ f ! correspond+ fr+e ( ! o!r set--by "s def9ite di/ance4 ,!n1 any subsequ5t v>iation 9 ! spe$ ( light along ! two arms w at once be detect$ by a %ift+ ( ! int]f]5ce b&s ?r\gh a di/ance :i* we %all be able to measure4 ,,! ,,v]dict ,"u ! !ories & assumptions gov]n+ at ! "t ( ! orig9al p]=mance ( ?is exp]im5t1 x w be readily se5 t if ?is ma*9e be set up 9 an e!r /ream ) "o arm p>allel to ! direction ( ! /ream & ! o!r at "r angles !reto1 !re w be a diff]5ce 9 ! spe$ ( ! light along ! two arms4 ,!n if ! app>atus be %ift$ to a position oblique to ! e!r /ream1 ! excess velocity ( ! light 9 ! "o arm w\ld be dim9i%$1 & gradually come to z]o at ! #de-;degree angle1 aft] :i* ! light travel+ along ! o!r arm w\ld assume ! great] spe$4 ,9 mak+ obs]vations1 !re=e1 ! entire app>atus 0 sl[ly rotat$1 ! obs]v]s walk+ ) x1 s t *anges ( ! sort anticipat$ w\ld be obs]v$4 ,! inve/igators 71 h[ev]1 ignorant ( ! position 9 :i* ! app>atus ought to be set to insure t "o ( ! arms lie across ! e!r drift2 & !y 7 ignorant ( ! "t ( ye> at :i* ! e>?'s maximum velocity ?r\gh ! e!r 0 to be look$ =4 ,9 p>ticul>1 x is pla9 t if ! sol> sy/em z a :ole is mov+ ?r\gh ! e!r at a rate less ?an ! e>?'s orbital velocity1 !re is a po9t 9 our orbit :]e our velocity ?r\gh ! e!r & t ar\nd ! sun j cancel out & leave u tempor>ily 9 a /ate ( absolute re/4 ,s x 0 anticipat$ t ! exp]im5t might h to be repeat$ 9 _m ori5tations ( ! ma*9e & at _m seasons ( ! ye> 9 ord] to give a s]ies ( read+s f :i* ! true motion ( ! e>? ?r\gh ! e!r might be d$uc$4 ,= ^? :o h a little algebra ! demon/ration :i* ,dr4 ,russell gives on a subsequ5t page w be int]e/+ z %[+ ! situation 9 p]fectly g5]al t]ms4 ,x w be realiz$ t ! m complicat$ arrangem5t ( mirrors 9 ! exp]im5t z j describ$ is simply an eightfold repetition ( ! simple exp]im5t z outl9$ by ,dr4 ,russell1 & t x 0 done s = ! m]e sake ( multiply+ by eight ! di/ances travell$ & h5ce ! diff]5ce 9 "t & 9 phase4 ,& n[ = ! gr& climax4 ,! exp]im5t 0 repeat$ _m times1 ) ! orig9al & ) o!r app>atus1 indoors & outdoors1 at all seasons ( ! ye>1 ) v>iation ( e condition t c\ld imag9ably affect ! result4 ,! app>atus 0 ord9>ily su* t a %ift 9 ! fr+es ( any:]e f "o-t5? to "o "o-hundr$? ( t :i* w\ld h foll[$ f any reasonable value = ! e>?'s motion ?r\gh ! e!r w\ld h be5 sy/ematically app>5t4 ,! result 0 uni=mly negative4 ,at all times & 9 all directions ! velocity ( light pa/ ! e>?-b\nd obs]v] 0 ! same4 ,! e>? has no motion ) ref]5ce to ! e!r6 ,! amaz+ "* ( ?is result is n by any possibility to be exagg]at$499 ,accord+ to "o exp]im5t ! e!r 0 c>ri$ along by a rapidly mov+ body & accord+ to ano!r equally well-plann$ & well-execut$ exp]im5t a rapidly mov+ body did n di/urb ! e!r at all4 ,?is 0 ! bl9d alley into :i* sci5ce _h be5 l$4#bcb ,,! ,,contraction ,,hypo!sis ,num]\s ef=ts 7 made to expla9 ! contradiction499 ,x is inde$ a v puzzl+ "o1 & x gave physici/s no end ( tr\ble4 ,h[ev] ,lor5tz & ,fitzg]ald f9ally put =w>d an +5i\s explanation1 to ! effect t ! actual motion ( ! e>? ?r\gh ! e!r is balanc$1 z f> z ! ability ( our measur+ in/rum5ts is conc]n$1 by a contraction ( ^! same in/rum5ts 9 ! direction ( _! motion4 ,?is contraction obvi\sly _c be obs]v$ directly because all bodies1 includ+ ! measur+ in/rum5ts !mselves 7:i* aft] all are only arbitr>y guides71 w suff] ! contraction equally4 ,accord+ to ?is !ory1 call$ ! ,lor5tz-,fitzg]ald contraction !ory1#bgb all bodies 9 motion suff] su* contraction ( _! l5g? 9 ! direction ( _! motion2#bhc ! contraction be+ made evid5t by our inability to obs]ve ! absolute motion ( ! e>?1 :i* x is assum$ mu/ exi/4#bgb ,?is w\ld suffice to %[ :y ! ,mi*elson-,morley exp]im5t gave a negative result1 & w\ld pres]ve ! concept ( absolute motion ) ref]5ce to ! e!r4#bhc ,?is proposal ( ,lor5tz & ,fitzg]ald loses its />tl+ aspect :5 we consid] t all matt] appe>s to be an electrical /ructure1 & t ! dim5sions ( ! electric & magnetic fields :i* accompany ! electrons ( :i* x is con/itut$ *ange ) ! velocity ( motion4#bfg ,! =ces ( cohesion :i* det]m9e ! =m ( a rigid body are held to be electromagnetic 9 nature2 ! contraction may be reg>d$ z due to a *ange 9 ! electromagnetic =ces betwe5 ! molecules4#aj ,z "o writ] has put x1 ! ori5tation1 9 ! electromagnetic m$ium1 ( a body dep5d+ = its v exi/5ce ^u electromagnetic =ces is n necess>ily a matt] ( indiff]5ce499 ,grant+ ! plausibility ( all ?is1 on ! basis ( an electromagnetic !ory ( matt]1 x leaves u 9 an unsatisfactory position4 ,we are left ) a fix$ e!r ) ref]5ce to :i* absolute motion has a mean+1 b t motion rema9s undetect$ & app>5tly undetectable4 ,fur!r1 if we on %ore measure ! l5g? ( a mov+ %ip1 us+ a y>d-/ick :i* is /ation>y on %ore1 we %all obta9 "o result4 ,if we take our /ick abo>d x contracts1 & s we obta9 a great] l5g? = ! %ip4 ,n kn[+ our real motion ?r\gh ! e!r1 we _c say :i* is ! true l5g?4 ,is x n1 !n1 m satisfactory to disc>d all notion ( true l5g? z an inh]5t quality ( bodies1 &1 by reg>d+ l5g? z ! measure ( a relation betwe5 a p>ticul> object & a p>ticul> obs]v]1 to make "o l5g? z true z ! o!r8#ahb ,! oppon5ts ( su* a viewpo9t cont5d t ,mi*elson's result 0 due to a fluke2 "s my/]i\s c\nt]balanc+ influ5ce 0 = "s reason at "w1 conceal+ ! result :i* %\ld normally h be5 expect$4 ,e9/e9 refuses to accept ?is explanation2#aib he refuses to believe t all nature is 9 a contemptible conspiracy to delude u499 ,! ,fitzg]ald sugge/ion is fur!r unsatisfactory because x assumes all sub/ances1 ( :atev] d5sity1 to und]go ! same contraction2 & above all = ! reason t x %$s no light ^u o!r ph5om5a4#aid ,x is inde$ a v special explanation2 t is1 x applies only to ! p>ticul> exp]im5t 9 "q4 ,& inde$ x is only "o ( _m possible explanations4 ,e9/e9 conceiv$ ! notion t x might be inf9itely m valuable to take ! mo/ g5]al explanation possible1 & !n try to f9d f ?is its logical consequ5ces4 ,?is mo/ g5]al explanation is1 ( c\rse1 simply t x is impossible 9 any way :atev] to measure ! absolute motion ( a body 9 space4#bgb ,accord+ly ,e9/e9 enunciat$1 fir/ ! ,special ,!ory ( ,relativity1 & lat] ! ,g5]al ,!ory ( ,relativity4 ,! special !ory 0 s call$ because x 01 limit$ to uni=m rectil9e> & non-rot>y motions4 ,! g5]al !ory1 on ! o!r h&1 dealt n only ) uni=m rectil9e> motions1 b ) any arbitr>y motion :atev]4 ,,tak+ ,,! ,,bull ,,by ,,! ,,horns ,! hypo!sis ( relativity ass]ts t !re c be no su* concept z absolute position1 absolute motion1 absolute "t2 t space & "t are int]-dep5d5t1 n indep5d5t2 t ev]y?+ is relative to some?+ else4 ,x ?us accords ) ! philosophical notion ( ! relativity ( all k4#bhc ,k is bas$1 ultimately1 ^u measurem5t2 & cle>ly all measurem5t is relative1 consi/+ m]ely 9 ! application ( a /&>d to ! magnitude measur$4 ,all metric numb]s are relative2 divid+ ! unit multiplies ! metric numb]4 ,moreov]1 if measure & measur$ *ange proportionately1 ! measur+ numb] is un*ang$4 ,%\ld space ) all its cont5ts swell 9 fix$ ratio ?r\gh\t1 no measurem5t c\ld detect ?is2 nor ev5 %\ld x pulse uni=mly ?r\gh\t4 ,fur!rmore1 7 space & space-cont5ts 9 any way sy/ematically trans=m$ 7z by reflection 9 curv$ mirrors7 po9t = po9t1 cont9u\sly1 )\t r5d+1 no measurem5t c\ld reveal ?is di/ortion2 exp]i5ce w\ld proce$ undi/urb$4#bfc ,m>k ,twa9 said t ! /reet 9 ,damascus :i* is call$ /raight1 is s call$ because :ile x is n z /raight z a ra9b[ x is /raight] ?an a corkscrew4 ,?is expresses ! basic idea ( relativity--! idea ( comp>ison4 ,all our k is relative1 n absolute4 ,?+s are big or little1 long or %ort1 light or heavy1 fa/ or sl[1 only by comp>ison4 ,an atom may be z l>ge1 comp>$ to an electron1 z is a ca!dral comp>$ to a fly4 ,! relativity !ory ( ,e9/e9 emphasizes two cases ( relative k2 our k ( "t & space1 & our k ( motion4#baf ,& 9 ea* case1 in/ead ( all[+ ! notions ( relativity to guide u only s f> z x pleases u to foll[ !m1 !re ab&on+ !m = ideas m 9 accord ) :at we f9d x easy to take = grant$1 ,e9/e9 builds 8 /ructure on ! !sis t relativity mu/ be admitt$1 mu/ be foll[$ out to ! bitt] end1 9 spite ( any?+ t x may d to our preconceiv$ notions4 ,if relativity is to be admitt$ at all1 x mu/ be admitt$ 9 toto2 no matt] :at else x contradicts1 we h no appeal f its conclusions s long z x refra9s f contradict+ itself499 ,! hypo!sis ( relativity 0 develop$ by ,e9/e9 ?r\gh a priori me?ods1 n ! m usual a po/]iori ones4 ,t is1 c]ta9 pr9ciples 7 enunciat$ z probably true1 ! consequ5ces ( ^! 7 develop$1 & ^! d$uctions te/$ by comp>ison ( ! pr$ict$ & ! obs]v$ ph5om5a4 ,x 0 9 no s5se atta9$ by ! m usual proc$ure ( obs]v+ gr\ps ( ph5om5a & =mulat+ a law or =mula :i* w\ld embrace !m & correctly describe ! r\t9e or sequ5ce ( ph5om5a4 ,! fir/ pr9ciple ?us enunciat$ is t x is impossible to measure or detect absolute translatory motion ?r\gh space1 "u any circum/ances or by any means4 ,! second is t ! velocity ( light 9 free space appe>s ! same to all obs]v]s reg>dless ( ! relative motion ( ! s\rce ( light & ! obs]v]4 ,?is velocity is n affect$ by motion ( ! s\rce t[>d or away f ! obs]v]1#bhc if we may = ! mom5t use ?is expression ) its implication ( absolute motion499 ,b univ]sal relativity insi/s t motion ( ! s\rce t[>d ! obs]v] is id5tical ) motion ( ! obs]v] t[>d ! s\rce4#bhc ,x w be se5 t we are at once on ! horns ( a dilemma4 ,ei!r we mu/ give up relativity be=e we get fairly />t$ on x1 or we mu/ ov]turn ! f\ndations ( common s5se by admitt+ t "t & space are s con/itut$ t :5 we g to meet an advanc+ light-impulse1 or :5 we retreat f x1 x /ill rea*es u ) ! same velocity z ?\gh we /ood /ill wait+ = x4 ,we %all f9d :5 we are ?r\gh ) our inve/igation t common s5se is at fault2 t our fix$ impression ( ! absurdity ( ! /ate ( affairs j outl9$ spr+s f a confusion betwe5 relativism & absolutism :i* has h]et(ore dom9at$ our ?\ght & gone unque/ion$4 ,! impression ( absurdity w vani% :5 we h resolv$ ?is confusion499 ,,que/ions ,,( ,,common ,,s5se ,b x is obvi\s f :at has j be5 said t if we are to adopt ,e9/e9's !ory1 we mu/ make v radical *anges 9 "s ( our fundam5tal notions1 *anges t seem 9 viol5t conflict ) common s5se4 ,x is un=tunate t _m popul>iz]s ( relativity h be5 m conc]n$ to a/oni% _! read]s ) incr$ible p>adoxes ?an to give an acc\nt su* z w\ld appeal to s\nd judgm5t4 ,_m ( ^! p>adoxes d n belong ess5tially to ! !ory at all4 ,!re is no?+ 9 ! latt] t an enl>g$ & enlight5$ common s5se w\ld n readily endorse4 ,b common s5se mu/ be educat$ up to ! necess>y level4#ada ,!re 0 a "t :5 x 0 believ$1 z a result ( c5turies ( exp]i5ce1 t ! _w 0 flat4 ,?is belief *eck$ up ) ! kn[n facts1 & x c\ld be us$ z ! basis = a sy/em ( sci5ce :i* w\ld acc\nt = ?+s t _h happ5$ & t 7 to happ54 ,x 0 entirely suffici5t = ! "t 9 :i* x prevail$4 ,!n "o day a man arose to po9t out t all ! kn[n facts 7 equally acc\nt$ = on ! !ory t ! e>? 0 a sph]e4 ,x 0 9 ord] = 8 contempor>ies to admit ?is1 to say t s f> z ! facts 9 h& 7 conc]n$ !y c\ld n tell :e!r ! e>? 0 flat or r\nd--t new facts w\ld h to be s\ght t w\ld contradict "o or ! o!r hypo!sis4 ,in/ead ( ?is ! _w laugh$ & insi/$ t ! e>? c\ld n be r\nd because x 0 flat2 t x c\ld n be r\nd because !n ! p w\ld fall (f ! o!r side4 ,b ! field ( exp]im5tation wid5$1 & m5 7 able to obs]ve facts t _h be5 hidd5 f !m4 ,pres5tly a man sail$ we/ & arriv$ ea/2 & x became cle> t 9 spite ( previ\sly accept$ facts to ! contr>y1 ! e>? 0 really r\nd4 ,! previ\sly accept$ facts 7 !n revis$ to fit ! newly discov]$ tru?2 & f9ally a new sy/em ( sci5ce came into be+1 :i* acc\nt$ = all ! old facts & all ! new ones4 ,at int]vals ?is sort ( ?+ has be5 repeat$4 ,a ,galileo %[s t preconceiv$ ideas ) reg>d to ! heav5s are wrong1 & mu/ be revis$ to accord ) 8 newly promulgat$ pr9ciples4 ,a ,newton does ! same = physics--& p unle>n ! fact t motion has to be support$ by cont9u$ application ( =ce1 sub/itut+ ! new idea t x actually requires =ce to /op a mov+ body4 ,a ,h>vey %[s t ! ?+s :i* h be5 kn[n = g5]ations ab\t ! human body are n s4 ,a ,lyell & a ,d>w9 =ce m5 to ?r[ ov]bo>d ! ?+s !y h always believ$ ab\t ! way 9 :i* ! e>? & its creatures came into be+4 ,e sci5ce we possess has pass$ ?r\gh "o or m ( ^! p]iods ( readju/m5t to new facts4 ,,%ift+ ,,! ,,m5tal ,,ge>s ,n[ we are apt to lose sight ( ! true significance ( ?is4 ,x is n alone our op9ions t are alt]$2 x is our fundam5tal concepts4 ,we get concepts :olly f our p]ceptions1 mak+ !m to fit ^? p]ceptions4 ,:5ev] a new vi/a is op5$ to our p]ceptions1 we f9d facts t we nev] c\ld h suspect$ f ! re/rict$ viewpo9t4 ,we mu/ !n actually alt] our concepts to make ! new facts fit 9 ) ! greate/ degree ( h>mony4 ,& we mu/ n hesitate to und]take ?is alt]ation1 ?r\gh any feel+ t fundam5tal concepts are m sacr$ & less freely to be tamp]$ ) ?an d]iv$ facts499 ,we d1 to be sure1 want fundam5tal concepts t are easy = a human m9d to conceive2 b we also want our laws ( nature to be simple4 ,if ! laws beg9 to become1 intricate1 :y n re%ape1 some:at1 ! fundam5tal concepts1 9 ord] to simplify ! sci5tific laws8 ,ultimately x is ! simplicity ( ! sci5tific sy/em z a :ole t is our pr9cipal aim4#agh ,z a fair example1 see :at ! acceptance ( ! e>?'s sph]icity did to ! idea repres5t$ by ! ^w d[n4 ,) a flat e>?1 d[n is a s+le direction1 ! same ?r\gh\t ! univ]se2 ) a r\nd e>?1 d[n becomes m]ely ! direction lead+ t[>d ! c5t] ( ! p>ticul> heav5ly body on :i* we happ5 to be locat$4 ,x is s ) e concept we h4 ,no matt] h[ intr9sic a "p ( nature & ( our be+ a c]ta9 notion may seem1 we c nev] "k t new facts w n develop :i* w %[ x to be a mi/ak5 "o4 ,today we are m]ely confront$ by a gigantic example ( ?is sort ( ?+4 ,e9/e9 tells u t :5 velocities are atta9$ :i* h j n[ come )9 ! range ( our close inve/igation1 extraord9>y ?+s happ5--?+s q irreconcilable ) our pres5t concepts ( "t & space & mass & dim5sion4 ,we are tempt$ to laugh at him1 to tell him t ! ph5om5a he sugge/s are absurd because !y contradict ^! concepts4 ,no?+ c\ld be m ra% ?an ?is4 ,:5 we consid] ! results :i* foll[ f physical velocities comp>able ) t ( light1 we mu/ confess t "h are conditions :i* h nev] be=e be5 c>efully inve/igat$4 ,we mu/ be q z well prep>$ to h ^! conditions reveal "s epo*-mak+ fact z 0 ,galileo :5 he turn$ ! fir/ telescope ^u ! skies4 ,& if ?is fact requires t we disc>d pres5t ideas ( "t & space & mass & dim5sion1 we mu/ be prep>$ to d s q z ?or\ghly z our m$ieval fa!rs _h to disc>d _! notions ( cele/ial p]fection :i* dem&$ t !re be b sev5 major heav5ly bodies & t ev]y?+ c5t] ab\t ! e>? z a common univ]sal hub4 ,we mu/ be prep>$ to revise our concepts ( ^! or any o!r fundam5tals q z sev]ely z did ! fir/ philosoph] :o realiz$ t d[n 9 ,london 0 n p>allel to d[n 9 ,bagdad or on ,m>s499 ,9 all ord9>y t]re/rial matt]s we take ! e>? z a fix$ body1 light z in/antane\s4 ,?is is p]fectly prop]1 = su* matt]s4 ,b we c>ry our e>?-acquir$ habits ) u into ! cele/ial regions4 ,?\gh we h no long] ! e>? to /& on1 yet we assume1 z on ! e>?1 t all measurem5ts & movem5ts mu/ be ref]r$ to "s fix$ body1 & are only !n valid4 ,we cl+ to our e>?-b\nd notion t !re is an absolute up-&-d[n1 back-&-=?1 "r-&-left1 9 space4 ,we may admit t we c nev] f9d x1 b we /ill ?9k x is !re1 & seek to approa* x z ne>ly z possible4 ,& simil>ly f our e>? exp]i5ces1 :i* are suffici5tly 9 a s+le place to make possible ?is simplify+ assumption1 we get ! idea t !re is "o univ]sal "t1 applicable at once to ! entire univ]se4#ada ,! difficulty 9 accept+ ,e9/e9 is entirely ! difficulty 9 gett+ away f ^! e>?-b\nd habits ( ?\ght499 ,,iv ,,! ,,special ,,!ory ,,( ,,relativity ,:at ,e9/e9's ,/udy ( ,uni=m ,motion ,tells ,u ,ab\t ,"t & ,space & ! ,nature ( ! ,ext]nal ,reality ,,by ,,v>i\s ,,contributors ,,& ,,! ,,editor ,:atev] ! explanation adopt$ = ! negative result ( ! ,mi*elson-,morley exp]im5t1 "o ?+ /&s out cle>ly3 ! attempt to isolate absolute motion has aga9 fail$499 ,e9/e9 g5]alizes ?is ) all ! o!r & old] negative results ( simil> sort into a negative d$uction to ! effect t no exp]im5t is possible ^u two sy/ems :i* w det]m9e t "o ( !m is 9 motion & ! o!r at re/4#aba ,he elevates ! repeat$ failure to detect absolute motion ?r\gh space into ! pr9ciple t exp]im5t w nev] reveal any?+ 9 ! nature ( absolute velocities4 ,he po/ulates t all laws ( nature c & %\ld be enunciat$ 9 su* =ms t !y are z true 9 ^! =ms = "o obs]v] z = ano!r1 ev5 ?\gh ^! obs]v]s ) _! frames ( ref]5ce be 9 motion relative to "o ano!r4#bfd ,!re are v>i\s ways ( /at+ ! pr9ciple ( ! relativity ( uni=m motion :i* has be5 ?us arriv$ at1 & :i* =ms ! basis ( ! ,special ,!ory ( ,e9/e94 ,if we c>e to emphasize ! rle ( ma!matics & ! ref]5ce frame we may say t99 any coord9ate sy/em hav+ a uni=m rectil9e> motion ) respect to ! bodies "u obs]vation may be int]*angeably us$ ) any o!r su* sy/em 9 describ+ _! motions2#bcb or t ! unaccel]at$ motion ( a sy/em ( ref]5ce _c be detect$ by obs]vations made on ?is sy/em alone4#aid ,or we c let ?is aspect ( ! matt] g1 & /ate ! relativity po/ulate 9 a =m m intelligible to ! non-ma!matician by simply insi/+ t x is impossible by any means :atev] to di/+ui% any o!r ?an ! relative motion betwe5 two sy/ems t are mov+ uni=mly4 ,z ,dr4 ,russell puts x on a lat] page1 we c assume boldly t ! univ]se is s con/itut$ t uni=m /raight-ahead motion ( an obs]v] & all 8 app>atus w n produce any diff]5ce :atev] 9 ! result ( any physical process or exp]im5t ( any k9d4 ,z we h se51 ?is is entirely reasonable1 on philosophical gr\nds1 until we come to consid] ! assumptions ( ! pa/ c5tury ) reg>d to light & its propagation4 ,on ! basis ( ^! assumptions we _h expect$ ! ,mi*elson-,morley exp]im5t to produce a result negativ+ ! notion ( univ]sal relativity4 ,x refus$ to d ?is1 & we agree ) ,e9/e9 t ! be/ explanation is to return to ! notion ( relativity1 r ?an to inv5t a =c$ & special hypo!sis to acc\nt = ! exp]im5t's failure4 ,b we mu/ n[ inve/igate ! assumptions und]ly+ ! !ory ( light1 & remove ! "o t requires ! e!r to s]ve z a univ]sal /&>d ( absolute motion4 ,,light ,,& ,,! ,,e!r ,x is among ! possibilities t ! wave !ory ( light itself w 9 ! end be m or less s]i\sly modifi$4 ,x is ev5 m def9itely among ! possibilities t ! e!r w be disc>d$499 ,c]ta9ly :5 ,"l ,kelv9 e/imates t its mass p] cubic c5timet] is 4#jjj1jjj1jjj1jjj1jjj1jja gram1 :ile ,sir ,oliv] ,lodge insi/s t ! correct figure is #a1jjj1jjj1jjj1jjj1jjj grams1 x is q evid5t t we "k s little ab\t x t x is bett] to get along )\t x if we c4#baf ,b to avoid confusion we mu/ emphasize t ,e9/e9 makes no m5tion :atsoev] ( ! e!r2 8 !ory is absolutely indep5d5t ( any !ory ( ! e!r4#aci ,save z he =bids u to employ ! e!r z a /&>d ( absolute motion1 ,e9/e9 does n 9 ! lea/ c>e :at qualities we assign to x1 or :e!r we reta9 x at all4 ,8 dem&s are go+ to be made ^u light itself1 n ^u ! alleg$ m$ium ( light transmission4 ,:5 two obs]v]s 9 relative motion to "o ano!r measure _! velocities ) respect to a ?ird mat]ial object1 !y expect to get diff]5t results4 ,_! velocities ) reg>d to ?is object prop]ly diff]1 = x is no m to be tak5 z a univ]sal sup]-obs]v] ?an ei!r ( !m4 ,b if !y get diff]5t results :5 !y come to measure ! velocity ) :i* light passes _! respective sy/ems1 relativity is *all5g$4 ,light is ) "s propriety to be reg>d$ z a univ]sal obs]v]2 & if x w measure our velocities aga9/ ea* o!r we _c d5y x rank z an absolute /&>d4 ,if we are n prep>$ to ab&on univ]sal relativity1 & adopt "o ( ! fluke explanations = ! ,mi*elson-,morley result1 we mu/ boldly po/ulate t 9 free space light pres5ts ! same velocity ,c to all obs]v]s--:atev] ! s\rce ( ! light1 :atev] ! relative motion betwe5 s\rce & obs]v]1 :atev] ! relative motion betwe5 ! sev]al obs]v]s4 ,! dep>ture "h f ! old assumption lies 9 ! circum/ance t ! old physics ) its e!r assign$ to light a velocity univ]sally con/ant 9 ?is e!r2 we h /opp$ talk+ ab\t ! m$ium & h made ! con/ant ,c ref] to ! obs]v]'s measur$ value ( ! velocity ( light ) reg>d to himself4 ,we are =tifi$ 9 ?is assumption by ! ,mi*elson-,morley result & by all o!r obs]vations be>+ directly ^u ! matt]4 ,nev]!less1 z ,mr4 ,francis says 9 8 essay1 we feel in/9ctively t space & "t are n s con/itut$ z to make x possible1 if ,i pass y at #ajj miles p] h\r1 = ! same light-impulse to pass u bo? at ! same spe$ ,c499 ,! implicit assumptions und]ly+ ?is feel+1 be !y true or false1 are n[ s int]wov5 ) ! commonly receiv$ notions ( space & "t t any !ory :i* que/ions !m has all ! appe>ance ( a fanta/ic & un?9kable ?+4#aae ,we _c1 h[ev]1 g back on our relativity2 s :599 ,e9/e9 %[s u t an entirely new set ( "t & space concepts is necess>y to reconcile univ]se relativity ) ?is fundam5tal fact ( ! absolute con/ancy ( ! obs]v$ velocity ( light 9 vacuo1#ah all t is left = u to d is to inquire :at revisions are necess>y1 & submit to !m499 ,! conceptual difficulties ( ! !ory arise pr9cipally f attribut+ to space & "t ! prop]ties ( ?+s4 ,no portion ( space c be comp>$ ) ano!r1 save by conv5tion2 x is ?+s :i* we comp>e4 ,no int]val ( "t c be comp>$ ) ano!r1 save by conv5tion4 ,! fir/ has gone :5 ! second becomes n[4#adi ,x is ev5ts t we comp>e1 ?r\gh ! int]v5tion ( ?+s4 ,our measurem5ts are nev] ( space or ( "t1 b only ( ! ?+s & ! ev5ts t occupy space & "t4 ,& s9ce ! measurem5ts :i* we deal ) z ?\gh !y 7 ( space & ( "t lie at ! f\ndation ( all physical sci5ce1 :ile at ! same "t !mselves con/itut+1 z we h se51 ! only reality ( :i* we are entitl$ to speak1 x is 9 ord] to exam9e ) ! utmo/ c>e ! assumptions und]ly+ !m4 ,t !re are su* assumptions is cle>--! v possibility ( mak+ measurem5ts is itself an assumption1 & e te*nique = c>ry+ !m out re/s on an assumption4 ,let u inquire :i* ( ^! x is t relativity asks u to revise499 ,,! ,,measurem5t ,,( ,,"t ,,& ,,space ,"t is g5]ally conceiv$ z p]fectly uni=m4 ,h[ d we judge ab\t x8 ,:at tells u t ! second j elaps$ is equal to ! "o foll[+8 ,by ! v nature ( "t ! sup]position ( its successive int]vals is impossible4 ,h[ !n c we talk ab\t ! relative duration ( ^! int]vals8 ,x is cle> t any relation%ip betwe5 !m c only be conv5tional4#agh ,z a matt] ( fact1 we habitually measure "t 9 t]ms ( mov+ bodies4 ,! simple/ me?od is to agree t "s entity moves ) uni=m velocity4 ,x w be consid]$ z travell+ equal di/ances 9 equal int]vals ( "t1 ! di/ances to be measur$ z may be specifi$ by our assumptions gov]n+ ?is dep>tm5t ( inve/igation4#agi ,! motions ( ! e>? ?r\gh :i* we ultimately def9e ! l5g? ( day & ye>1 ! division ( ! =m] into #hf1djj equal int]vals z def9$ by ! motions ( p5dulum or balance :eel ?r\gh equal di/ances1 are examples ( ?is conv5tion ( "t measurem5t4 ,ev5 :5 we correct ! motions ( ! e>?1 on ! basis ( :at our clocks tell u ( ^! motions1 we are foll[+ ?is lead2 ! e>? & ! clocks fall out1 x is pla9 t "o ( !m does n satisfy our assumption ( equal l5g?s 9 equal times1 & we decide to believe ! clock499 ,! =ego+ conc]n+ "t may be accept$ z inh]5t 9 "t itself4 ,b conc]n+ l5g?s x may be ?\ght t we are able to v]ify absolutely _! equality & especially _! inv>iability4 ,let u h ! audacity to v]ify ?is /atem5t4 ,we h two l5g?s1 9 ! %ape ( two rods1 :i* co9cide p]fectly :5 br\ght toge!r4 ,:at may we conclude f ?is co9cid5ce8 ,only t ! two rods s consid]$ h equal l5g?s at ! same place 9 space & at ! same mom5t4 ,x may v well be t ea* rod has a diff]5t l5g? at diff]5t locations 9 space & at diff]5t times2 t _! equality is purely a local matt]4 ,su* *anges c\ld nev] be detect$ if !y affect$ all objects 9 ! univ]se4 ,we _c ev5 asc]ta9 t bo? rods rema9 /raight :5 we transport !m to ano!r location1 = bo? c v well take ! same curvature & we %all h no means ( detect+ x4 ,euclidean geometry assumes t geometrical objects h sizes & %apes indep5d5t ( position & ( ori5tation 9 space1 & equally inv>iable 9 "t4 ,b ! prop]ties ?us presuppos$ are only conv5tional & 9 no way subject to direct v]ification4 ,we _c ev5 asc]ta9 space to be indep5d5t ( "t1 because :5 comp>+ geometrical objects we h to conceive !m z br\ght to ! same place 9 space & 9 "t4#agh ,ev5 ! /atem5t t :5 !y are made to co9cide _! l5g?s are equal is1 aft] all1 itself an assumption inh]5t 9 our ideas ( :at con/itutes l5g?4 ,& c]ta9ly ! notion t we c %ift !m f place to place & f mom5t to mom5t1 = purposes ( comp>ison1 is an assumption2 ev5 ,euclid1 loose z he 0 f mod]n /&>ds 9 ?is bus9ess ( axioms1 knew ?is & includ$ a sup]position axiom among 8 assumptions4 ,z a matt] ( fact1 ?is proc$ure = det]m9+ equality ( l5g?s is n always available4 ,x assumes1 x w be not$1 t we h free access to ! object :i* is to be measur$--:i* is to say1 x assumes t ?is object is at re/ ) respect to u4 ,if x is n s at re/1 we mu/ employ at lea/ a modification ( ?is me?od2 a modification t w 9 "s mann] involve ! s5d+ ( signals4 ,ev5 :5 we employ ! ,euclidean me?od ( sup]position directly1 we mu/ be assur$ t ! respective ends ( ! l5g?s "u comp>ison co9cide at ! same "t4 ,! obs]v] _c be pres5t at bo? ends simultane\sly2 at be/ he c only be pres5t at "o end & receive a signal f ! o!r end4 ,,! ,,problem ,,( ,,communication ,accord+ly1 9 mak+ ! necess>y assumptions to cov] ! matt] ( measur+ l5g?s1 we mu/ make "o ) reg>d to ! "* ( ! signals :i* are to be employ$ = ?is purpose4 ,if we c\ld assume a sy/em ( signall+ t w\ld consume no "t 9 transmission all w\ld be simple en\gh4 ,b we h no exp]i5ce ) su* a sy/em4 ,ev5 if we believe t x ought to be possible ?us to transmit signals at inf9ite velocity1 we may n1 9 ! abs5ce ( our pres5t ability to d ?is1 assume t x is possible4 ,s we may only assume1 ) ,e9/e91 t = our signals we %all employ ! spe$ie/ mess5g] ) :i* we are at pres5t acqua9t$4 ,?is ( c\rse is light1 ! t]m includ+ any ( ! electromagnetic impulses t travel at ! spe$ ,c4 ,( c\rse 9 ! va/ majority ( cases ! di/ance t any light signal 9 :i* we are int]e/$ mu/ g to rea* u is s small t ! "t tak5 by its transmission c by no means be measur$4 ,we are !n1 to all int5ts & purposes1 at bo? places--! po9t ( orig9 ( ! signal & ! po9t ( receipt--simultane\sly4 ,b ?is is n ! "q at all4 ,waiv+ ! fact t 9 a/ronomical inve/igations ?is approximation no long] holds1 ! fact rema9s t x is1 9 e case1 m]ely an approximation4 ,approximations are all "r 9 obs]vations1 :]e we "k t !y are approximations & act accord+ly4 ,b 9 ! conceptual univ]se t p>allels ! ext]nal reality1 computation is z good an ag5t ( obs]vation z visual or auditory or tactile s5sation2 if we c compute ! error involv$ 9 a wrong proc$ure ! error is !re1 reg>dless ( :e!r we c see x or n4 ,we mu/ h me?ods :i* are conceptually free f error2 & if we attempt to ignore ! velocity ( our light signals we d n meet ?is condition4 ,! measurem5t ( l5g?s dem&s t we h a crit]ion ( simultaneity betwe5 two remote po9ts--remote 9 in*es or remote 9 light-ye>s1 x does n matt] :i*4 ,!re is no difficulty 9 def9+ simultaneity ( two ev5ts t fall 9 ! same po9t--or r1 9 agree+ t we "k :at we mean by su* simultaneity4 ,b ) reg>d to two ev5ts t occur 9 remote places !re may be a "q4 ,a sci5tific def9ition diff]s f a m]e description 9 t x mu/ af=d u a means ( te/+ :e!r a giv5 item comes "u ! def9ition or n4 ,!re is "s difficulty 9 sett+ up a def9ition ( simultaneity betwe5 di/ant ev5ts t satisfies ?is requirem5t4 ,if we try simply to fall back ^u our inh]5t ideas ( :at we mean by ! same in/ant we see t ?is is n adequate4 ,we mu/ lay d[n a proc$ure = det]m9+ :e!r two ev5ts at remote po9ts occur at ! same in/ant1 & *eck up alleg$ simultaneity by means ( ?is proc$ure4 ,e9/e9 says1 & we mu/ agree ) him1 t he c f9d b "o reasonable def9ition to cov] ?is gr\nd4 ,an obs]v] c tell :e!r he is locat$ half way betwe5 two po9ts ( 8 obs]vation2 he c h mirrors set up at ^! po9ts1 s5d out light-signals1 & note ! "t at :i* he gets back ! reflection4 ,he kn[s t ! velocity ( bo? signals1 go+ & com+1 is ! same2 if he obs]ves t !y return to him toge!r s t _! "t ( transit = ! r\nd trip is ! same1 he mu/ accept ! di/ances z equal4 ,he is !n at ! mid-po9t ( ! l9e jo9+ ! two po9ts "u obs]vation2 & he may def9e simultaneity z foll[s1 )\t introduc+ any?+ new or indet]m9ate3 ,two ev5ts are simultane\s if an obs]v] midway betwe5 !m sees !m at ! same in/ant1 by means1 ( c\rse1 ( light orig9at+ at ! po9ts ( occurr5ce499 ,x is ?is def9ition ( simultaneity1 c\pl$ ) ! assumption t all obs]v]s1 on :atev] uni=mly mov+ sy/ems1 w\ld obta9 ! same exp]im5tal value = ! velocity ( light1 t leads to ! app>5t p>adoxes ( ! ,special ,!ory ( ,relativity4 ,if x be ask$ :y we adopt x1 we mu/ 9 turn ask ! inquir] to propose a bett] sy/em = def9+ simultane\s ev5ts on diff]5t mov+ bodies4#aih ,!re is no?+ 9 ?is def9ition to indicate1 directly1 :e!r simultaneity p]si/s = all obs]v]s1 or :e!r x is relative1 s t ev5ts simultane\s to "o obs]v] are n s to ano!r4 ,! "q mu/ !n be inve/igat$2 & ! answ]1 ( c\rse1 w h+e ^u ! possibility ( mak+ prop] all[ances = ! "t ( transit ( ! light signals t may be involv$4 ,x seems z ?\gh ?is ought to be possible2 b a simple exp]im5t w indicate t x is n1 unless ! obs]v]s involv$ are at re/ ) respect to "o ano!r4 ,,an ,,e9/e9ian ,,exp]im5t ,let u imag9e an indef9itely long1 /raight railroad track1 ) an obs]v] locat$ some:]e along x at ! po9t ,m4 ,accord+ to ! conv5tion sugge/$ above1 he has det]m9$ po9ts ,a & ,b 9 opposite directions f him along ! track1 & equally di/ant f him4 ,we %all imag9e1 fur!r1 ?an a b5efic5t ,provid5ce supplies two lightn+ fla%es1 "o /rik+ at ,a & "o at ,b1 9 su* a way t obs]v] ,m f9ds !m to be simultane\s4 ,:ile all ?is is go+ on1 a tra9 is pass+--a v long tra91 amply long en\gh to ov]lap ! section ,,amb ( ! track4 ,among ! pass5g]s !re is "o1 :om we may call ,m'1 :o is directly opposite ,m at ! in/ant :51 accord+ to ,m1 ! lightn+ /rikes4 ,obs]ve he is n opposite ,m :5 ,m sees ! fla%es1 b a brief "t e>li]--at ! in/ant :51 accord+ to ,m's computation1 ! simultane\s fla%es occurr$4 ,at ?is in/ant !re are def9itely det]m9$ ! po9ts ,a' & ,b'1 on ! tra92 & s9ce we may q well ?9k ( ! two sy/ems--tra9-sy/em & track-sy/em--z 9 co9cid5ce at ?is in/ant1 ,m' is midway betwe5 ,a' & ,b'1 & likewise is midway betwe5 ,a & ,b4 ,n[ if we ?9k ( ! tra9 z mov+ ov] ! track 9 ! direction ( ! arr[1 we see v easily t ,m' is runn+ away f ! light f ,a & t[>d t f ,b1 & t1 despite--or if y pref] because (--! uni=m velocity ( ^! light signals1 ! "o f ,b rea*es him1 ov] a slightly %ort] c\rse1 soon] ?an ! "o f ,a1 ov] ! slightly long] c\rse4 ,:5 ! light signals rea* ,m1 ,m' is no long] abrea/ ( him b has mov$ along a wee bit1 s t at ?is in/ant :5 ,m has ! two signals1 "o ( ^! has pass$ ,m' & ! o!r has yet to rea* him4 ,! up%ot is t ! ev5ts :i* 7 simultane\s to ,m are n s to ,m'4 ,x w probably be felt t ?is result is due to our hav+1 some:at unju/ifiably & inconsi/5tly1 localiz$ on ! tra9 ! relative motion betwe5 tra9 & track4 ,b if we ?9k ( ! track z slid+ back "u ! tra9 9 ! direction opposite to ! arr[1 & c>ry+ ) x ! po9ts ,a & ,b2 & if we rememb] t ?is 9 no way affects ,m's obs]v$ velocity ( light or ! di/ances ,,am & ,,bm z he obs]ves !m3 we c /ill accept 8 claim t ! fla%es 7 simultane\s4 ,!n we h aga9 ! same situation3 :5 ! fla%es f ,a & f ,b rea* ,m at ! same mom5t1 9 8 new position a trifle to ! left ( 8 initial position ( ! diagram1 ! fla% f ,a has n yet rea*$ ,m' 9 8 orig9al position :ile t f ,b has pass$ him4 ,reg>dless ( :at assumption we make conc]n+ ! motion betwe5 tra9-sy/em & track-sy/em1 or m elegantly reg>dless ( :at coord9ate sy/em we use to def9e t motion1 ! ev5t at ,b prec$es t at ,a 9 ! obs]vation ( ,m'4 ,if we introduce a second tra9 mov+ on ! o!r track 9 ! opposite direction1 ! obs]v] on x w ( c\rse f9d t ! fla% at ,a prec$es t at ,b--a disagreem5t n m]ely z to simultaneity b actually z to ! ord] ( two ev5ts6 ,if we conceive ! lightn+ z /rik+ at ! po9ts ,a' & ,b' on ! tra91 ^! po9ts travel ) ,m' in/ead ( ) ,m2 !y are fix$ to 8 coord9ate sy/em in/ead ( to ! o!r4 ,if y c>ry out ! argum5t n[1 y w f9d t :5 ! fla%es are simultane\s to ,m'1 ! "o at ,a prec$es t at ,b 9 ,m's obs]vation4 ,a l>ge numb] ( exp]im5ts m or less simil> 9 outl9e to ?is "o c be set up to demon/rate ! consequ5ces1 ) reg>d to measur$ values ( "t & space1 ( relative motion betwe5 two obs]v]s4 ,i d n believe t a multiplicity ( su* demon/rations contributes to ! intelligibility ( ! subject1 & x is = ?is reason t ,i h cut loose f imm$iate dep5d5ce ^u ! essayi/s 9 ?is "p ( ! discussion1 conc5trat+ ^u ! s+le exp]im5t to :i* ,e9/e9 himself gives ! place ( importance4 ,,:o ,,is ,,"r8 ,we may p]mit ,mr4 ,francis to rem9d u "h t nei!r ,m nor ,m' may correct 8 obs]vation to make x accord ) ! o!r fell['s4 ,! "o :o does ?is is admitt+ t ! o!r is at absolute re/ & t he is himself 9 absolute motion2 & ?is _c be4 ,!y are simply 9 disagreem5t z to ! simultaneity ( two ev5ts1 j z two obs]v]s might be 9 disagreem5t ab\t ! di/ance or ! direction ( a s+le ev5t4 ,?is c mean no?+ else ?an t1 "u ! assumptions we h made1 simultaneity is n an absolute *>act]i/ic z we _h suppos$ x to be1 b1 l di/ance & direction1 is 9 fact m]ely a relation betwe5 obs]v] & objective1 & !re=e dep5ds ^u ! p>ticul> obs]v] :o happ5s to be op]at+ & ^u ! ref]5ce frame he is us+4 ,b ?is is s]i\s4 ,my "t measurem5ts dep5d ultimately ^u my space measurem5ts2 ! latt]1 & h5ce bo?1 dep5d closely ^u my ideas ( simultaneity4 ,y\rs dep5d ^u y\r read+ ( simultaneity 9 precisely ! same way499 ,suppose ! obs]v] on ! track1 9 ! above exp]im5t1 wants to measure ! l5g? ( some?+ on ! c>1 or ! obs]v] on ! c> some?+ on ! track4 ,! obs]v]1 or 8 assi/ant1 mu/ be at bo? ends ( ! l5g? to be measur$ at ! same "t1 or get simultane\s reports 9 "s way f ^! ends2 else !y w obta9 false results4 ,x is pla91 !n1 t ) diff]5t crit]ia ( :at ! same "t is1 ! obs]v]s 9 ! two sy/ems may get diff]5t values = ! measur$ l5g?s 9 "q4#bbj ,:o is "r8 ,accord+ to ! pr9ciple ( relativity a decision on ?is "q is absolutely impossible4 ,bo? p>ties are "r f _! own po9ts ( view2 & we mu/ admit t two ev5ts 9 two diff]5t places may be simultane\s = c]ta9 obs]v]s1 & yet n simultane\s = o!r obs]v]s :o move ) respect to ! fir/ ones4 ,!re is no contradiction 9 ?is /atem5t1 al?\gh x is n 9 accordance ) common op9ion1 :i* believes simultane\sness to be some?+ absolute4 ,b ?is common op9ion lacks f\ndation4 ,x _c be prov$ by direct p]ception1 = simultaneity ( ev5ts c be p]ceiv$ directly1#bd & 9 a mann] involv+ none ( our arbitr>y assumptions199 only if !y happ5 at ! same place2 if ! ev5ts are di/ant f ea* o!r1 _! simultaneity or succession c be /at$ only ?r\gh "s me?od ( communicat+ by signals4 ,!re is no logical reason :y su* a me?od %\ld n lead to diff]5t results = obs]v]s :o move ) reg>d to "o ano!r4 ,f :at we h said1 x foll[s imm$iately t 9 ! new !ory n only ! concept ( simultane\sness b also t ( duration is reveal$ z dep5d5t on ! motion ( ! obs]v]4#bd ,demon/ration ( ?is %\ld be sup]flu\s2 x ought to be pla9 )\t argum5t t if two obs]v]s _c agree :e!r two in/ants are ! same in/ant or n1 !y _c agree on ! int]val ( "t betwe5 in/ants4 ,9 ! v example :i* we h already exam9$1 "o obs]v] says t a c]ta9 "t-int]val is z]o1 & ano!r gives x a value diff]5t f z]o4 ,! same ?+ happ5s :5ev] ! obs]v]s are 9 relative motion499 ,two physici/s :o measure ! duration ( a physical process w n obta9 ! same result if !y are 9 relative motion ) reg>d to "o ano!r4 ,!y w also f9d diff]5t results = ! l5g? ( a body4 ,an obs]v] :o wants to measure ! l5g? ( a body :i* is mov+ pa/ him mu/ 9 "o way or ano!r hold a measur+ rod p>allel to its motion & m>k ^? po9ts on 8 rod ) :i* ! ends ( ! body come into simultane\s co9cid5ce4 ,! di/ance betwe5 ! two m>ks w !n indicate ! l5g? ( ! body4 ,b if ! two m>k+s are simultane\s = "o obs]v]1 !y w n be s = ano!r "o :o moves ) a diff]5t velocity1 or :o is at re/1 ) reg>d to ! body "u obs]vation4 ,he w h to ascribe a diff]5t l5g? to x4 ,& !re w be no s5se 9 ask+ :i* ( !m is "r3 l5g? is a purely relative concept1 j z well z duration4#bd ,,! ,,relativity ,,( ,,"t ,,& ,,space ,! degree to :i* di/ance & "t become relative in/ead ( absolute quantities "u ! ,special ,!ory ( ,relativity c be /at$ v def9itely4 ,9 ! fir/ place1 we mu/ po9t out t ! relativity ( l5g?s applies ) full =ce only to l5g?s t lie p>allel to ! direction ( relative motion4 ,^? t lie exactly p]p5dicul> to t direction come out ! same = bo? obs]v]s2 ^? t lie obliquely to x %[ an effect1 dep5d+ ^u ! angle1 :i* ( c\rse becomes great] & great] z ! direction ( p>allelism is approa*$4 ,! magnitude ( ! effect is easily demon/rat$1 b ) ?is demon/ration we d n ne$ to be conc]n$ "h4 ,x turns out t if an obs]v] mov+ ) a sy/em f9ds t a c]ta9 "t int]val 9 ! sy/em is ,t seconds & t a c]ta9 l5g? 9 ! sy/em is ,l in*es1 !n an obs]v] mov+ p>allel ) ,l & ) a velocity v relative to ! sy/em w f9d = ^! ! respective values ,t div ,k & ,l times ,k1 :]e ,k sqrt#a - v#b_/;,c#b4 ,c 9 ?is expression ( c\rse repres5ts ! velocity ( light4 ,x w be not$ t ! fraction v#b_/;,c#b is ord9>ily v small2 t ! expression "u ! radical is !re=e less ?an #a b by a v slight m>g92 & t ! entire expression ,k is itself !re=e less ?an #a b by an ev5 slight] m>g94 ,?is means1 !n1 t ! obs]v] outside ! sy/em f9ds ! l5g?s 9 ! sy/em to be a wee bit %ort] & ! "t int]vals a wee bit long] ?an does ! obs]v] 9 ! sy/em4 ,ano!r way ( putt+ ! matt] is bas$1 ultimately1 ^u ! fact t 9 ord] = ! obs]v] 9 ! sy/em to get ! l>g] value = di/ance & ! small] value = "t1 8 measur+ rod mu/ g into ! di/ance "u measurem5t m times ?an t ( ! mov+ obs]v]1 :ile 8 clock mu/ beat a long] second 9 ord] t less ( !m %all be record$ 9 a giv5 int]val betwe5 two ev5ts4 ,s x is (t5 said t ! measur+ rod z obs]v$ f )\t is contract$ & ! clock runs sl[4 ,?is does n impress me z a happy /atem5t1 ei!r 9 =m or 9 cont5t499 ,! argum5t t ^! =mulae are contradict$ by human exp]i5ce c be refut$ by exam9+ a concrete in/ance4 ,if a tra9 is #a1jjj feet long at re/1 h[ long w x be :5 runn+ a mile a m9ute8#bcb ,i h quot$ ?is "q exactly z x appe>s 9 ! essay f :i* x is tak51 because x is su* a capital example ( ! objectionable way 9 :i* ?is bus9ess is cu/om>ily put4 ,= ! /atem5t t l5g?s decrease & "t-int]vals increase ) velocity is n true 9 j ?is =m4 ,! velocity1 to h mean+1 mu/ be relative to "s ext]nal sy/em2 & x is ! obs]vations f t ext]nal sy/em t are affect$4 ,s long z we conf9e ourselves to ! sy/em 9 :i* ! alleg$ modifications ( size are /at$ z hav+ tak5 place1 !re is no?+ to obs]ve t is any diff]5t f :at is usual2 !re is no way to e/abli% t we are enjoy+ a velocity1 & 9 fact )9 ! int5t ( ! relativity !ory we are n enjoy+ a velocity1 = we are mov+ ) ! objects :i* we are obs]v+4 ,x is int]-sy/emic obs]vations1 & ^! alone1 t %[ ! effect4 ,:5 we travel ) ! sy/em "u obs]vation1 we get ! same results z any o!r obs]v] on ?is sy/em2 :5 we d n s travel1 we mu/ conduct our obs]vations f our own sy/em1 9 relative motion to ! o!r1 & ref] our results to our sy/em4 ,n[ :5 no p>ticul> obs]v] is specifi$1 we mu/ ( c\rse assume an obs]v] connect$ ) ! tra91 or ) :atev] ! body m5tion$4 ,to t obs]v] x doesn't make ! slighte/ diff]5ce :at ! tra9 does2 x may /& at re/ ) respect to "s ext]nal sy/em or x may move at any velocity :atsoev]2 its l5g? rema9s always #a1jjj feet4 ,9 ord] = ?is "q to h ! significance :i* its prop\nd] means x to h1 ,i mu/ re/ate x z foll[s3 ,a tra9 is #a1jjj feet long z measur$ by an obs]v] travell+ ) x4 ,if x passes a second obs]v] at #fj miles p] h\r1 :at is its l5g? z obs]v$ by him8 ,! answ] is n[ easy499 ,accord+ to ! =mula ! l5g? ( ! mov+ tra9 z se5 f ! gr\nd w be #a1jjj times sqrt#a - 7#hh7b _/ 7#ahf1jjj times #e1bhj7b #iii4iii1iii1iii1iif feet1 a *ange entirely too small = detection by ! mo/ delicate in/rum5ts4 ,exam9ation ( ! expression ,k %[s t 9 s f> z t]re/rial movem5ts ( mat]ial objects are conc]n$ x is equal to #abcb )9 a f> small] m>g9 ?an we c ev] hope to make our obs]vations4 ,ev5 ! diamet] ( ! e>?1 z _m ( ! essayi/s po9t out1 w be %ort5$ only #b #a_/b in*es = an outside obs]v] pa/ :om x ru%es ) its orbital spe$ ( #ah4e miles p] second4 ,b slight z ! diff]5ce may be 9 ^! famili> cases1 its sci5tific importance rema9s ! same499 ,,relativity ,,& ,,reality ,a simple computation %[s t ?is effect is exactly ! am\nt sugge/$ by ,lor5tz & ,fitzg]ald to expla9 ! ,mi*elson-,morley exp]im5t4#ahh ,?is ought n to surprise u1 s9ce bo? t explanation & ! pres5t "o are got up ) ! same purpose4 ,if !y bo? a*ieve t purpose !y mu/1 num]ically1 come to ! same ?+ 9 any num]ical case4 ,x is1 h[ev]1 mo/ emphatically to be insi/$ t ! pres5t %ort5+ ( l5g?s99 no long] appe>s z a physical %ort5+ caus$ by absolute motion ?r\gh ! e!r b is simply a result ( our me?ods ( measur+ space & "t4#ahh ,:]e ,fitzg]ald & ,lor5tz _h assum$ t a body 9 motion has its dim5sions %ort5$ 9 ! direction ( its motion1#bbj ?is v =m ( /atem5t ceases to possess significance "u ! relativity assumption499 ,= if we _c tell :i* ( two bodies is mov+1 :i* "o is %ort5$8 ,! answ] is1 bo?--= ! o!r fell[4 ,= ea* frame ( ref]5ce !re is a scale ( l5g? & a scale ( "t1 & ^! scales = diff]5t frames are relat$ 9 a mann] involv+ bo? ! l5g? & ! "t4#bbj ,b we mu/ n yield to ! temptation to say t all ?is is n real2 ! conf9em5t ( a c]ta9 scale ( l5g? & ( "t to a s+le obs]vation sy/em does n 9 ! lea/ make x unreal499 ,! situation is real--z real z any o!r physical ev5t4#afe ,! ^w physical is us$ 9 two s5ses 9 ! above p>agraph4 ,x is d5i$ t ! obs]v$ v>iability 9 l5g?s indicates any physical contraction or %r9kage2 & on ! heels ( ?is x is ass]t$ t ?is obs]v$ v>iability is ( itself an actual physical ev5t4 ,x is difficult to express 9 words ! di/9ction betwe5 ! two s5ses 9 :i* ! t]m physical is employ$ 9 ^! two /atem5ts1 b ,i ?9k ?is di/9ction ought to be cle> once its exi/5ce is emphasiz$4 ,!re is no mat]ial contraction2 x is n "r to say t objects 9 motion contract or are %ort]2 !y are n %ort] to an obs]v] 9 motion ) !m4 ,! :ole ?+ is a ph5om5on ( obs]vation4 ,! def9itions :i* we are oblig$ to lay d[n & ! assumptions :i* we are oblig$ to make 9 ord]1 fir/1 t we %all be able to measure at all1 & second1 t we %all be able to escape ! inadmissible concept ( absolute motion1 are su* t c]ta9 realities :i* we _h suppos$ ought to be ! same = all obs]v]s turn out n to be ! same = obs]v]s :o are 9 relative motion ) respect to "o ano!r4 ,we h f\nd ?is out1 & we h f\nd out ! num]ical relation :i* holds betwe5 ! reality ( ! "o obs]v] & t ( ! o!r4 ,we h f\nd t ?is relation dep5ds ^u no?+ save ! relative velocity ( ! two obs]v]s4 ,z good a way ( emphasiz+ ?is z any is to po9t out t two obs]v]s :o h ! same velocity ) respect to ! sy/em "u exam9ation 7& ^: mutual relative velocity is !re=e z]o7 w always get ! same results :5 measur+ l5g?s & times on t sy/em4 ,! object does n g ?r\gh any process ( contraction2 x is simply %ort] because x is obs]v$ f a /ation ) respect to :i* x is mov+4 ,simil> rem>ks might be made ab\t ! "t effect2 b ! "t-int]val is n s easily visualiz$ z a concrete ?+ & h5ce does n (f] su* temptation = loose /atem5t4 ,! purely relative aspect ( ! matt] is fur!r br\ght out if we consid] a s+le example bo? backw>ds & =w>ds4 ,sy/ems ,s & ,s' are 9 relative motion4 ,an object 9 ,s :i* to an obs]v] 9 ,s is ,l units long1 is %ort] = an obs]v] 9 ,s'--%ort] by an am\nt indicat$ ?r\gh ! correction factor ,k4 ,n[ if we h1 9 ! fir/ in/ance1 made ! objectionable /atem5t t objects are %ort] 9 sy/em ,s' ?an !y are 9 ,s1 x w be q natural = u to inf] f ?is t objects 9 ,s mu/ be long] ?an ^? 9 ,s'2 & f ?is to ass]t t :5 ! obs]v] 9 ,s measures objects ly+ 9 ,s'1 he gets = !m great] l5g?s ?an does ! home obs]v] 9 ,s'4 ,b if we h1 9 ! fir/ in/ance1 avoid$ ! objectionable /atem5t ref]r$ to1 we %all be mu* bett] able to realize t ! :ole bus9ess is q reciprocal2 t ! ph5om5a are symmetric ) respect to ! two sy/ems1 to ! ext5t t we c int]*ange ! sy/ems 9 any ( our /atem5ts )\t modify+ ! /atem5ts 9 any o!r way4 ,objects 9 ,s appe> %ort] & times 9 ,s appe> long] to ! ext]nal mov+ obs]v] 9 ,s' ?an !y d to ! dome/ic obs]v] 9 ,s4 ,exactly 9 ! same way1 objects 9 ,s' appe> %ort] to obs]v]s 9 ! =eign sy/em ,s ?an to ! home obs]v] 9 ,s'1 :o rema9s at re/ ) respect to !m4 ,i ?9k t :5 we get ! "r angle ^u ?is situation1 x loses ! alleg$ />tl+ "* :i* has be5 impos$ ^u x by _m writ]s4 ,! app>5t size ( ! a/ronom] is an analogy 9 po9t4 ,objects on ! moon1 by virtue ( _! great di/ance1 look small] to obs]v]s on ! e>? ?an to obs]v]s on ! moon4 ,d objects on ! e>?1 on ?is acc\nt1 look l>g] to a moon obs]v] ?an !y d to u8 ,!y d n2 any sugge/ion t !y d we %\ld receive ) appropriate scorn4 ,! v>iation 9 size introduc$ by di/ance is reciprocal1 & ?is reciprocity does n 9 ! lea/ puzzle u4 ,:y1 !n1 %\ld t introduc$ by relative motion puzzle u8 ,,"t ,,& ,,space ,,9 ,a ,,s+le ,,package ,our old1 accu/om$ concepts ( "t & space1 :i* h gr[n up ?r\gh c\ntless g5]ations ( our ance/ors1 & be5 h&$ d[n to u 9 ! =m 9 :i* we are famili> ) !m1 leave no room = a condition :]e "t int]vals & space int]vals are n univ]sally fix$ & inv>iant4 ,!y leave no room = u to say t99 "o _c "k ! "t until he kn[s :]e he is1 nor :]e he is until he kn[s ! "t1#bbj nor ei!r "t or place until he kn[s some?+ ab\t velocity4 ,b 9 ?is concise =mulation ( ! diff]5ce betwe5 :at we h always believ$ & :at we h se5 to be among ! consequ5ces ( ,e9/e9's po/ulates ( ! univ]sal relativity ( uni=m motion1 we may at once locate ! assumption :i*1 und]ly+ all ! old ideas1 is ! root ( all ! tr\ble4 ,! fact is we h always suppos$ "t & space to be absolutely di/9ct & indep5d5t entities499 ,! concept ( "t has ev] be5 "o ( ! mo/ absolute ( all ! categories4 ,x is true t !re is mu* ( ! my/]i\s ab\t "t2 & philosoph]s h sp5t mu* ef=t try+ to cle> up ! my/]y--) unsatisfactory results4 ,h[ev]1 to mo/ p]sons x has seem$ possible to adopt an arbitr>y measure or unit ( duration & to say t ?is is absolute1 indep5d5t ( ! /ate ( ! body or bodies on :i* x is us$ = practical purposes4#bgb ,"t has ?us be5 reg>d$ z some?+ :i* ( itself fl[s on regul>ly & cont9u\sly1 reg>dless ( physical ev5ts conc]n+ matt]4#aej ,9 o!r words1 accord+ to ?is view1 "t is n affect$ by conditions or motions 9 space4#bgb ,we h delib]ately *os5 to ignore ! obvi\s fact t "t c nev] appe> to u1 be measur$ by u1 or h ! lea/ significance = u1 save z a measure ( some?+ t is closely ti$ up ) space & ) mat]ial space-dim5sions4 ,n m]ely h we suppos$ t "t & space are sep>at$ 9 nature z 9 our easie/ p]ceptions1 b we h suppos$ t !y are ( su* fundam5tally di/9ct "* t !y c nev] be ti$ up toge!r4 ,9 no way :atev]1 assumes ! ,euclidean & ,newtonian intellect1 may space ev] dep5d ^u "t or "t ^u space4 ,?is is ! assumption :i* we mu/ remove 9 ord] to atta9 univ]sal relativity2 & :ile x may come h>d1 x w n come s h>d z ! alt]native4 ,= ?is alt]native is no?+ o!r ?an to ab&on univ]sal relativity4 ,?is c\rse w\ld leave u ) logical contradictions & discrepancies t c\ld n be resolv$ by any revision ( fundam5tal concepts or by any clean+ out ( ! ,augean /ables ( old assumptions2 :]eas ! relativity doctr9e z built up by ,e9/e9 requires only su* a clean+ out 9 ord] to leave u ) a /rictly logical & consi/5t :ole4 ,! rle ( ,h]cules is a v difficult "o = u to play4 ,e9/e9 has play$ x = ! race at l>ge1 b ea* ( u mu/ foll[ him 9 play+ x = himself4 ,,"s ,,fur!r ,,consequ5ces ,i ne$ n trespass ^u ! subject matt] ( ^? essays :i* appe> 9 full by go+ "h into any details ) reg>d to ! mann] 9 :i* "t & space are f9ally f\nd to dep5d ^u "o ano!r & to =m ! p>ts ( a s+le univ]sal :ole4 ,b ,i may appropriately po9t out t if "t & space are f\nd to be relative1 we may surely expect "s ( ! less fundam5tal concepts t dep5d ^u !m to be relative also4 ,9 ?is expectation we are n disappo9t$4 ,= "o ?+199 mass has always be5 assum$ to be a con/ant1 indep5d5t ( any motion or en]gy :i* x might possess4 ,j z l5g?s & times dep5d ^u relative motion1 h[ev]1 x is f\nd t mass1 :i* is ! rema9+ factor 9 ! expression = en]gy due to motion1 also dep5ds ^u relative velocities4 ,! dep5d5ce is su* t if a body takes up an am\nt ( en]gy ,e ) respect to a c]ta9 sy/em1 ! body behaves1 to measurem5ts made f t sy/em1 z ?\gh its mass _h be5 increas$ by an am\nt ,e_/,c#b1 :]e ,c is z usual ! velocity ( light4#aid ,?is %\ld n />tle u4 ,! key to ! situation lies 9 ! italiciz$ words above1 :i* indicate t ! answ] to ! qu]y :e!r a body has tak5 up en]gy or n dep5ds ^u ! seat ( obs]vation4 ,if ,i take up my location on ! sy/em ,s1 & y on ! sy/em ,s'1 & if we f9d t we are 9 relative motion1 we mu/ make "s assumption ab\t ! en]gy :i* 0 necess>y1 initially1 to get u into ?is condition4 ,suppose we are on two pass+ tra9s499 ,! *ances are t ei!r ( u w assume t he is at re/ & t x is ! o!r tra9 :i* moves1 al?\gh if suffici5tly sophi/icat$ "o ( u may assume t he is mov+ & t ! o!r tra9 is at re/4#bgb ,:atev] our assumption1 :atev] ! sy/em1 ! localization ( ! en]gy t is c>ri$ 9 lat5t =m by our sy/ems dep5ds ^u ?is assumption4 ,inde$1 if our sy/ems are ( diff]+ mass1 our assumptions w ev5 gov]n our ideas ( ! am\nt ( en]gy :i* is repres5t$ by our relative motion2 if y\r sy/em be ! m massive1 m en]gy w\ld h to be localiz$ 9 x ?an 9 m9e to produce our relative motion4 ,if we did n h ! univ]sal pr9ciple ( relativity to =bid1 we might make an arbitr>y assumption ab\t our motions & h5ce ab\t our respective lat5t en]gies2 9 ! pres5ce ( ?is veto1 ! only *ance ( adju/m5t lies 9 our masses1 :i* mu/ diff] accord+ to :e!r y or ,i obs]ve !m499 ,= mo/ ( ! velocities ) :i* we are famili> ,e_/,c#b is1 l ! diff]5ce betwe5 ,k & unity1 su* an extremely small quantity t ! mo/ delicate measurem5ts fail to detect x4 ,b ! electrons 9 a highly evacuat$ tube & ! p>ticles %ot out f radioactive mat]ials atta9 9 "s cases velocities z high z eight-t5?s t ( light4 ,:5 we measure ! mass ( su* p>ticles at diff]5t velocities we f9d t x actually increases ) ! velocity1 & 9 accordance ) ! =ego+ law4#aid ,?is obs]vation1 9 fact1 ant$ates ,e9/e9's explanation1 :i* is f> m satisfactory ?an ! e>li] diff]5tiation betwe5 normal mass & electrical mass :i* 0 call$ ^u to acc\nt = ! increase499 ,b if ! quantity ,e_/,c#b is to be consid]$ z an actual increase 9 mass1 may x n be possible t all mass is en]gy8 ,?is w\ld lead to ! conclusion t ! en]gy /or$ up 9 any mass is m,c#b4 ,! value is v great1 s9ce ,c is s l>ge2 b x is 9 good agreem5t ) ! int]nal en]gy ( ! atom z calculat$ f o!r consid]ations4 ,x is obvi\s t cons]vation ( mass & ( mom5tum _c bo? hold good "u a !ory t translates ! "o into ! o!r4 ,mass is !n n consid]$ by ,e9/e9 z cons]vative 9 ! ord9>y s5se1 b x is ! total quantity ( mass plus en]gy 9 any clos$ sy/em t rema9s con/ant4 ,small am\nts ( en]gy may be trans=m$ into mass1 & vice v]sa4#aid ,o!r features ( ! !ory :i* are (t5 display$ z consequ5ces are really m 9 ! nature ( assumptions4 ,x w be recall$ t :5 we _h agre$ ^u ! necessity ( employ+ signals ( "s sort1 we select$ z ! means ( signall+ ! spe$ie/ mess5g] ) :i* we happ5$ to be acqua9t$4 ,our subsequ5t difficulties 7 l>gely due to ! impossibility ( mak+ a prop] all[ance = ?is mess5g]'s spe$1 ev5 ?\gh we knew its num]ical value2 & z a consequ5ce1 ?is spe$ ent]s into our =mulae4 ,n[ we h n said 9 s _m words t ,c is ! greate/ spe$ atta9able1 b we h tacitly assum$ t x is4 ,we ne$ n1 !re=e1 be surpris$ if our =mulae give u absurd results = spe$s high] ?an ,c1 & indicate ! impossibility ( ev] atta9+ ^!4 ,:atev] we put into a problem ! algebra is b\nd to give u back4 ,if we look at our =mula = ,k1 we see t 9 ! ev5t ( v equall+ ,c1 l5g?s become z]o & times inf9ite4 ,! light mess5g] itself1 !n1 has no dim5sion2 & = x "t /&s /ill4 ,if we suppose v to be great] ?an ,c1 we get ev5 m biz>re results1 = !n ! factor ,k is ! squ>e root ( a negative numb]1 or z ! ma!matician calls x an imag9>y quantity2 & ) x1 l5g?s & times become imag9>y too4 ,! fact t "t /ops = x1 & ! fact t x is ! limit+ velocity1 give to ,c c]ta9 ( ! attributes ( ! ma!matician's inf9ity4 ,c]ta9ly if x c nev] be exce$$1 we mu/ h a new =mula = ! composition ( velocities4 ,o!rwise :5 my sy/em passes y\rs at a spe$ ( #ajj1jjj miles p] second1 :ile y\rs passes a ?ird 9 ! same direction at ! same velocity1 ,i %all be pass+ ?is ?ird framework at ! =bidd5 velocity ( #bjj1jjj miles p] second--great] ?an ,c4 ,9 fact ,e9/e9 is able to %[ t an old =mula1 :i* _h already be5 f\nd to connect ! spe$ ( light 9 a mat]ial m$ium ) ! spe$ ( t m$ium1 w n[ s]ve univ]sally = ! composition ( velocities4 ,:5 we comb9e ! velocities v & u1 in/ead ( gett+ ! resultant vu z we w\ld h suppos$1 we get ! resultant 7v u7 _/ 7#a 7uv _/ ,c#b7711 or ,c#b7v u7 _/ 7,c#b uv7 ,?is ne$ n surprise u ei!r1 if we w b reflect t ! second velocity effects a second revision ( l5g? & "t measurem5ts betwe5 ! sy/ems involv$4 ,& n[1 if we let ei!r v1 or u1 or ev5 bo? ( !m1 take ! value ,c1 ! resultant /ill is ,c4 ,9 ano!r way we h f\nd ,c to behave l ! ma!matician's inf9ity1 to :i*1 9 ! words ( ! bl9d poet1 if we add untold ?\s&s1 we effect no real increm5t4 ,,assumption ,,& ,,consequ5ce ,a good _m correspond5ts :o h giv5 ! subject suffici5t ?\ght to realize t ! limit+ "* ( ! velocity ,c is really read into ,e9/e9's sy/em by assumption h writt51 9 m or less p]turb$ inquiry1 to "k :e!r ?is does n invalidate ! :ole /ructure4 ,! answ]1 ( c\rse1 is yes--provid$ y c %[ ?is assumption to be invalid4 ,! same answ] may be made ( any sci5tific doctr9e :atev]1 & 9 ref]5ce to any "o ( ! multitud9\s assumptions und]ly+ x4 ,if we 7 to discov]1 tomorr[1 a way ( s5d+ signals absolutely in/antane\sly1 ,e9/e9's :ole /ructure w\ld collapse z soon z we _h agre$ to use ?is new me?od4 ,if we 7 to discov] a signall+ ag5t ) f9ite velocity great] ?an t ( light1 relativity w\ld p]si/ ) ?is velocity writt5 9 its =mulae 9 ! place ( ,c4 ,x is a mi/ake to quote ,e9/e9's !ory 9 support ( ! /atem5t t su* a velocity c nev] be4 ,an assumption proves its consequ5ces1 b nev] c prove itself2 x mu/ rema9 always an assumption4 ,b 9 ! pres5ce ( long human exp]i5ce support+ ,e9/e9's assumption t no velocity 9 excess ( ,c c be f\nd1 x is fair to dem& t x be disput$ n ) argum5t b ) demon/ration4 ,! "o l9e ( argum5t t w\ld hold out a priori hope ( r$uc+ ! assumption to an absurdity w\ld be "o bas$ on ! famili> idea ( add+ velocities2 b ,e9/e9 has spik$ ?is argum5t be=e x is />t$ by replac+ ! direct addition ( velocities ) ano!r me?od ( comb9+ !m t fits 9 ) 8 assumption & z well ) ! obs]v$ facts4 ,! burd5 ( pro( is !n on ! prosecution2 anyone :o w\ld contradict our ass]tion t ,c is ! greate/ velocity atta9able may d s only by %[+ u a great] "o4 ,until ?is has be5 done1 ! admission t x may prop]ly be attempt$ c 9 no way be con/ru$ z a confession ( weakness on ! "p ( ,e9/e94 ,x may be well to po9t out t 9 no ev5t may analogy be drawn ) s\nd1 z _m h tri$ to d4 ,9 ! fir/ place s\nd requires a mat]ial m$ium & its velocity ) reg>d to ?is r ?an relative to ! obs]v] we "k to be fix$2 9 ! second place1 requir+ a mat]ial m$ium1 s\nd is n a univ]sal signall+ ag5t2 9 ! ?ird place1 we "k def9itely t its velocity c be exce$$1 & are !re=e b>r$ f mak+ ! assumption necess>y to e/abli% ! analogy4 ,! v extraord9>y behavior ( light 9 pres5t+ a velocity t is ! same = all obs]v]s1 & 9 refus+ to betray ! lea/ mat]ial evid5ce ( any m$ium = its transmission1 r =tifies u 9 believ+ t ,e9/e9's assumption reg>d+ ! ultimate "* ( ?is velocity is 9 accord ) ! nature ( ?+s4 ,,relativity ,,& ,,! ,,layman ,a great deal c be said 9 ! direction ( g5]al comm5t mak+ ! ,special ,!ory & its surpris+ accompanim5ts easi] ( acceptance1 & we %all conclude ! pres5t discussion by say+ "s ( ^! ?+s499 ,x has be5 object$ t ! v>i\s effects catalogu$ above are only app>5t1 due to ! f9ite velocity ( light--t ! real %ape & size ( a body or ! real "t ( an ev5t _c be affect$ by ! po9t ( view or ! motion ( an obs]v]4 ,?is argum5t w\ld be p]fectly valid1 if !re 7 real times & di/ances2 b !re are n4 ,^! are e>?-b\nd notions1 due to our exp]i5ce on an app>5tly motionless plat=m1 ) sl[-mov+ bodies4 ,"u ^! circum/ances diff]5t obs]vations ( ! same ?+ or ( ! same ev5t agree4 ,b :5 we no long] h ! solid e>? to /& on1 & are deal+ ) velocities s high t ! relativity effects become appreciable1 !re is no /&>d by :i* to resolve ! disagreem5ts4 ,no "o ( ! obs]vations c claim to be ne>] reality ?an any o!r4 ,to dem& ! real size ( a ?+ is to dem& a /ation>y obs]v] or an in/antane\s means ( in=mation4 ,bo? are impossible4 ,:5 relativity asks u to give up our e>?-b\nd notions ( absolute space & absolute "t ! s5sation1 at fir/1 is t we h no?+ left to /& on4 ,s mu/ ! contempor>ies ( ,columbus h felt :5 told t ! e>? re/$ on--no?+4 ,! rem$y too is simil>4 ,j z !y _h to be taught t fall+ is a local affair1 t ! e>? is self-conta9$1 & ne$s no ext]nal support--s we mu/ be taught t space & "t /&>ds are local affairs4 ,ea* mov+ body c>ries its own space & "t /&>ds ) x2 x is self-conta9$4 ,x does n ne$ to rea* out = et]nal support1 = an absolute space & "t t c nev] q be atta9$4 ,all we ev] ne$ to "k is ! relation ( ! o!r fell['s space & "t /&>ds to our own4 ,?is is ! fir/ ?+ relativity tea*es u4#ada ,! consequ5ces ( ,e9/e9's assumptions h l$ _m to reject ! !ory ( relativity1 on ! gr\nd t its conclusions are contr>y to common s5se--z !y und\bt$ly are4 ,b to ! contempor>ies ( ,cop]nicus & ,galileo ! !ory t ! e>? rotates on its axis & revolves ar\nd ! sun 0 contr>y to common s5se2 yet ?is !ory prevail$4 ,!re is no?+ sacr$ ab\t common s5se2 9 ! la/ analysis its judgm5ts are bas$ on ! accumulat$ exp]i5ce ( ! human race4 ,f ! beg9n+ ( ! _w up to ! pres5t g5]ation1 no bodies 7 kn[n ^: velocities 7 n extremely small comp>$ ) t ( light4 ,! developm5t ( mod]n physics has l$ to discov]y ( v mu* l>g] velocities1 "s z high z #afe1jjj miles p] second4 ,x is n to be wond]$ at t su* an enl>gem5t ( our exp]i5ce requires a correspond+ enl>gem5t or g5]alization ( ! concepts ( space & "t4 ,j z ! presupposition ( primitive man t ! e>? 0 flat _h to be giv5 up 9 ! light ( advanc+ k1 s we are n[ call$ ^u to give up our presupposition t space & "t are absolute & indep5d5t 9 _! nature4 ,! read] mu/ n expect to und]/& ! !ory ( relativity 9 ! s5se ( mak+ x fit 9 ) 8 previ\s ideas4 ,if ! !ory be "r ^! ideas are wrong & mu/ be modifi$1 a process apt to be pa9ful4#bbc ,all ! read] c d is to become famili> ) ! new concepts1 j z a *ild gets us$ to ! simple relations & quantities he meets until he und]/&s !m4#bba ,mr4 ,francis has said some?+ ( ! utmo/ significance :5 he po9ts out t und]/&+ really means no?+ 9 ! _w except famili>ity & accu/om$ness499 ,! "o ?+ ab\t ! relativity doctr9e t we c hope ?us to und]/& at once & )\t pa9 is ! logical process us$ 9 arriv+ at our results4#bba ,p>ticul>ly is x h>d to give a satisfactory explanation ( ! !ory 9 popul> language1 because ! language itself is bas$ on ! old concepts2 ! only language :i* is really adequate is t ( ma!matics4#bbc ,unless we h1 9 addition to ! t]ms ( our ord9>y k1 a set ( def9itions t comes ) a wide k ( ma!matics & a lively s5se ( ! reality ( ma!matical con/ructions1 we are likely to view ! !ory ( relativity ?r\gh a fog ( famili> t]ms sudd5ly become self-contradictory & deceptive4 ,n t we are unfamili> ) ! idea t "s ( our habitual notions may be wrong2 b k ( _! illusory nature arises & becomes conv9c+ only ) "t4 ,we may n[ be ready to grant t ! e>?1 seem+ly s solid1 is really a :irl+ globe ru%+ ?r\gh space2 b we are no m ready imm$iately to accept ! bald ass]tion t ?is space is n :at x seems ?an our ance/ors 7 to accept ! idea t ! e>? 0 r\nd or t x mov$4#aef ,:at we mu/ h1 if we are to compreh5d relativity ) any degree ( ?or\ghness1 is ! ma!matician's attitude t[>d 8 assumptions1 & 8 complete read9ess to swap "o set ( assumptions = ano!r z a m]e "p ( ! day's "w1 ! _s ( :i* ,i h endeavor$ to convey 9 ! *apt] on non-,euclidean geometry499 ,,physics ,,vs4 ,,metaphysics ,! ideas ( relativity may seem1 at fir/ sight1 to be giv+ u a new & metaphysical !ory ( "t & space4 ,new1 d\btless2 b c]ta9ly ! !ory 0 meant by its au?or to be q ! opposite ( metaphysical4 ,our actual p]ception ( space is by measurem5t1 real & imag9$1 ( di/ances betwe5 objects1 j z our actual p]ception ( "t is by measurem5t4 ,is x n less metaphysical to accept space & "t z our measurem5ts pres5t !m to u1 ?an to inv5t hypo!ses to =ce our p]ceptual space into an absolute space t is =ev] hidd5 f u8#ahb ,9 ord] n to be metaphysical1 we mu/ elim9ate our preconceiv$ notions ( space & "t & motion1 & focus our att5tion ^u ! indications ( our in/rum5ts ( obs]vation1 z af=d+ ! only objective manife/ations ( ^! qualities & !re=e ! only attributes :i* we c consid] z functions ( obs]v$ ph5om5a4#dg ,e9/e9 has consi/5tly foll[$ ! tea*+s ( exp]i5ce1 & completely fre$ himself f metaphysics4#aad ,t ?is is n always easy to d is cle>1 ,i ?9k1 if we w recall ! highly metaphysical "* (t5 tak5 by ! objections to action-at-a-di/ance !ories & concepts2 & if we w rem9d ourselves t x 0 on purely metaphysical gr\nds t ,newton refus$ to c\nt5ance ,huygh5s' wave !ory ( light4 ,:e!r1 z 9 ! "o case1 x leads u to valid conclusions1 or1 z 9 ! o!r1 to false ones1 metaphysical reason+ is some?+ to avoid4 ,e9/e91 ,i ?9k1 has avoid$ x ab\t z ?or\ghly z anyone ev] did499 ,v ,,t ,,p>allel ,,po/ulate ,mod]n ,geometric ,me?ods2 ! ,divid+ ,l9e ,betwe5 ,euclidean & ,non-,euclidean2 & ! ,significance ( ! ,latt] ,,by ,,! ,,editor ,! sci5ce ( geometry has und]gone a revolution ( :i* ! outsid] is n in=m$1 b :i* x is necess>y to und]/& if we are to atta9 any compreh5sion ( ! geometric =mulation ( ,e9/e9's results2 & especially if we are to appreciate :y x is prop] & desirable to =mulate ^! results geometrically at all4 ,! classical geomet] reg>d$ 8 sci5ce f a n>r[ viewpo9t1 z ! /udy ( a c]ta9 set ( obs]v$ ph5om5a--^? ( ! space ab\t u1 consid]$ z an entity 9 itself & divorc$ f ev]y?+ 9 x4 ,x is cle> t "s ?+s ab\t t space are n z !y appe> 7optical illusions71 & t o!r ?+s ab\t x are true b by no means app>5t 7! sum-(-squ>es prop]ty ( a "r triangle1 ! =mul = surface & volume ( a sph]e1 etc474 ,:ile _m ?+s ab\t space are obvi\s1 ^! ne$ 9 ! "o case dispro( & 9 ! o!r discov]y & pro(4 ,) all _! love ( m5tal processes = _! own sake1 x is !n n surpris+ t ! ,greeks %\ld h set !mselves ! task ( prov+ by logical process ! prop]ties ( space1 :i* a less ?\ghtful folk w\ld h reg>d$ z a subject only = obs]vational & exp]im5tal det]m9ation4 ,b1 ab/ract or concrete1 ! logical /ructure mu/ h a />t+ po9t2 & x is fair to dem& t ?is consi/ 9 a /atem5t ( ! t]ms we are go+ to use & ! mean+s we are go+ to atta* to !m4 ,9 o!r words1 ! fir/ ?+ on ! program w be a def9ition1 or m probably1 sev]al def9itions4 ,n[ ! mod]n sci5ti/ has a some:at iconocla/ic viewpo9t t[>d def9itions1 & especially t[>d ! def9ition ( 8 v mo/ fundam5tal ideas4 ,we d n speak "h 9 t]ms ( diction>y def9itions4 ,^! h = object ! em95t necessity ( expla9+ ! mean+ & use ( a ^w to "s "o :o has j met x = ! fir/ "t4 ,x is easy en\gh to d ?is1 if ! do] possesses a good comm& ( ! language4 ,x is n ev5 a matt] ( grave conc]n t ! words us$ 9 ! def9ition be !mselves kn[n to ! read]2 if !y are n1 he mu/ make _! acqua9tance too4 ,dr4 ,johnson's celebrat$ def9ition ( a ne$le /&s z p]petual evid5ce t :5 he _c def9e a simple ?+ 9 t]ms ( ?+s /ill simpl]1 ! lexicograph] is =c$ to def9e x 9 t]ms ( ?+s m complex4 ,or we might demon/rate ?is by not+ t ! be/ diction>ies are driv5 to def9e su* words z & & b by us+ su* complex notions z are embodi$ 9 connective1 cont9uative1 adv]sative1 & p>ticle4 ,x is o!rwise ) ! sci5ti/ :o und]takes to lay d[n a def9ition z ! basis ( fur!r proc$ure 9 build+ up ! tissue ( 8 sci5ce4 ,"h a degree ( rigor\s logic is call$ = :i* w\ld be z sup]flu\s 9 ! diction>y z ! ef=t !re to atta9 x w\ld be out ( place4 ,! sci5ti/1 9 build+ up a logical /ructure t w )/& e assault1 mu/ def9e ev]y?+1 n 9 t]ms ( some?+ :i* he is m or less w>rant$ 9 suppos+ 8 audi5ce to "k ab\t1 b actually 9 t]ms ( ?+s t h already be5 def9$4 ,?is really means t he mu/ expla9 :at he is talk+ ab\t 9 t]ms ( simpl] ideas & simpl] ?+s1 :i* is precisely :at ! lexicograph] does n h to worry ab\t4 ,?is is :y x is q trivial to quote a diction>y def9ition ( "t or space or matt] or =ce or motion 9 settlem5t ( a controv]sy ( sci5tific or semi-sci5tific nature4 ,,t]ms ,,we ,,_c ,,def9e ,b ! sci5ti/ :o attempts to c>ry out ?is ideal sy/em ( def9+ ev]y?+ 9 t]ms ( :at prec$es meets "o ob/acle :i* he _c surm\nt directly4 ,ev5 a layman c con/ruct a passable def9ition ( a complex ?+ l a p>allelopip$1 9 t]ms ( simpl] concepts l po9t1 l9e1 plane & p>allel4 ,b :o %all def9e po9t 9 t]ms ( some?+ simpl] & some?+ :i* prec$es po9t 9 ! =mulation ( geometry8 ,! sci5ti/ is emb>rass$1 n 9 h&l+ ! complicat$ lat] p>ts ( 8 "w1 b 9 ! v beg9n+1 9 deal+ ) ! simple/ concepts ) :i* he has to deal4 ,suppose a diction>y 7 to be compil$ ) ! def9itions arrang$ 9 logical r ?an alphabetical ord]3 e ^w to be def9$ by ! use only ( words t h already be5 def9$4 ,! fur!r back t[>d ! beg9n+ we pu% ?is project1 ! h>d] x gets4 ,obvi\sly we c nev] def9e ! fir/ ^w1 or ! second1 save z synonym\s ) ! fir/4 ,9 fact we %\ld ne$ a doz5 words1 m or less1 to />t )--,god-giv5 words :i* we _c def9e & %all n try to def9e1 b ( :i* we mu/ agree t we "k ! significance4 ,!n we h tools = fur!r proc$ure2 we c />t )1 say1 ! ?irte5? ^w & def9e all ! re/ ( ! words 9 ! language1 9 /rictly logical fa%ion4 ,:at we h said ab\t def9itions applies equally to /atem5ts ( fact1 ( ! sort :i* are go+ to con/itute ! body ( our sci5ce4 ,9 ! abs5ce ( simpl] facts to cite z au?ority1 we %all nev] be able to prove any?+1 h[ev] simple ?is may itself be2 & 9 fact ! simpl] x be1 ! h>d] x is to f9d some?+ simpl] to und]lie x4 ,if we are to h a logical /ructure ( any sort1 we mu/ beg9 by lay+ d[n c]ta9 t]ms :i* we %all n attempt to def9e1 & c]ta9 /atem5ts :i* we %all n try to prove4 ,ma!matics1 physics1 *emi/ry--9 ! l>ge & 9 all _! _m m9or fields--all ^! mu/ />t some:]e4 ,in/ead ( deceiv+ ourselves z to ! circum/ances surr\nd+ _! />t1 we pref] to be q frank 9 recogniz+ t !y />t :]e we decide to />t !m4 ,if we don't l "o set ( undef9$ t]ms z ! f\ndation1 by all means let u try ano!r4 ,b always we mu/ h su* a set4 ,! classical geomet] s5s$ ! difficulty ( def9+ 8 fir/ t]ms4 ,b he suppos$ t he _h met x :5 he def9$ ^! 9 words free ( te*nical significance4 ,a po9t is t :i* has position )\t size seem$ to him an adequate def9ition1 because position & size are words ( ! ord9>y language ) :i* we may all be assum$ famili>4 ,b today we feel t position & size repres5t ideas t are n necess>ily m fundam5tal ?an ^? ( l9e & po9t1 & t su* a def9ition begs ! "q4 ,we get n[h]e by replac+ ! undef9$ t]ms po9t & l9e & plane1 :i* really ev]ybody und]/&s1 by o!r undef9$ t]ms :i* nobody und]/&s any bett]4 ,9 h&l+ ! facts t x 0 inconv5i5t to prove1 ! classical geomet] came clos] to mod]n practice4 ,he laid d[n at ! beg9n+ a few /atem5ts :i* he call$ axioms1 & :i* he consid]$ to be s self-evid5t t demon/ration 0 sup]flu\s4 ,t ! t]m self-evid5t left room = a va/ am\nt ( ambiguity appe>s to h escap$ him altoge!r4 ,8 axioms 7 axioms solely because !y 7 obvi\sly true4 ,,lay+ ,,! ,,f\ndation ,! mod]n geomet] falls 9 ) ,euclid :5 he writes an elem5t>y text1 satisfy+ ! beg9n]'s dem& = app>5t rigor by def9+ po9t & l9e 9 "s fa%ion4 ,b :5 he addresses to 8 pe]s an ef=t to cl>ify ! f\ndations ( geometry to a fur!r degree ( rigor & lucidity ?an has ev] be=e be5 atta9$1 he meets ^! difficulties f ano!r qu>t]4 ,9 ! fir/ place he is always 9 se>* ( ! utmo/ possible g5]ality1 = he has f\nd ?is to be 8 mo/ effective tool1 enabl+ him z x does to make a s+le g5]al /atem5t take ! place & d ! "w ( _m p>ticul> /atem5ts4 ,! classical geomet] atta9$ g5]ality ( a sort1 = all 8 /atem5ts 7 ( any po9t or l9e or plane4 ,b ! mod]n geomet]1 confront$ ) a relation t holds among po9ts or betwe5 po9ts & l9es1 at once goes to speculat+ :e!r !re are n o!r elem5ts among or betwe5 :i* x holds4 ,! classical geomet] isn't int]e/$ 9 ?is "q at all1 because he is seek+ ! absolute tru? ab\t ! po9ts & l9es & planes :i* he sees z ! elem5ts ( space2 to him x is actually an object s to circumscribe 8 /atem5ts t !y may by no possibility ref] to any?+ o!r ?an ^! elem5ts4 ,:]eas ! mod]n geomet] feels t 8 prim>y conc]n is ) ! fabric ( logical propositions t he is build+ up1 & n at all ) ! elem5ts ab\t :i* ^? propositions revolve4 ,x is ( obvi\s value if ! ma!matician c lay d[n a proposition true ( po9ts1 l9es & planes4 ,b he w\ld mu* r lay d[n a proposition true at once ( ^! & ( num]\s o!r ?+s2 = su* a proposition w gr\p m ph5om5a "u a s+le pr9ciple4 ,he feels t on pure sci5tific gr\nds !re is q z mu* int]e/ 9 any "o set ( elem5ts to :i* 8 proposition applies z !re is 9 any o!r2 t if any p]son is to conf9e 8 att5tion to ! set t /&s = ! physici/'s space1 t p]son ought to be ! physici/1 n ! geomet]4 ,if he has produc$ a tool :i* ! physici/ c use1 ! physici/ is welcome to use x2 b ! geomet] _c und]/& :y1 on t gr\nd1 he %\ld be ask$ to conf9e 8 att5tion to ! mat]ials on :i* ! physici/ employs t tool4 ,x w be alleg$ t po9ts & l9es & planes lie 9 ! ma!matician's doma91 & t ! o!r ?+s to :i* 8 propositions may apply may n s lie--& especially t if he w n "n !m 9 advance he _c expect t !y w s lie4 ,b ! ma!matician w n admit ?is4 ,if ma!matics is def9$ on n>r[ gr\nds z ! sci5ce ( numb]1 ev5 ! po9t & l9e & plane may be exclud$ f its field4 ,if any wid] def9ition be s\ght--& ( c\rse "o mu/ be--!re is j "o def9ition t ! ma!matician w accept3 ,dr4 ,keys]'s /atem5t t ma!matics is ! art or sci5ce ( rigor\s ?9k+4 ,! imm$iate conc]n ( ?is sci5ce is ! means ( rigor\s ?9k+--undef9$ t]ms & def9itions1 axioms & propositions4 ,its collat]al conc]n is ! ?+s to :i* ^! may apply1 ! ?+s :i* may be ?\ght ab\t rigor\sly--ev]y?+4 ,b n[ ! ma!matician's doma9 is s va/ly ext5d$ t x becomes m ?an ev] important = him to atta9 ! utmo/ g5]ality 9 all 8 pron\ncem5ts4 ,"o b>ri] to su* g5]alization is ! v "n geometry1 ) ! re/rict$ significance :i* its d]ivation & long usage c>ry4 ,! geomet] !re=e mu/ h x di/9ctly und]/ood t = him geometry means simply ! process ( d$uc+ a set ( propositions f a set ( undef9$ primitive t]ms & axioms2 & t :5 he speaks ( a geometry he means "s p>ticul> set ( propositions s d$uc$1 toge!r ) ! axioms1 etc41 on :i* !y are bas$4 ,if y take a new set ( axioms y get a new geometry4 ,! geomet] w1 if y insi/1 g on call+ 8 undef9$ t]ms by ! famili> names po9t1 l9e1 plane4 ,b y mu/ di/9ctly und]/& t ?is is a concession to usage1 & t y are n = a mom5t to re/rict ! application ( 8 /atem5ts 9 any way4 ,he w\ld mu* pref]1 h[ev]1 to be all[$ new names = 8 elem5ts1 to say ,we />t ) ?ree elem5ts ( diff]5t sorts1 :i* we assume to exi/1 & to :i* we atta* ! names ,a1 ,b & ,c--or if y pref]1 prim>y1 second>y & t]ti>y elem5ts--or yet aga91 names possess+ no intr9sic significance at all1 su* z *+1 *ang & *ung4 ,he w !n lay d[n :atev] /atem5ts he requires to s]ve ! purposes ( ! anci5t axioms1 all ( ^! ref]r+ to "s "o or m ( 8 elem5ts4 ,!n he is ready = ! s]i\s bus9ess ( prov+ t1 all 8 hypo!ses be+ grant$1 8 elem5ts ,a1 ,b & ,c1 or ,i1 ,,ii & ,,iii1 or *+1 *ang & *ung1 are subject to ?is & t & ! o!r propositions4 ,! objection w be urg$ t ! ma!matician :o does all ?is usurps ! place ( ! logician4 ,a little reflection w %[ ?is n to be ! case4 ,! logician 9 fact occupies ! same position ) ref]5ce to ! geomet] t ! geomet] occupies ) ref]5ce to ! physici/1 ! *emi/1 ! ari?metician1 ! eng9e]1 or anybody else ^: prim>y int]e/ lies ) "s p>ticul> set ( elem5ts to :i* ! geomet]'s sy/em applies4 ,! ma!matician is ! tool-mak] ( all sci5ce1 b he does n make 8 own tools--^! ! logician supplies4 ,! logician 9 turn nev] desc5ds to ! actual practice ( rigor\s ?9k+1 save z he mu/ necess>ily d ?is 9 lay+ d[n ! g5]al proc$ures :i* gov]n rigor\s ?9k+4 ,he is int]e/$ 9 processes1 n 9 _! application4 ,he tells u t if a proposition is true its conv]se may be true or false or ambigu\s1 b its contrapositive is always true1 :ile its negative is always false4 ,b he nev]1 f a p>ticul> proposition ,if ,a is ,b !n ,c is ,d1 draws ! p>ticul> contrapositive inf]5ce ,if ,c is n ,d !n ,a is n ,b4 ,t is ! ma!matician's bus9ess4 ,,! ,r,,le ,,( ,,geometry ,! ma!matician is ! quantity-production man ( sci5ce4 ,9 8 abs5ce1 ! work] 9 ea* n>r[] field :]e ! elem5ts "u discussion take p>ticul> concrete =ms c\ld "w out1 = himself1 ! propositions ( ! logical /ructure t applies to ^? elem5ts4 ,b x w\ld !n be f\nd t ! eng9e] _h duplicat$ ! "w ( ! physici/1 & s = _m o!r cases2 = ! :ole tr5d ( mod]n sci5ce is t[>d %[+ t ! same backgr\nd ( pr9ciples lies at ! root ( all ?+s4 ,s ! ma!matician develops ! fabric ( propositions t foll[s f ?is1 t & ! o!r gr\p ( assumptions1 & does ?is )\t 9 ! lea/ conc]n+ himself z to ! nature ( ! elem5ts ( :i* ^! propositions may be true4 ,he kn[s only t !y are true = any elem5ts ( :i* 8 assumptions are true1 & t is all he ne$s to "k4 ,:5ev] ! work] 9 "s p>ticul> field f9ds t a c]ta9 gr\p ( ! geomet]'s assumptions is true = 8 elem5ts1 ! geometry ( ^? elem5ts is ready at h& = him to use4 ,n[ x is all "r purposely to avoid kn[+ :at x is t we are talk+ ab\t1 s t ! names ( ^! ?+s %all con/itute m]e blank =ms :i* may be fill$ 91 :5 & if we wi%1 by ! names ( any ?+s 9 ! univ]se ( :i* our axioms turn out to be true4 ,b :at ab\t ^! axioms !mselves8 ,:5 we lay !m d[n 9 ignorance ( ! id5tity ( ! elem5ts to :i* !y may ev5tually apply1 !y _c by any possibility be self-evid5t4 ,we may1 at pleasure1 accept z self-evid5t a /atem5t ab\t po9ts & l9es & planes2 or "o ab\t electrons1 c5timet]s & seconds2 or "o ab\t integ]s1 fractions1 & irrational numb]s2 or "o ab\t any o!r concrete ?+ or ?+s :atev]4 ,b we _c accept z self-evid5t a /atem5t ab\t *+s1 *angs & *ungs4 ,s we mu/ base our axioms on "s o!r gr\nd ?an ?is2 & our mod]n geomet] has 8 gr\nd ready & wait+4 ,he accepts 8 axioms on ! gr\nd t x pleases him to d s4 ,to avoid all sugge/ion t !y are suppos$ to be self-evid5t1 or ev5 necess>ily true1 he drops ! t]m axiom & sub/itutes = x ! m color-less ^w po/ulate4 ,a po/ulate is m]ely some?+ t we agre$ to accept1 = ! "t be+1 z a basis ( fur!r argum5t4 ,if x turns out to be true1 or if we c f9d circum/ances "u :i* & elem5ts to :i* x applies1 any conclusions :i* we d$uce f x by tru/wor?y processes are valid )9 ! same limitations4 ,& ! propositions :i* tell u t1 if our po/ulates are true1 su* & su* conclusions are true--!y1 too1 are valid1 b )\t any res]vation at all6 ,p]haps an illu/ration ( j :at ?is means w n be out ( place4 ,let x be admitt$1 z a po/ulate1 t #gbj is great]1 by #a1 ?an #gai4 ,let u !n consid] ! /atem5t3 ,if #g #ai #fe1 !n #g #bj #ff4 ,we "k--at lea/ we are q c]ta9--t #g #ai is n equal to #fe1 if by #g & #ai & #fe we mean :at y ?9k we mean4 ,we are equally sure1 on ! same gr\nds1 t #g #bj is n equal to #ff4 ,b1 "u ! "o assumption t we h p]mitt$ ourselves1 x is unque/ionable t if #g #ai 7 equal to #fe1 !n #g #bj c]ta9ly w\ld be equal to #ff4 ,s1 :ile ! conclusion ( ! proposition :i* ,i h put 9 quotation m>ks is altoge!r false1 ! proposition itself1 "u our assumption1 is entirely true4 ,i h tak5 an illu/ration design$ to be /rik+ r ?an to possess sci5tific int]e/2 ,i c\ld j z easily h %[n a true proposition lead+ to a false conclusion1 b ( su* sort t x w\ld be ( decid$ sci5tific int]e/ z tell+ u "o ( ! consequ5ces ( a c]ta9 assumption4 ,,:at ,,may ,,we ,,take ,,= ,,grant$8 ,?is is all v f9e2 b h[ does ! geomet] "k :at po/ulates to lay d[n8 ,"o is tempt$ to say t he is at lib]ty to po/ulate any?+ he pleases1 & inve/igate ! results2 & t :e!r or n 8 po/ulate ev] be realiz$1 ! propositions t he d$uces f x1 be+ true1 are ( sci5tific int]e/4 ,actually1 h[ev]1 x is n q z simple z all t4 ,if x 7 suffici5t to make a s+le po/ulate x w\ld be z simple z all t2 b x turns out t ?is is n suffici5t any m ?an x is suffici5t to h a s+le undef9$ t]m4 ,we mu/ h sev]al po/ulates2 & !y mu/ be su*1 z a :ole1 t a geometry fl[s out ( !m4 ,! requirem5ts are ?ree4 ,9 ! fir/ place1 ! sy/em ( po/ulates mu/ be categorical or complete--!re mu/ be en\gh ( !m1 & !y mu/ cov] en\gh gr\nd1 = ! support ( a complete sy/em ( geometry4 ,9 practice ! te/ = ?is is direct4 ,if we got to a po9t 9 ! build+ up ( a geometry :]e we c\ld n prove :e!r a c]ta9 ?+ 0 "o way always1 or always ! o!r way1 or sometimes "o way & sometimes ! o!r1 we %\ld conclude t we ne$$ an additional po/ulate cov]+ ?is gr\nd directly or indirectly4 ,& we %\ld make t po/ulate--because x is precisely ! ?+s t we c't prove :i*1 9 practical "w1 we agree to assume4 ,ev5 ,euclid _h to adopt ?is philosophy4 ,9 ! second place1 ! sy/em ( po/ulates mu/ be consi/5t--no "o or m ( !m may lead1 individually or collectively1 to consequ5ces t contradict ! results or any o!r or o!rs4 ,if 9 ! c\rse ( build+ up a geometry we f9d we h prov$ two propositions t d5y "o ano!r1 we se>* out ! impli$ contradiction 9 our po/ulates & rem$y x4 ,f9ally1 ! po/ulates ought to be indep5d5t4 ,x %\ld n be possible to prove any "o ( !m z a consequ5ce ( ! o!rs4 ,if ?is prop]ty fails1 ! geometry does n fail ) x2 b x is s]i\sly disfigur$ by ! sup]fluity ( assumptions1 & "o ( !m %\ld be elim9at$4 ,if we are to assume any?+ unnecess>ily1 we may z well assume ! :ole geometry & be done ) x4 ,! geomet]'s bus9ess !n is to draw up a set ( po/ulates4 ,?is he may d on any basis :atev]4 ,!y may be sugge/$ to him by ! behavior ( po9ts1 l9es & planes1 or by "s o!r concrete ph5om5a2 !y may ) equal propriety be ! product ( an inv5tive imag9ation4 ,on proce$+ to d$uce _! consequ5ces1 he w discov] & rem$y any lack ( categoricity or consi/5ce or indep5d5ce :i* 8 orig9al sy/em ( po/ulates may h lack$4 ,9 ! end he w h s l>ge a body ( propositions )\t contradiction or failure t he w conclude ! propriety ( 8 po/ulates to h be5 e/abli%$1 & ! geometry bas$ on !m to be a valid "o4 ,,& ,,:at ,,is ,,x ,,all ,,ab\t8 ,is ?is geometry ev] realiz$8 ,/rictly x is n ! geomet]'s bus9ess to ask or answ] ?is "q4 ,b rese>* develops two viewpo9ts4 ,!re is always ! man :o indulges 9 ! pursuit ( facts = _! sake alone1 & equally ! man :o wants to see 8 new facts lead to some?+ else4 ,"o great ma!matician is quot$ z enunciat+ a new !ory ( surpass+ ma!matical beauty ) ! climact]ic rem>k ,&1 ?ank ,god1 no "o w ev] be able to f9d any use = x4 ,an equally di/+ui%$ contempor>y1 on be+ int]rogat$ conc]n+ possible applications = "o ( 8 mo/ ab/ruse !orems1 repli$ t he knew no pres5t use = x2 b t long exp]i5ce _h made him confid5t t ! ma!matician w\ld nev] develop any tool1 h[ev] remote f imm$iate utility1 = :i* ! delv]s 9 o!r fields w\ld n pres5tly f9d "s use4 ,if we wi%1 h[ev]1 we may inquire ) p]fect propriety1 f ! side l9es1 :e!r a giv5 geometry is ev] realiz$4 ,we may le>n t s f> z has yet be5 discov]$ !re are no elem5ts = :i* all its po/ulates are v]ifi$1 & t !re is !re=e no realization kn[n4 ,on ! o!r h&1 we may m likely f9d t _m diff]5t sets ( elem5ts are su* t ! po/ulates c be int]pret$ z apply+ to !m1 & t we !re=e h num]\s realizations ( ! geometry4 ,z a human be+ ! geomet] may be int]e/$ 9 all ?is1 b z a geomet] x really makes little diff]5ce to him4 ,:5 we look at space ab\t u1 we see x1 = "s reason gr\nd$ 9 ! psy*ological hi/ory ( ! human race1 z made up 9 ! small ( po9ts1 :i* g to make up l9es1 :i* 9 turn con/itute planes4 ,or we c />t at ! o!r end & break space d[n fir/ into planes1 !n into l9es1 f9ally into po9ts4 ,our p]ceptions & conceptions ( ^! po9ts1 l9es & planes are v def9ite inde$2 x seems inde$1 z ! ,greeks ?\ght1 t c]ta9 ?+s ab\t !m are self-evid5t4 ,if we wi% to take ^! self-evid5t prop]ties ( po9t1 l9e & plane1 & comb9e ) !m en\gh additional hair-splitt+ specifications to assure ! mod]n geomet] t we h really a categorical sy/em ( assumptions1 we %all h ! basis ( a p]fectly good sy/em ( geometry4 ,?is w be :at we unavoidably ?9k ( z ! absolute tru? ) reg>d to ! space ab\t u2 b y mu/n't say s 9 ! pres5ce ( ! geomet]4 ,x w also be :at we call ! ,euclidean geometry4 ,x has be5 satisfactory 9 ! la/ degree1 because n only space1 b pretty mu* e o!r sy/em ( two or ?ree elem5ts be>+ any relations to "o ano!r c be made1 by employ+ z a means ( int]pretation ! ,c>tesian s*eme ( plott+1 to fit into ! framework ( ,euclidean geometry4 ,b x is n ! only ?+ 9 ! _w ( conceptual possibilities1 & x beg9s to appe> t x may n ev5 be ! only ?+ 9 ! _w ( cold h>d fact t surr\nds u4 ,to see j h[ ?is is s we mu/ return to ,euclid1 & survey ! hi/orical developm5t ( geometry f 8 day to ! pres5t "t4 ,,euclid',s ,,geometry ,po9t1 l9e & plane ,euclid attempts to def9e4 ,mod]n objection to ^! ef=ts 0 made cle> above4 ,aga9/ ,euclid's specific p]=mance we urge ! fur!r specific fault t 8 def9itions are really assumptions be/[+ c]ta9 prop]ties ^u po9ts1 l9es & planes4 ,^! assumptions ,euclid supplem5ts 9 8 axioms2 & 9 ! process ( prov+ propositions he unconsci\sly supplem5ts !m /ill fur!r4 ,?is is to be expect$ f "o ^: ju/ification = lay+ d[n an axiom 0 ! alleg$ obvi\s "* ( ! /atem5t made4 ,if "s ?+s are too obvi\s to require demon/ration1 o!rs may be admitt$ z too obvi\s to dem& explicit /atem5t at all4 ,?us1 if ,euclid has two po9ts ,a & ,b 9 a plane1 on opposite sides ( a l9e ,m1 he w draw ! l9e ,,ab & )\t fur!r =mality speak ( ! po9t ,c 9 :i* x int]sects ,m4 ,t x does s int]cept ,m1 r ?an 9 "s way dodges x1 is really an assumption z to ! nature ( l9es & planes4 ,or aga91 ,euclid w speak ( a po9t ,d on ! l9e ,,ab1 betwe5 or outside ! po9ts ,a & ,b1 )\t mak+ ! =mal assumption necess>y to insure t ! l9e is full ( po9ts s t su* a po9t z ,d mu/ exi/4 ,t su* assumptions z ^! are necess>y foll[s f our previ\s rem>ks4 ,if we ?9k ( our geometry z deal+ ) *+s1 *angs1 & *ungs1 or ) elem5ts ,i1 ,,ii & ,,iii1 x is no long] 9 ! lea/ degree obvi\s t ! simple/ prop]ty 9 ! _w applies to ^! elem5ts4 ,if we wi% any prop]ty to prevail we mu/ /ate x explicitly4 ,) ! po/ulates embodi$ 9 8 def9itions1 ^? /at$ 9 8 axioms1 & ^? :i* he reads into 8 /ructure by 8 me?ods ( pro(1 ,euclid has a categorical set--en\gh to s]ve z f\ndation = a geometry4 ,we may !n climb into ,euclid's %oes & take ! next /ep ) him4 ,we foll[ him :ile he proves a numb] ( ?+s ab\t int]sect+ l9es & ab\t triangles4 ,to be sure1 :5 he proves t two triangles are id5tically con/itut$ by mov+ "o ( !m ov] on top ( ! o!r1 we may prote/ on ! gr\nd t ! admission ( motion1 especially ( motion ?us impos$ f )\t1 into a geometry ( ?+s is n beyond dispute4 ,if ,euclid has caught our mod]n viewpo9t1 he w rejo9 t if we h any d\bts z to ! admissibility ( motion he w lay d[n a po/ulate admitt+ x1 & we %all be sil5c$4 ,hav+ exhau/$ = ! pres5t ! int]e/ ( int]sect+ l9es1 our guide n[ passes to a consid]ation ( l9es 9 ! same plane t nev] meet4 ,he def9es su* l9es z p>allel4 ,if we object t he %\ld %[ ! exi/5ce ( a d]iv$ concept l ?is be=e lay+ d[n a def9ition t calls = x to exi/1 he c %[ t two l9es drawn p]p5dicul> to ! same l9e nev] meet4 ,he w execute ?is pro( by a special sort ( sup]position1 :i* requires t ! plane be fold$ ov] on itself1 ?r\gh ! ?ird dim5sion ( surr\nd+ space1 r ?an m]ely slid along ^u itself4 ,we rema9 quiet :ile ,euclid demon/rates t if two l9es are cut by any transv]sal 9 su* a way z to make correspond+ angles at ! two int]sections equal1 ! l9es are p>allel4 ,x is !n 9 ord] to inve/igate ! conv]se3 if ! l9es are p>allel to beg9 )1 are ! angles equal8 ,,axioms ,,made ,,to ,,ord] ,?is s\nds innoc5t en\gh2 b 9 no way 0 ,euclid able to devise a pro(--or1 = t matt]1 a dispro(4 ,s he took ! only way out1 & said t if ! l9es 7 p>allel1 obvi\sly !y ext5d$ 9 ! same direction & made ! angles equal4 ,! ?+ 0 s obvi\s1 he argu$1 t x 0 really an axiom & he didn't h to prove x2 s he /at$ x z an axiom & proce$$4 ,he didn't /ate x 9 precisely ! =m ,i h us$2 he app>5tly ca/ ab\t = ! =m 9 :i* x w\ld appe> mo/ obvi\s1 & f\nd a /atem5t t suit$ him bett] ?an ?is "o1 & t comes to ! same ?+4 ,?is /atem5t tells u t if ! transv]sal makes two correspond+ angles unequal1 ! l9es t x cuts are n p>allel & d meet if suffici5tly prolong$4 ,b wisely en\gh1 he did n transplant ?is axiom1 once he _h arriv$ at x1 to ! beg9n+ ( ! book :]e ! o!r axioms 7 gr\p$2 he left x "r :]e x 01 foll[+ ! proposition t if ! angles 7 equal ! l9es 7 p>allel4 ,?is ( c\rse 0 s t x might appeal back1 = its claim to obvi\sness1 to its demon/rat$ conv]se ( ! proposition4 ,euclid mu/ h be5 dissatisfi$ ) ?is cutt+ ( ! ,gordian knot2 8 successors 7 acutely s4 ,= tw5ty c5turies ! p>allel axiom 0 reg>d$ z ! "o blemi% 9 an o!rwise p]fect "w2 e respectable ma!matician _h 8 %ot at remov+ ! defect by prov+ ! objectionable axiom4 ,! proc$ure 0 always ! same3 expunge ! p>allel axiom1 9 its place write ano!r m or less obvi\s assumption1 & f ?is d]ive ! p>allel /atem5t m or less directly4 ,?us if we may assume t ! sum ( ! angles ( a triangle is always exactly #ahj degrees1 or t !re c be drawn only "o l9e ?r\gh a giv5 po9t p>allel to a giv5 l9e1 we c prove ,euclid's axiom4 ,sometimes ! sub/itute assumption 0 op5ly made & /at$1 z 9 ! two in/ances cit$2 z (t5 x 0 admitt$ into ! demon/ration implicitly1 z :5 x is quietly assum$ t we c draw a triangle simil> to any giv5 triangle & ) area z great z we please1 or :5 p>allels are def9$ z ev]y:]e equidi/ant4 ,b su* pro(s nev] satisfi$ anyone o!r ?an ! man :o made !m2 ! se>* w5t m]rily on = a valid pro( t %\ld n 9 sub/ance assume ! ?+ to be prov$4 ,,locat+ ,,! ,,discrepancy ,sac*]i1 an ,italian ,jesuit1 w\ld h /ruck bottom if he _h _h a little m imag9ation4 ,he gave an exhau/ive r$uctio ad absurdum1 on ! basis ( ! angle-sum !orem4 ,?is sum mu/ be 7a7 great] ?an or 7b7 equal to or 7c7 less ?an #ahj degrees4 ,sac*]i %[$ t if "o ( ^! alt]natives occurs 9 a s+le triangle1 x mu/ occur 9 e triangle4 ,! fir/ case gave little tr\ble2 admitt+ ! possibility ( sup]pos+ 9 ! special mann] m5tion$ above1 :i* he did implicitly1 he %[$ t ?is obtuse-angl$ hypo!sis contradict$ itself4 ,he pursu$ ! acute-angl$ hypo!sis = a long "t be=e he satisfi$ himself t he _h caught x1 too1 9 an inconsi/5cy4 ,?is left only ! "r-angl$ hypo!sis1 prov+ ! ,euclidean angle-sum !ory & ?r\gh x ! p>allel po/ulate4 ,b ,sac*]i 0 wrong3 he _h f\nd no actual contradiction 9 ! acute-angl$ hypo!sis--= none exi/s !re94 ,! full facts 7 probably fir/ kn[n to ,gauss1 :o _h a f+] 9 e ma!matical pie t _h to d ) ! transition to mod]n times4 ,!y 7 fir/ publi%$ by ,lobat*ewsky1 ! ,russian1 :o anticipat$ ! ,hung>ian ,john ,bolyai by a n>r[ m>g94 ,all ?ree work$ indep5d5tly ( ,sac*]i1 ^: book1 ?\gh !oretically available 9 ,italian libr>ies1 0 actually lo/ to sight & _h to be r$iscov]$ 9 rec5t ye>s4 ,l ,sac*]i1 ,lobat*ewsky inve/igat$ alt]native possibilities4 ,b he *ose ano!r po9t ( attack3 ?r\gh a giv5 po9t x mu/ be possible to draw1 9 ! same plane ) a giv5 l9e 7a7 no l9es or 7b7 "o l9e or 7c7 a plurality ( l9es1 :i* %all n meet ! giv5 l9e4 ,! ^w p>allel is def9$ only 9 t]ms ( ! second ( ^! hypo!ses1 s we avoid x "h4 ,^! ?ree cases correspond1 respectively1 to ^? ( ,sac*]i4 ,! fir/ case ,lobat*ewsky rul$ out j z did ,sac*]i1 b accept+ consci\sly ! proviso atta*$ to its elim9ation2 ! ?ird he c\ld n rule out4 ,he develop$ ! consequ5ces ( ?is hypo!sis z f> z ,euclid develops ^? ( ! second "o1 sket*+ 9 a full outl9e = a sy/em ( geometry & trigonometry bas$ on a plurality ( non-cutt]s4 ,?is geometry con/itutes a coh]5t :ole1 )\t a logical flaw4 ,?is made x pla9 :at 0 ! matt] ) ,euclid's p>allel axiom4 ,nobody c\ld prove x f 8 o!r assumptions because x is n a consequ5ce ( ^!4 ,true or false1 x is indep5d5t ( !m4 ,tr9ity ,*ur* is 9 ,new ,york1 ,faneuil ,hall is 9 ,bo/on1 b ,faneuil ,hall is n 9 ,bo/on because ,tr9ity is 9 ,new ,york2 & we c\ld n prove t ,faneuil ,hall 0 9 ,bo/on if we knew no?+ ab\t ,am]ica save t ,tr9ity is 9 ,new ,york4 ,! ma!maticians ( #b1jjj ye>s _h be5 pursu+1 on a gigantic scale1 a delusion ( po/ hoc1 ergo propt] hoc4 ,,:at ,,! ,,po/ulate ,,really ,,does ,moreov]1 9 ! abs5ce ( an assumption cov]+ ! gr\nd1 we %all n "k :i* ( ! alt]natives 7a71 7b71 7c7 holds4 ,b :5 "o holds 9 a s+le case x holds p]man5tly1 z ,sac*]i & ,lobat*ewsky bo? %[$4 ,s we _c proce$ on ?is indef9ite basis2 we mu/ "k :i* "o is to hold4 ,)\t ! p>allel po/ulate or a sub/itute !re= t %all tell u ! same ?+ or tell u some?+ diff]5t1 we h n got a categorical set ( assumptions--we _c build a geometry at all4 ,t is :y ,euclid _h to h 8 p>allel po/ulate be=e he c\ld proce$4 ,t is :y 8 successors _h to h an assumption equival5t to 84 ,! reason :y x took s long = ?is to p]colate into ! und]/&+ ( ! ma!maticians 0 t !y 7 ?9k+1 n 9 t]ms ( ! mod]n geometry & ab\t undef9$ elem5ts2 b 9 t]ms ( ! old geometry & ab\t /rictly def9$ & circumscrib$ elem5ts4 ,if we und]/& :at is meant by ,euclidean l9e & plane1 ( c\rse ! p>allel po/ulate1 to use ! old geomet]'s ^w1 is true--( c\rse1 to adopt ! mod]n viewpo9t1 if we agree to employ an elem5t to :i* t assumption applies1 ! assumption is realiz$4 ,! v fact ( accept+ ! /raight l9e & ! flat plane ( ,euclid con/itutes acceptance ( 8 p>allel po/ulate--! only ?+ t c sep>ate 8 geometry f o!r geometries4 ,b ( c\rse we c't prove x2 ! prior po/ulates :i* we w\ld h to use 9 su* an attempt apply :]e x does n apply1 & h5ce x _c possibly be consequ5ces (4 ,to all ?is ! classical ,euclidean rejo9s t we seem to h 9 m9d elem5ts ( "s sort to :i*1 ) "o res]vation1 8 po/ulates apply4 ,he wants to "k :at ^! elem5ts look l4 ,we c1 & mu/1 produce !m--else our talk ab\t g5]ality is m]e drivel4 ,b we mu/ take c>e t ! ,euclidean geomet] does n try to apply to our elem5ts ! notions ( /raightness & flatness :i* inh]e 9 ! p>allel po/ulate4 ,we _c satisfy & defy t po/ulate at ! same "t4 ,if we d n insi/ on ?is po9t1 we %all f9d t we are read+ non-,euclidean prop]ties into ,euclidean geometry1 & int]pret+ ! elem5ts ( ! latt] z /raight l9es t are n /raight1 flat planes t are n flat4 ,x is n ! mission ( non-,euclidean geometry ?us to d5y ! possibility ( ,euclidean geometry2 x m]ely dem&s a place ( equal honor4 ,,! ,,geometry ,,( ,,surfaces ,let u ask ! ,euclidean geomet] :e!r he c recognize 8 plane aft] we h crumpl$ x up l a piece ( pap] en r\te to ! wa/e basket4 ,he w hesitate only long en\gh to recall t 9 ! special case ( sup]position he has res]v$ = himself ! privilege ( de=m+ 8 own plane1 & to realize t he c always iron 8 plane out smoo? aga9 aft] we are ?r\gh ) x4 ,?is emphasizes ! true nature ( ! two-dim5sionality :i* is ! fundam5tal *>act]i/ic ( ! plane 7& ( o!r ?+s1 z we %all directly see74 ,! plane is two-dim5sional 9 po9ts n because two sets ( mutually p]p5dicul> ,euclidean /raight l9es c be drawn 9 x def9+ directions ( nor?-s\? & ea/-we/1 b because a po9t 9 x c be locat$ by means ( two measures4 ,! same /atem5t may be made ( any?+ :atev] to :i* ! t]m surface is applicable2 any?+1 h[ev] crumpl$ or irregul> x be1 t possesses l5g? & bread? )\t ?ickness4 ,! surface ( a sph]e1 ( a cyl9d]1 ( an ellipsoid1 ( a cone1 ( a d\ghnut 7ma!matically kn[n z a torus71 ( a ge> :eel1 ( a ,fr5* horn1 all ^! possess two-dim5sionality 9 po9ts2 on all ( !m we c draw l9es & curves & d]ive a geometry ( ^! figures4 ,if we get away f ! notion t geometry ( two dim5sions mu/ deal ) planes1 & adopt 9 place ( ?is idea ! broad] re/riction t x %all deal ) surfaces1 we %all h ! g5]alization :i* ! ,euclidean has dem&$ t we produce1 & ! "o :i* 9 ! h&s ( ! mod]n geomet] has %[n results4 ,9 ?is two-dim5sional geometry ( surfaces 9 g5]al1 t ( ! plane is m]ely "o special case4 ,c]ta9 ( ! features met 9 t case are g5]al4 ,if we agree t we "k :at we mean by di/ance1 we f9d t on e surface !re is a %orte/ di/ance betwe5 two po9ts1 toge!r ) a s]ies ( l9es or curves along :i* su* di/ances are tak54 ,^! l9es or curves we call geodesics4 ,on ! plane ! geodesic is ! /raight l9e4 ,on surfaces 9 g5]al ! geodesic1 :atev] its p>ticul> & peculi> %ape1 plays ! same rle t is play$ by ! /raight l9e 9 ! plane2 x is ! second>y elem5t ( ! geometry1 ! surface itself & all o!r surfaces ( its type are ! t]ti>y elem5ts4 ,& x is a fact t we c take all ! possible sph]es1 or all ! possible ,fr5*-horn surfaces1 & conceive ( space z we "k x be+ brok5 d[n by analysis into ^! surfaces in/ead ( into planes4 ,! only reason we habitually decompose space into planes is because x comes natural to u to ?9k t way4 ,b geometric po9ts1 l9es & surfaces mu/ be recogniz$ z ab/ractions )\t actual exi/5ce1 = all ( !m lack "o or m ( ! ?ree dim5sions :i* su* exi/5ce implies4 ,^! figures exi/ 9 our m9ds b n 9 ! ext]nal _w ab\t u4 ,s any decomposition ( space into geometric elem5ts is a ph5om5on ( ! m9d only2 x has no p>allel & no significance 9 ! ext]nal _w1 & is made 9 "o way or 9 ano!r purely at our pleasure4 ,!re isn't a true1 hone/-to-goodness geometrical plane 9 exi/5ce any m ?an !re is an hone/-to-goodness sph]ical surface3 s on intr9sic gr\nds "o decomposition is z reasonable z ano!r4 ,c]ta9 ( ! mo/ fundam5tal po/ulates are obey$ by all surfaces4 ,z we attempt to discrim9ate betwe5 surfaces ( diff]5t types1 & get1 = in/ance1 a geometry t %all be valid = sph]es & ellipsoids b n = conicoids 9 g5]al1 we mu/ d s by br++ 9 additional po/ulates t embody ! necess>y re/rictions4 ,a *>act]i/ic %>$ by planes1 sph]es1 & v>i\s o!r surfaces is t ! geodesics c be freely slid along ^u !mselves & w co9cide ) !mselves 9 all positions :5 ?us slid2 ) a simil> arrangem5t = ! surface itself4 ,b ! plane /&s almo/ unique among surfaces 9 t x does n =ce u to di/+ui% betwe5 its two sides2 we c turn x ov] & /ill x w co9cide ) itself2 & ?is prop]ty belongs also to ! /raight l9e4 ,x does n belong to ! sph]e1 or to ! great circles :i* are ! geodesics ( sph]ical geometry2 :5 we turn "o ( ^! ov]1 ?r\gh ! ?ree-dim5sional space t surr\nds x1 we f9d t ! curvature lies 9 ! wrong way to make sup]position possible4 ,if we po/ulate t sup]position be possible "u su* treatm5t1 we ?r[ out ! sph]e & sph]ical geometry2 if we po/ulate t sup]position be only by slid+ ! surface ^u itself we admit t geometry--z ,sac*]i fail$ to see1 z ,lobat*ewsky realiz$1 & z ,riemann %[$ at great l5g? 9 rehabilitat+ ! obtuse-angl$ hypo!sis4 ,lobat*ewsky's acute-angl$ geometry is realiz$ on a surface ( ! prop] sort1 :i* admits ( unre/rict$ sup]position2 b x is n ! sort ( a surface t ,i c>e to discuss 9 an article ( ?is scope4 ,euclidean geometry is ! natural & easy "o1 ,i suppose1 because x makes x easy to /op ) ?ree dim5sions4 ,if we take a second>y elem5t1 a geodesic1 :i* is curv$ 9 ! ,euclidean s5se1 we get a t]ti>y elem5t1 a surface1 :i* is likewise curv$4 ,!n unless we are to make an altoge!r abrupt & unreasonable break1 we %all f9d t j z ! curv$ geodesic g5]at$ a curv$ surface1 ! curv$ surface mu/ give rise to a curv$ space2 & j z ! curv$ geodesic ne$$ a second dim5sion to curve into1 & ! curv$ surface a ?ird1 s ! curv$ ?ree-space requires a f\r?4 ,once />t$ on ?is sort ( ?+1 !re doesn't really seem to be any end4 ,,euclidean ,,or ,,non-,,euclidean ,nev]!less1 we mu/ face ! possibility t ! space we live 91 or any o!r manifold ( any sort :atev] ) :i* we deal on geometric pr9ciples1 may turn out to be non-,euclidean4 ,h[ %all we f9ally det]m9e ?is8 ,by measures--! ,euclidean measures ! angles ( an actual triangle & f9ds ! sum to be exactly #ahj degrees2 or he draws p>allel l9es ( indef9ite ext5t & f9ds !m to be ev]y:]e equally di/ant2 & f ^! data he concludes t our space is really ,euclidean4 ,b he is n necess>ily "r4 ,we ask him to level (f a plot ( gr\nd by means ( a plumb l9e4 ,s9ce ! l9e always po9ts to ! e>?'s c5t]1 ! level plot is actually a v small piece ( a sph]ical surface4 ,any te/ conduct$ on ?is plot w exhibit ! num]ical *>act]i/ics ( ! ,euclidean geometry2 yet we "k ! geometry ( ?is surface is ,riemannian4 ,! angle-sum is really great] ?an #ahj degrees2 l9es t are ev]y:]e equidi/ant are n bo? geodesics4 ,! tr\ble1 ( c\rse1 is t on ?is plot we deal ) s m9ute a fraction ( ! :ole sph]e t we _c make measurem5ts suffici5tly ref9$ to detect ! dep>ture f ,euclidean /&>ds4 ,s x is altoge!r s5sible = u to ask3 ,is ! univ]se ( space ab\t u really ,euclidean 9 :atev] ( realiz$ geometry x pres5ts to u8 ,or is x really non-,euclidean1 b s va/ 9 size t we h nev] yet be5 able to ext5d our measures to a suffici5tly l>ge portion ( x to make ! div]g5ce f ! ,euclidean /&>d disc]nible to u8 ,?is discussion is necess>ily fragm5t>y1 leav+ out mu* t ! writ] w\ld pref] to include4 ,b x is hop$ t x w nev]!less make x cle> t :5 ! conte/ants 9 ! ,e9/e9 competition speak ( a non-,euclidean univ]se z app>5tly hav+ be5 reveal$ by ,e9/e91 !y mean simply t to ,e9/e9 has occurr$ a happy exp$i5t = te/+ ,euclideanism on a small] scale ?an has h]et(ore be5 suppos$ possible4 ,he has devis$ a new & +5i\s sort ( measure :i*1 if 8 results be valid1 enables u to op]ate 9 a small] region :ile yet anticipat+ t any non-,euclidean *>act]i/ics ( ! manifold ) :i* we deal w rise above ! ?re%old ( measurem5t4 ,?is does n mean t ,euclidean l9es & planes1 z we picture !m 9 our m9d1 are no long] non-,euclidean1 b m]ely t ^! concepts d n q s closely correspond ) ! ext]nal reality z we _h suppos$4 ,z to ! precise "* ( ! non-,euclideanism :i* is reveal$1 we may leave ?is to lat] *apt]s & to ! compet+ essayi/s4 ,we ne$ only po9t out "h t x w n necess>ily be re/rict$ to ! matt] ( p>allelism4 ,! p>allel po/ulate is ( extreme int]e/ to u = two reasons2 fir/ because hi/orically x 0 ! means by :i* ! possibilities & ! importance ( non-,euclidean geometry 7 =c$ ^u our att5tion2 & second because x happ5s to be ! imm$iate gr\nd ( di/9ction betwe5 ,euclidean geometry & two ( ! mo/ int]e/+ alt]natives4 ,b ,euclidean geometry is *>act]iz$1 n by a s+le po/ulate1 b by a consid]able numb] ( po/ulates4 ,we may attempt to omit any "o ( ^! s t its gr\nd is n specifically cov]$ at all1 or to replace any "o ( !m by a direct alt]native4 ,we might conceivably d away ) ! sup]position po/ulate entirely1 & dem& t figures be prov$ equival5t1 if at all1 by "s m dra/ic te/4 ,we might d away ) ! po/ulate1 fir/ prop]ly =mulat$ by ,hilb]t1 on :i* our ideas ( ! prop]ty repres5t$ 9 ! ^w betwe5 dep5d4 ,we might d away ) any s+le "o ( ! ,euclidean po/ulates1 or ) any comb9ation ( two or m ( !m4 ,9 "s cases ?is w\ld lead to a lack ( categoricity & we %\ld get no geometry at all2 9 mo/ cases1 provid$ we br\ght a prop] degree ( a/ut5ess to ! =mulation ( alt]natives = ! reject$ po/ulates1 we %\ld get a p]fectly good sy/em ( non-,euclidean geometry3 "o realiz$1 if at all1 by o!r elem5ts ?an ! ,euclidean po9t1 l9e & plane1 & "o ^: elem5ts behave t[>d "o ano!r diff]5tly f ! ,euclidean po9t1 l9e & plane4 ,m]ely to add def9it5ess to ?is *apt]1 ,i annex "h ! /atem5t t 9 ! geometry :i* ,e9/e9 builds up z m ne>ly repres5t+ ! true ext]nal _w ?an does ,euclid's1 we %all disp5se ) ,euclid's 7implicit7 assumption1 und]ly+ 8 7explicitly /at$7 sup]position po/ulate1 to ! effect t ! act ( mov+ ?+s ab\t does n affect _! l5g?s4 ,we %all at ! same "t disp5se ) 8 p>allel po/ulate4 ,& we %all add a f\r? dim5sion to 8 ?ree--n1 ( c\rse1 any?+ 9 ! nature ( a f\r? ,euclidean /raight l9e p]p5dicul>1 9 ,euclidean space1 to ?ree l9es t are already p]p5dicul> to ea* o!r1 b some?+ q di/9ct f ?is1 ^: nature we %all see m exactly 9 ! next *apt]4 ,if ! pres5t *apt] has made x cle> t x is prop] = u to d ?is1 & has prev5t$ anyone f suppos+ t ! results ( do+ x mu/ be visualiz$ 9 a ,euclidean space ( ?ree dim5sions or ( any numb] ( dim5sions1 x w h s]v$ its purpose4 ,,vi ,,! ,,space-,,"t ,,cont9uum ,m9k[ski's ,_w ( ,ev5ts1 & ! ,way ,x ,fits ,into ,e9/e9's ,/ructure ,,by ,,! ,,editor1 ,,except ,,z ,,not$ ,seek+ a basis = ! secure =mulation ( 8 results1 & especially a means = express+ ma!matically ! facts ( ! dep5d5ce :i* he _h f\nd to exi/ betwe5 "t & space1 ,e9/e9 fell back ^u ! prior "w ( ,m9k[ski4 ,x may be /at$ "r "h t ! idea ( "t z a f\r? dim5sion is n p>ticul>ly a new "o4 ,x has be5 a topic ( ab/ract speculation = ! be/ "p ( a c5tury1 ev5 on ! "p ( ^? ^: notions ( ! f\r? dim5sion 7 pretty closely ti$ d[n to ! idea ( a f\r? dim5sion ( ,euclidean po9t-space1 :i* w\ld be m>k$ by a f\r? real l9e1 p]p5dicul> to ! o!r ?ree1 & visible to u if we 7 only able to see x4 ,moreov]1 e ma!matician1 :e!r or n he be incl9$ to ?is sort ( m5tal ex]cise1 kn[s well t :5ev] "t ent]s 8 equations at all1 x does s on an absolutely equal foot+ ) ea* ( 8 space coord9ates1 s t z f> z 8 algebra is conc]n$ he c\ld nev] di/+ui% betwe5 !m4 ,:5 ! v>iables x1 y1 z1 t come to ! ma!matician 9 connection ) "s physical inve/igation1 he kn[s be=e he />ts t ! fir/ ?ree repres5t ! dim5sions ( ,euclidean ?ree-space & t ! la/ /&s = "t4 ,b if ! algebraic expressions ( su* a problem 7 h&$ to him indep5d5tly ( all physical tie-up1 he w\ld nev] be able to tell1 f !m alone1 :e!r "o ( ! f\r v>iables repres5t$ "t1 or if s1 :i* "o to pick out = ?is di/9ction4 ,x 0 ,m9k[ski :o fir/ =mulat$ all ?is 9 a =m susceptible ( use 9 connection ) ! !ory ( relativity4 ,8 />t+ po9t lies 9 ! di/9ction betwe5 ! po9t & ! ev5t4 ,mr4 ,francis has br\ght ?is out r well 9 8 essay1 be+ ! only competitor to pres5t ! ,euclidean geometry z a real pr$ecessor ( ,newtonian sci5ce1 r ?an z a m]e "p ( ! ,newtonian sy/em4 ,i ?9k 8 po9t "h is v well tak54 ,z he says1 ,euclid look$ into ! _w ab\t him & saw x compos$ ( po9ts4 ,ignor+ all dynamic consid]ations1 he built up 9 8 m9d a /atic _w ( po9ts1 & con/ruct$ 8 geometry z a sci5tific ma*9e = deal+ ) ?is _w 9 :i* motion play$ no "p4 ,x c\ld to be sure be introduc$ by ! obs]v] = 8 own purposes1 b :5 s introduc$ x 0 specifically po/ulat$ to be a matt] ( no mom5t at all to ! po9ts or l9es or figures t 7 mov$4 ,x 0 purely an obs]vational device1 int5d$ = ! obs]v]'s conv5i5ce1 & 9 ! b>ga9 a m5tal device1 call+ = no physical action & ! play ( no =ce4 ,s f> z ,euclid 9 8 daily life 0 oblig$ to take cognizance ( ! fact t 9 ! _w ( "w-a-day realities motion exi/$1 he mu/1 z a true ,greek1 h look$ ^u ?is z a mo/ un=tunate deviation ( ! reality f 8 beautiful _w ( intellectual ab/raction1 & z some?+ to be deplor$ & ignor$4 ,ev5 9 _! /atu>y ! ,greeks clung to ?is idea4 ,a gr\p ( m>vel\s action1 l ! ,laocoon1 !y held to be di/9ctly a second rate production1 a pro/itution ( ! noble art2 _! ideal 0 a figure l ! maje/ic ,zeus--n necess>ily a m]e bu/1 be x und]/ood1 b always a figure 9 repose )\t action4 ,_! /atu>y /ood = ?+s1 n = action1 j z _! geometry /ood = po9ts1 n = ev5ts4 ,galileo & ,newton took a diff]5t viewpo9t4 ,!y 7 int]e/$ 9 ! _w z x is1 n z x ought to be2 & if motion appe>s to be a fundam5tal "p ( t _w1 !y 7 b\nd to include x 9 _! s*eme4 ,?is made x necess>y = !m to pay mu* m att5tion to ! concept ( "t & its place 9 ! _w ?an did ! ,greeks4 ,9 ! sup]position process1 & ev5 :5 he all[$ a curve to be g5]at$ by a mov+ po9t1 ! sole int]e/ :i* ,euclid _h 9 ! motion 0 ! effect :i* 0 to be obs]v$ ^u 8 /atic figures aft] its completion4 ,9 ?is effect ! rate ( ! motion did n ent]4 ,s all que/ions ( velocity & "t are completely ignor$1 & we h 9 fact ! curi\s spectacle ( motion )\t "t4 ,to ,galileo & ,newton1 on ! o!r h&1 ! "t :i* x took a body to pass f "o po9t ( its pa? to ano!r 0 ( p>am\nt importance4 ,! motion itself 0 ! object ( _! /udy1 & !y recogniz$ ! "p play$ by velocity4 ,b ,galileo & ,newton 7 /ill suffici5tly "u ! influ5ce ( ,euclid to fit ! obs]v$ ph5om5a ( motion1 s f> z !y c\ld1 ^u ,euclid's /atic _w ( po9ts4 ,?is !y effect$ by fall+ 9 ) ! age-old proc$ure ( reg>d+ "t & space z some?+ entirely disassociat$ & di/9ct4 ,! motion ( an object--9 !ory1 ( a po9t--0 to be record$ by obs]v+ its successive positions4 ,) ea* ( ^! positions a "t 0 to be associat$1 m>k+ ! in/ant at :i* ! po9t atta9$ t position4 ,b 9 ! face ( ?is association1 space & "t 7 to be ma9ta9$ z entirely sep>ate entities4 ,,! ,,f\r-,,dim5sional ,,_w ,,( ,,ev5ts ,?is sev]e sep>ation ( "t & space ,m9k[ski has n[ que/ion$1 ) ! /atem5t t ! elem5ts ( :i* ! ext]nal _w is compos$1 & :i* we obs]ve1 are n po9ts at all1 b are ev5ts4 ,?is calls = a revision ( our :ole habit ( ?\ght4 ,x means t ! p]ceptual _w is f\r-dim5sion$1 n ?ree-dim5sion$ z we h always suppos$2 & x means1 at ! v lea/1 t ! di/9ction betwe5 "t & space is n s fundam5tal z we _h suppos$4 ,?is %\ld n impress u z /range or incompreh5sible4 ,:at d we mean :5 we say t a plane is two-dim5sional8 ,simply t two coord9ates1 two numb]s1 mu/ be giv5 to specify ! position ( any po9t ( ! plane4 ,simil>ly = a po9t 9 ! space ( our accu/om$ concepts we mu/ give ?ree numb]s to fix ! position--z by giv+ ! latitude & longitude ( a po9t on ! e>? & its height above sea-level4 ,s we say ?is space is ?ree-dim5sional4 ,b a mat]ial body is n m]ely some:]e2 x is some:]e n[1#ahb or 0 some:]e ye/]day1 or w be some:]e tomorr[4 ,! /atem5t ( position = a mat]ial object is mean+less unless we at ! same "t specify ! "t at :i* x held t position4 ,if ,i am consid]+ ! life-hi/ory ( an object on a mov+ tra91 ,i mu/ give ?ree space-coord9ates & "o "t-coord9ate to fix ea* ( its positions4#ahb ,& ea* ( its positions1 ) ! "t p]ta9+ to t position1 con/itutes an ev5t4 ,! dynamic1 ev]-*ang+ _w ab\t u1 t %[s ! same aspect at no two diff]5t mom5ts1 is a _w ( ev5ts2 & s9ce f\r measures or coord9ates are requir$ to fix an ev5t1 we say ?is _w ( ev5ts is f\r-dim5sional4 ,if we wi% to te/ out ! s\ndness ( ?is viewpo9t1 we may well d s by ask+ :e!r ! nam+ ( values = ! f\r coord9ates fixes ! ev5t uniquely1 z ! nam+ ( ?ree "u ! old sy/em fixes ! po9t uniquely4 ,suppose we take "s p>ticul> ev5t z ! "o f :i* to measure1 & agree ^u ! directions to be tak5 by our space axes1 & make any conv5tion ab\t our "t-axis :i* subsequ5t inve/igation may %[ to be necess>y4 ,c]ta9ly !n ! act ( measur+ s _m miles nor?1 & s _m we/1 & s _m d[n1 & s _m seconds backw>d1 br+s u to a def9ite "t & place--:i* is to say1 to a def9ite ev5t4 ,p]haps no?+ happ5$ !re1 9 ! s5se 9 :i* we usually employ ! ^w2 b t is no m s]i\s ?an if we 7 to locate a po9t ) ref]5ce to our famili> space coord9ate sy/em1 & f9d x to lie 9 ! empty void ( int]/ell> space1 ) no mat]ial body occupy+ x4 ,9 ?is second case we /ill h a po9t1 :i* requires1 to insure its exi/5ce & location1 ?ree coord9ates & no?+ m2 9 ! fir/ case we /ill h an ev5t1 :i* requires = its exi/5ce & def9ition f\r coord9ates & no?+ m4 ,x is n an ev5t ab\t :i* ! headl9e writ]s are likely to get greatly excit$2 b :at ( t8 ,x is !re1 ready & wait+ to def9e any physical happ5+ t falls ^u x1 j z ! geomet]'s po9t is ready & wait+ to def9e any physical body t *ances to fall ^u x4 ,a ,,cont9uum ,,( ,,po9ts ,x is n[ 9 ord] to introduce a ^w1 :i* ,i %all h to confess ! great majority ( ! essayi/s introduce1 some:at improp]ly1 )\t explanation4 ,b :5 ,i attempt to expla9 x1 ,i realize q well :y !y did ?is4 ,!y _h to h x2 & !y didn't h space 9 _! ?ree ?\s& words to talk adequately ab\t x & ab\t any?+ else besides4 ,! ma!matician kn[s v well inde$ :at he means by a cont9uum2 b x is f> f easy to expla9 x 9 ord9>y language4 ,i ?9k ,i may d be/ by talk+ fir/ at "s l5g? ab\t a /raight l9e1 & ! po9ts on x4 ,if ! l9e conta9s only ! po9ts correspond+ to ! integral di/ances #a1 #b1 #c1 etc41 f ! />t+ po9t1 x is obvi\sly n cont9u\s--!re are gaps 9 x va/ly m inclusive ?an ! few 7comp>atively speak+7 po9ts t are pres5t4 ,if we ext5d ! limitations s t ! l9e includes all po9ts correspond+ to ord9>y prop] & improp] fractions l #a_/d & #ag_/bi & #afcc_/g--:at ! ma!matician calls ! rational numb]s--we %all app>5tly fill 9 ^! gaps2 & ,i ?9k ! layman's fir/ impulse w\ld be to say t ! l9e is n[ cont9u\s4 ,c]ta9ly we _c /& n[ at "o po9t on ! l9e & "n ! next po9t1 z we c\ld a mom5t ago4 ,!re is no next rational numb] to #aaf_/abe1 = in/ance2 #aae_/abd comes be=e x & #aag_/abf comes aft] x1 b betwe5 x & ei!r1 or betwe5 x & any o!r rational numb] we might "n1 lie _m o!rs ( ! same sort4 ,yet 9 spite ( ! fact t ! l9e conta9+ all ^! rational po9ts is n[ d5se 7! te*nical t]m = ! prop]ty ,i h j indicat$71 x is /ill n cont9u\s2 = ,i c easily def9e numb]s t are n conta9$ 9 x--irrational numb]s 9 inf9ite v>iety l sqrt#b2 or1 ev5 worse1 ! numb] pi #c4adaeib 444 :i* def9es ! ratio ( ! circumf]5ce ( a circle to ! diamet]1 & _m o!r numb]s ( simil> sort4 ,if ! l9e is to be cont9u\s1 !re may be no holes 9 x at all2 x mu/ h a po9t correspond+ to e numb] ,i c possibly "n4 ,simil>ly = ! plane1 & = our ?ree-space2 if !y are to be cont9u\s1 ! "o mu/ conta9 a po9t = e possible pair ( numb]s x & y1 & ! o!r = e possible set ( ?ree numb]s x1 y & z1 t ,i c "n4 ,!re may be no holes 9 !m at all4 ,a l9e is a cont9uum ( po9ts4 ,a plane is a cont9uum ( po9ts4 ,a ?ree-space is a cont9uum ( po9ts4 ,^! ?ree cases diff] only 9 _! dim5sionality2 x requires b "o numb] to det]m9e a po9t ( ! fir/ cont9uum1 two & ?ree respectively 9 ! second & ?ird cases4 ,b ! ess5tial feature is n t a cont9uum %all consi/ ( po9ts1 or t we %all be able to visualize a pseudo-real exi/5ce = x ( j ! sort t we c visualize 9 ! case ( l9e1 plane & po9t4 ,! ess5tial ?+ is m]ely t x %all be an aggregate ( elem5ts num]ically det]m9$ 9 su* a way z to leave no holes1 b to be j z cont9u\s z ! real numb] sy/em itself4 ,examples1 h[ev]1 aside f ! ?ree :i* ,i h us$1 are difficult to con/ruct ( su* sort t ! layman %all grasp !m readily2 s p]haps1 =tifi$ ) ! backgr\nd ( example already pres5t$1 ,i may v5ture fir/ ^u a g5]al /atem5t4 ,,! ,,cont9uum ,,9 ,,g5]al ,suppose we h a set ( elem5ts ( "s sort--any sort4 ,suppose t ^! elem5ts possess "o or m fundam5tal id5tify+ *>act]i/ics1 analog\s to ! coord9ates ( a po9t1 & :i*1 l ^! coord9ates1 are capable ( be+ giv5 num]ical values4 ,suppose we f9d t no two elem5ts ( ! set possess id5tically ! same set ( def9+ values4 ,suppose f9ally--& ?is is ! critical te/--t ! elem5ts ( ! set are su* t1 no matt] :at num]ical values we may specify1 x we d specify ! prop] numb] ( def9+ magnitudes we def9e by ^! an actual elem5t ( ! set1 t corresponds to ?is p>ticul> collection ( values4 ,our elem5ts !n %>e ) ! real numb] sy/em ! prop]ty ( leav+ no holes1 ( con/itut+ a cont9u\s succession 9 e dim5sion :i* !y possess4 ,we h !n a cont9uum4 ,:atev] its elem5ts1 :atev] ! "* ( _! num]ical id5tifi]s1 :atev] ! numb] n ( ^! :i* /&s = its dim5sion1 !re may be no holes or we h no cont9uum4 ,!re mu/ be an elem5t = e possible comb9ation ( n numb]s we c "n1 & no two ( ^! comb9ations may give ! same elem5t4 ,grant$ ?is condition1 our elem5ts con/itute a cont9uum4 ,z ,i h rem>k$1 x is n easy to cite examples ( cont9ua :i* %all mean any?+ to ! p]son unaccu/om$ to ! t]m4 ,! totality ( c>bon-oxyg5-nitrog5-hydrog5 comp\nds sugge/$ by "o essayi/ z an example is n a cont9uum at all1 = ! set conta9s elem5ts correspond+ only to integ] values ( ! numb]s :i* tell u h[ _m atoms ( ea* sub/ance occur 9 ! molecule4 ,we _c h a comp\nd conta9+ sqrt#b c>bon atoms1 or #cpi oxyg5 atoms4 ,p]haps ! mo/ satisfactory ( ! cont9ua1 outside ! ?ree ,euclidean space-cont9ua already cit$1 is ! manifold ( music notes4 ,?is is f\r-dim5sional2 ea* note has f\r di/9ctions--l5g?1 pit*1 int5sity1 timbre--to di/+ui% x p]fectly1 to tell h[ long1 h[ high1 h[ l\d1 h[ ri*4#bfc ,we might h a little difficulty 9 r$uc+ ! *>act]i/ic ( ri*ness to num]ical expression1 b presumably x c\ld be done2 & we %\ld !n be satisfi$ t e possible comb9ation ( f\r values1 l1 p1 i1 t = ^! f\r id5tify+ *>act]i/ics w\ld give u a musical effect1 & "o to be confus$ ) no o!r4 ,!re is 9 ! physical _w a va/ quantity ( cont9ua ( "o sort or ano!r4 ,! music-note cont9uum br+s att5tion to ! fact t n all ( ^! are su* t _! elem5ts make _! appeal to ! visual s5se4 ,?is rem>k is a p]t95t "o2 = we are by e "r ( h]itage an eye-m9d$ race1 & x is frequ5tly necess>y = u to be rem9d$ t s f> z ! ext]nal _w is conc]n$1 ! v]dict ( e o!r s5se is entirely on a p> ) t ( sight4 ,! ?+s :i* we really see1 l matt]1 & ! ?+s :i* we ab/ract f ^! visual impressions1 l space1 are by no means all !re is to ! _w4 ,,euclidean ,,& ,,non-,,euclidean ,,cont9ua ,if we are deal+ ) a cont9uum ( any sort :atev] hav+ "o or two or ?ree dim5sions1 we are able to repres5t x graphically by means ( ! l9e1 ! plane1 or ! ?ree-space4 ,! same set ( numb]s t def9es an elem5t ( ! giv5 cont9uum likewise def9es an elem5t ( ! ,euclidean cont9uum ( ! same dim5sionality2 s ! "o cont9uum corresponds to ! o!r1 elem5t = elem5t1 & ei!r may /& = ! o!r4 ,b if we h a cont9uum ( f\r or m dim5sions1 ?is repres5tation breaks d[n 9 ! abs5ce ( a real1 f\r-dim5sional ,euclidean po9t-space to s]ve z a picture4 ,?is does n 9 ! lea/ detract f ! reality ( ! cont9uum :i* we are ?us prev5t$ f repres5t+ graphically 9 ! accu/om$ fa%ion4 ,! ,euclidean repres5tation1 9 fact1 may 9 "s cases be un=tunate--x may be s entirely )\t significance z to be actually mislead+4 ,= 9 ! ,euclidean cont9uum ( po9ts1 be x l9e1 plane or ?ree-space1 !re are c]ta9 ?+s :i* we ord9>ily reg>d z second>y d]iv$ prop]ties1 b :i* possess a great deal ( significance none ! less4 ,9 p>ticul>1 9 ! ,euclidean plane & 9 ,euclidean ?ree-space1 !re is ! di/ance betwe5 two po9ts4 ,i h indicat$1 9 ! *apt] on non-,euclidean geometry1 t ! p>allel po/ulate ( ,euclid1 :i* di/+ui%es 8 geometry f o!rs1 c\ld be replac$ by any "o ( num]\s o!r po/ulates4 ,grant ,euclid's po/ulate & y c prove any ( ^! sub/itutes2 grant any ( ! sub/itutes & y c prove ,euclid's po/ulate4 ,n[ x happ5s t !re is "o ( ^! sub/itutes to :i* mod]n analysis has giv5 a position ( consid]able importance4 ,x is m]ely our good old fri5d ! ,py?agorean !orem1 t ! squ>e on ! hypot5use equals ! sum ( ! squ>es on ! sides2 b x is dress$ 9 new clo!s = ! pres5t occasion4 ,mr4 ,francis' discussion ( ?is "p ( ! subject1 & especially 8 figure1 ought to make x cle> t ?is !orem c be consid]$ z deal+ ) ! di/ance betwe5 any two po9ts4 ,:5 we s consid] x1 & take x z ! fundam5tal1 def9+ po/ulate ( ,euclidean geometry :i* di/+ui%es ?is geometry f o!rs1 we h a /atem5t ( consid]able cont5t4 ,we h1 fir/1 t ! *>act]i/ic prop]ty ( ,euclidean space is t ! di/ance betwe5 two po9ts is giv5 by ! squ>e root ( ! sum ( ! squ>es ( ! coord9ate-diff]5ces = ^! po9ts--by ! expression ,d sqrt7,x - x7#b 7,y - y7#b 7,z - z7#b11 :]e ! l>ge lett]s repres5t ! coord9ates ( ! "o po9t & ! small ones ^? ( ! o!r4 ,we h m ?an ?is1 h[ev]2 we h t ?is di/ance is ! same = all obs]v]s1 no matt] h[ diff]5t _! values = ! individual coord9ates ( ! individual po9ts4 ,& we h1 f9ally1 z a direct result ( look+ ^u ! ?+ f ?is viewpo9t1 t ! expression = ,d is an inv>iant2 :i* simply means t e obs]v] may use ! same expression 9 calculat+ ! value ( ,d 9 t]ms ( 8 own values = ! coord9ates involv$4 ,! di/ance betwe5 two po9ts 9 our space is giv5 num]ically by ! squ>e root ( ! sum ( ! squ>es ( my coord9ate-diff]5ces = ! two po9ts involv$2 x is giv5 equally by ! squ>e root ( ! sum ( ! squ>es ( y\r coord9ate-diff]5ces1 or ^? ( any o!r obs]v] :atsoev]4 ,we h !n a natural law--! fundam5tal natural law *>act]iz+ ,euclidean space4 ,if we wi% to apply x to ! ,euclidean two-space 7! plane7 we h only to drop out ! sup]flu\s coord9ate-diff]5ce2 if we wi% to see by analogy :at w\ld be ! fundam5tal natural law = a f\r-dim5sional ,euclidean space1 we h only to introduce "u ! radical a f\r? coord9ate-diff]5ce = ! f\r? dim5sion4 ,if we 7 n able to atta* any concrete mean+ to ! expression = ,d ! value ( all ?is w\ld be mat]ially less5$4 ,consid]1 = in/ance1 ! cont9uum ( music notes4 ,!re is no di/ance betwe5 diff]5t notes4 ,!re is ( c\rse significance 9 talk+ ab\t ! diff]5ce 9 pit*1 9 int5sity1 9 duration1 9 timbre1 betwe5 two notes2 b !re is none 9 a mode ( spee* t implies a composite expression indicat+ h[ f> "o note escapes be+ id5tical ) ano!r 9 all f\r respects at once4 ,! tr\ble1 ( c\rse1 is t ! f\r dim5sions ( ! music-note cont9uum are n measurable 9 t]ms ( a common unit4 ,if !y 71 we %\ld expect to measure _! comb9ation m or less absolutely 9 t]ms ( ?is same unit4 ,we c make measurem5ts 9 all ?ree dim5sions ( ,euclidean space ) ! same unit1 ) ! same measur+ rod 9 fact4 ,?is pres5ts a peculi>ity ( our ?ree-space :i* is n possess$ by all ?ree-dim5sional manifolds4 ,riemann has giv5 ano!r illu/ration 9 ! sy/em ( all possible colors1 compos$ ( arbitr>y proportions ( ! ?ree prim>ies1 r$1 gre5 & violet4 ,?is sy/em =ms a ?ree-dim5sional cont9uum2 b we _c measure ! di/ance or diff]5ce betwe5 two colors 9 t]ms ( ! diff]5ce betwe5 two o!rs4#acj ,accord+ly1 9 spite ( ! fact t ! ,euclidean ?ree-space gives u a =mal repres5tation ( ! color cont9uum1 & 9 spite ( ! fact t ! hypo!tical f\r-dim5sional ,euclidean space w\ld p]=m a l (fice = ! music-note cont9uum1 ?is repres5tation w\ld be )\t significance4 ,we %\ld n say t ! geometry ( ^! two manifolds is ,euclidean4 ,we %\ld realize t any set ( num]ical elem5ts c be plott$ 9 a ,euclidean space ( ! appropriate dim5sionality2 & t accord+ly1 be=e all[+ su* a plot to influ5ce u to classify ! geometry ( ! giv5 manifold z ,euclidean1 we mu/ pause long en\gh to ask :e!r ! re/ ( ! ,euclidean sy/em fits into ! picture4 ,if ! squ>e root ( ! sum ( ! squ>es ( ! coord9ate-diff]5ces betwe5 two elem5ts possesses significance 9 ! giv5 cont9uum1 & if x is inv>iant betwe5 obs]v]s ( t cont9uum :o employ diff]5t bases ( ref]5ce1 !n & only !n may we allege ! ,euclidean "* ( ! giv5 cont9uum4 ,if "u ?is te/ ! giv5 cont9uum fails ( ,euclideanism1 x is 9 ord] to ask :at type ( geometry x does pres5t4 ,if x is ( su* "* t ! di/ance betwe5 two elem5ts possesses significance1 we %\ld answ] ?is "q by inve/igat+ t di/ance 9 ! hope ( discov]+ a non-,euclidean expression = x :i* w be inv>iant4 ,if x is n ( su* "*1 we %\ld seek "s o!r *>act]i/ic ( s+le elem5ts or gr\ps ( elem5ts1 ( real physical significance & ( su* sort t ! num]ical expression = x w\ld be inv>iant4 ,if ! cont9uum ) :i* we h to d is "o 9 :i* ! di/ance betwe5 two elem5ts possesses significance1 & if x turns out t ! inv>iant expression = ?is di/ance is n ! ,py?agorean "o1 b "o indicat+ ! non-,euclideanism ( our cont9uum1 we say t ?is cont9uum has a curvature4 ,?is means t1 if we int]pret ! elem5ts ( our cont9uum z po9ts 9 space 7:i* ( c\rse we may prop]ly d7 & if we !n try to sup]pose ?is po9t-cont9uum ^u a ,euclidean cont9uum1 x w n g2 we %all be caught 9 "s su* absurdity z try+ to =ce a sph]e into co9cid5ce ) a plane4 ,& ( c\rse if x won't g1 ! only possible reason is t x is curv$ or di/ort$1 l ! sph]e1 9 su* a way z to prev5t its go+4 ,x is un=tunate t ! visualiz+ ( su* curvature requires ! visualiz+ ( an additional dim5sion = ! curv$ cont9uum to curve into2 s t :ile we c picture a curv$ surface easily en\gh1 we c't picture a curv$ ?ree-space or f\r-space4 ,b t is a b>ri] to visualization alone1 & 9 no s5se to und]/&+4 ,,our ,,_w ,,( ,,f\r ,,dim5sions ,x w be obs]v$ t we h n[ a mu* broad] def9ition ( non-,euclideanism ?an ! "o :i* s]v$ u = ! inve/igation ( ,euclid's p>allel po/ulate4 ,if we may at pleasure accept ?is po/ulate or replace x by ano!r & diff]5t "o1 we may presumably d ! same = any o!r or any o!rs ( ,euclid's po/ulates4 ,! v /atem5t t ! di/ance betwe5 elem5ts ( ! cont9uum %all possess significance1 & %all be measurable by consid]+ a pa? 9 ! cont9uum :i* involves o!r elem5ts1 is an assumption4 ,if we disc>d x altoge!r1 or replace x by "o po/ulat+ t "s o!r jo9t prop]ty ( ! elem5ts ?an _! di/ance be ! c5t] ( int]e/1 we get a non-,euclidean geometry4 ,s = any o!r ( ,euclid's po/ulates2 !y are all necess>y = a ,euclidean sy/em1 & 9 ! abs5ce ( any "o ( !m we get a non-,euclidean sy/em4 ,n[ ! f\r-dim5sional "t-space cont9uum ( ,m9k[ski is pla9ly ( a sort :i* ought to make susceptible ( measurem5t ! sep>ation betwe5 two ( its ev5ts4 ,we c pass f "o elem5t to ano!r 9 ?is cont9uum--f "o ev5t to ano!r--by trav]s+ a pa? involv+ successive ev5ts4 ,our v lives consi/ 9 do+ j ?is3 we pass f ! initial ev5t ( our c>e] to ! f9al ev5t by trav]s+ a pa? lead+ u f ev5t to ev5t1 *ang+ our "t & space coord9ates cont9u\sly & simultane\sly 9 ! process4 ,& :ile we h n be5 9 ! habit ( measur+ any?+ except ! space int]val betwe5 two ev5ts & ! "t int]val betwe5 two ev5ts1 sep>ately1 ,i ?9k x is cle> en\gh t1 consid]$ z ev5ts1 z elem5ts 9 ! _w ( f\r dim5sions1 !re is a less sep>ation betwe5 two ev5ts t occur 9 my (fice on ! same day ?an betwe5 two :i* occur 9 my (fice a ye> ap>t2 or betwe5 two ev5ts occurr+ #aj m9utes ap>t :5 bo? take place 9 my (fice ?an :5 "o takes place !re & "o 9 ,london or on ,betelgeuse4 ,x is n at all unreasonable1 a priori1 !n1 to seek a num]ical measure = ! sep>ation1 9 space-"t ( f\r-dim5sions1 ( two ev5ts4 ,if we f9d x1 we %all d\btless be ask$ j :at its subjective significance to u is4 ,?is mu/ be answ]$ ) "s circumspection4 ,x w presumably be some?+ :i* we _c obs]ve ) ! visual s5se alone1 or x w\ld h =c$ itself ^u our att5tion ?\s&s ( ye>s ago4 ,x ought1 ,i %\ld ?9k1 to be some?+ t we w\ld s5se by employ+ at ! same "t ! visual s5se & ! s5se ( "t-passage4 ,9 fact1 ,i might v plausibly insi/ t1 by my v rem>ks ab\t x 9 ! above p>agraph1 ,i h s5s$ x4 ,m9k[ski1 h[ev]1 0 n worri$ ab\t ?is phase ( ! matt]4 ,he _h only to id5tify ! inv>iant expression = di/ance2 s5s+ x c\ld wait4 ,he f\nd1 ( c\rse1 t ?is expression 0 n ! ,euclidean expression = a f\r-dim5sional int]val4 ,he _h disc>d$ sev]al ( ! ,euclidean assumptions & c\ld n expect t ! po/ulate gov]n+ ! metric prop]ties ( ,euclid's space w\ld p]si/4 ,especially _h he violat$ ! ,euclidean canons 9 disc>d+1 ) ,e9/e91 ! notion t no?+ :i* may happ5 to a measur+ rod 9 ! way ( uni=m translation at high velocity c affect its measures4 ,s he _h to be prep>$ to f9d t 8 geometry 0 non-,euclidean2 yet x is surpris+ to le>n h[ slightly x deviates f t ( ,euclid4 ,)\t any ext5d$ discussion to support ! /atem5t1 we may say t he f\nd t :5 two obs]v]s measure ! "t- & ! space-coord9ates ( two ev5ts1 us+ ! assumptions & !re=e ! me?ods ( ,e9/e9 & h5ce subject+ !mselves to ! condition t _! measures ( ! pure "t-int]val & ( ! pure space-int]val betwe5 ^! ev5ts w n necess>ily be ! same1 !y w discov] t !y bo? get ! same value = ! expression ,s sqrt7,x - x7#b 7,y - y7#b 7,z - z7#b - 7,,ct - ,ct7#b14 ,if our acceptance ( ?is z ! num]ical measure ( ! sep>ation 9 space-"t betwe5 ! two ev5ts %\ld lead to contradiction we c\ld n s accept x4 ,no contradiction arises h[ev] & we may !re=e accept x4 ,& at once ! ma!matician is ready ) "s int]pretative rem>ks4 ,,! ,,curvature ,,( ,,space-,,"t ,! inv>iant expression = sep>ation1 x w be se51 is 9 ! same =m z t ( ! ,euclidean f\r-dim5sional inv>iant save = ! m9us sign be=e ! "t-diff]5ce 7! appe>ance ( ! con/ant ,c 9 connection ) ! "t coord9ate t is m]ely an adju/m5t ( units2 see page #aec74 ,?is tells u t n alone is ! geometry ( ! "t-space cont9uum non-,euclidean 9 its me?ods ( measurem5t1 b also 9 its results1 to ! ext5t t x possesses a curvature4 ,x comp>es ) ! ,euclidean f\r-dim5sional cont9uum 9 mu* ! same way t a sph]ical surface comp>es ) a plane4 ,z a matt] ( fact1 a m illum9at+ analogy "h w\ld be t betwe5 ! cyl9drical surface & ! plane1 ?\gh nei!r is q exact4 ,to make ?is cle> requires a little discussion ( an elem5t>y notion :i* we h n yet _h to consid]4 ,our ?ree-dim5sional exi/5ce (t5 r$uces1 = all practical purposes1 to a two-dim5sional "o4 ,! objects & ! ev5ts ( a c]ta9 room may q satisfactorily be def9$ by ?9k+ ( !m1 n z locat$ 9 space1 b z ly+ 9 ! floor ( ! room4 ,ma!matically ! ju/ification = ?is viewpo9t is got by say+ t we h elect$ to consid] a slice ( our ?ree-dim5sional _w ( ! sort :i* we "k z a plane4 ,:5 we consid] ?is plane & ! po9ts 9 x1 we f9d t we h tak5 a cross-section ( ! ?ree-dim5sional _w4 ,a l9e 9 t _w is n[ r$uc$1 = u1 to a s+le po9t--! po9t :]e x cuts our plane2 a plane is r$uc$ to a l9e--! l9e :]e x cuts our plane2 ! ?ree-dim5sional _w itself is r$uc$ to our plane itself4 ,ev]y?+ ?ree-dim5sional falls d[n into its %ad[ 9 our plane1 los+ 9 ! process t "o ( ! ?ree dim5sions :i* is n pres5t 9 our plane4 ,= simplicity's sake x is usual to take a cross-section ( space p>allel to "o ( our coord9ate axes4 ,we ?9k ( our ?ree dim5sions z ext5d+ 9 ! directions ( ^? axes2 & x is easi] to take a horizontal or v]tical section :i* %all simply wipe out "o ( ^! dim5sions ?an to take an oblique section :i* %all wipe out a dim5sion t consi/s p>tly ( our orig9al l5g?1 & p>tly ( our orig9al wid?1 & p>tly ( our orig9al height4 ,if we h a f\r-dim5sional manifold to beg9 )1 we may equally %ake out "o ( ! f\r dim5sions1 "o ( ! f\r coord9ates1 & consid] ! ?ree-dim5sional result ( ?is process z a cross-section ( ! orig9al f\r-dim5sional cont9uum4 ,& :]e1 9 cross-section+ a ?ree-dim5sion$ _w1 we h b ?ree *oices ( a coord9ate to elim9ate1 9 cross-section+ a _w ( f\r dim5sions we h f\r *oices4 ,by dropp+ out ei!r ! x1 or ! y1 or ! z1 or ! t1 we get a ?ree-dim5sion$ cross-section4 ,n[ our accu/om$ ?ree-dim5sional space is /rictly ,euclidean4 ,:5 we cross-section x1 we get a ,euclidean plane no matt] :at ! direction 9 :i* we make ! cut4 ,likewise ! ,euclidean plane is :olly ,euclidean1 because :5 we cross-section x 9 any direction :atev] we get a ,euclidean l9e4 ,a cyl9drical surface1 on ! o!r h&1 is nei!r :olly ,euclidean nor :olly non-,euclidean 9 ?is matt] ( cross-section+4 ,if we take a section 9 "o direction we get a ,euclidean l9e & if we take a section 9 ! o!r direction we get a circle 7if ! cyl9drical surface be a circul> "o74 ,& ( c\rse if we take an oblique section ( any sort1 x is nei!r l9e nor circle1 b a compromise betwe5 ! two--! significant ?+ be+ t x is /ill n a ,euclidean l9e4 ,! space-"t cont9uum pres5ts an analog\s situation4 ,:5 we cross-section x by dropp+ out any "o ( ! ?ree space dim5sions1 we get a ?ree-dim5sional complex 9 :i* ! di/ance =mula is /ill non-,euclidean1 reta9+ ! m9us sign be=e ! "t-diff]5ce & !re=e reta9+ ! geometric "* ( its p>5t4 ,b if we take our cross-section 9 su* a way z to elim9ate ! "t coord9ate1 ?is peculi>ity disappe>s4 ,! signs 9 ! inv>iant expression are !n all plus1 & ! cross-section is 9 fact our famili> ,euclidean ?ree-space4 ,if we set up a surface geometry on a sph]e1 we f9d t ! elim9ation ( "o dim5sion leaves u ) a l9e-geometry t is /ill non-,euclidean s9ce x p]ta9s to ! great circles ( ! sph]e r ?an to ,euclidean /raight l9es4 ,9 %ak+ ,m9k[ski's cont9uum d[n into a ?ree-dim5sional "o by elim9at+ any "o ( 8 coord9ates1 if we elim9ate ei!r ! x1 ! y or ! z1 we h left a ?ree-dim5sional geometry 9 :i* ! di/urb+ m9us sign /ill occurs 9 ! di/ance-=mula1 & :i* is !re=e /ill non-,euclidean4 ,if we omit ! t1 ?is does n occur4 ,we see1 !n1 t ! "t dim5sion is ! di/urb+ factor1 ! "o :i* gives to space-"t its non-,euclidean "* s f> z ! possession ( curvature is conc]n$4 ,& we see t ?is curvature is n ! same 9 all directions1 & 9 "o direction is actually z]o--:5ce ! attempt$ analogy ) a cyl9d] in/ead ( ) a sph]e4 ,_m writ]s on relativity try to give ! space-"t cont9uum an appeal to our reason & a "* ( inevitabl5ess by insi/+ on ! lack ( any fundam5tal di/9ction betwe5 space & "t4 ,! v expression = ! space-"t inv>iant d5ies ?is4 ,"t is di/+ui%able f space4 ,! ?ree dim5sions ( space are q indi/+ui%able--we c int]*ange !m )\t affect+ ! =mula1 we c drop "o out & nev] "k :i* is gone4 ,b ! v =mula s+les out "t z di/9ct f space1 z inh]5tly diff]5t 9 "s way4 ,x is n s inh]5tly diff]5t z we h always suppos$2 x is n suffici5tly diff]5t to (f] any ob/acle to our ?9k+ 9 t]ms ( ! f\r-dim5sional cont9uum4 ,b :ile we c gr\p space & "t toge!r 9 ?is way1 ?is does n mean at all t space & "t cease to diff]4 ,a cook may comb9e meat ) potatoes & call ! product ha%1 b meat & potatoes d n !reby become id5tical4#bbc ,,! ,,"q ,,( ,,visualization ,to ! layman !re is a great temptation to say t :ile1 ma!matically speak+1 ! space-"t cont9uum may be a great simplification1 x does n really repres5t ! ext]nal _w4 ,to be sure1 y c't see ! space-"t cont9uum 9 precisely ! same way t y c ! ?ree-dim5sional space cont9uum1 b ?is is only because ,e9/e9 f9ds ! "t dim5sion to be n q freely int]*angeable ) ! space dim5sion4 ,yet y d p]ceive ?is space-"t cont9uum1 9 ! mann] appropriate = its p]ception2 & x w\ld be j z s5sible to ?r[ out ! space cont9uum itself on ! gr\nd t p]ception ( ! two is n ( exactly ! same sort1 z to ?r[ out ! space-"t cont9uum on ?is gr\nd4 ,) appropriate conv5tions1 ei!r may /& z ! m5tal picture ( ! ext]nal _w2 x is = u to *oose :i* is ! m conv5i5t & useful image4 ,e9/e9 tells u t 8 image is ! bett]1 & tells u :y4 ,be=e we look into ?is1 we mu/ let him tell u some?+ m ab\t ! geometry ( 8 cont9uum4 ,:at he tells u is1 9 its ess5tials1 j ?is4 ,! obs]v] 9 a pure space cont9uum ( ?ree dim5sions f9ds t z he *anges 8 position1 8 "r-&-left1 8 backw>d-&-=w>d1 & 8 up-&-d[n are n fix$ directions inh]5t 9 nature1 b are fully int]*angeable4 ,! obs]v]s1 9 ! adjo9$ sket*1 ^: v]ticals are z indicat$ by ! arr[s1 f9d v diff]5t v]tical & horizontal compon5ts = ! di/ance betwe5 ! po9ts ,o & ,p2 a simil> situation w\ld prevail if we us$ all ?ree space directions4 ,! /atem5t analog\s to ?is = ,e9/e9's f\r-dim5sional cont9uum ( space & "t comb9$ is t1 z obs]v]s *ange _! relative motion1 _! "t axes take slightly diff]5t directions1 s t :at is purely space or purely "t = ! "o becomes space ) a small compon5t 9 ! "t direction1 or "t ) a small compon5t 9 ! space direction1 = ! o!r4 ,?is x w be se5 expla9s fully :y obs]v]s 9 relative motion c diff] ab\t space & "t measurem5ts4 ,we %\ld n be at all surpris$ if ! two obs]v]s ( ! figure report$ diff]5t values = horizontals & v]ticals2 we %\ld realize t :at 0 v]tical = "o _h become p>tly horizontal = ! o!r4 ,x is j s1 says ,e9/e91 ) 8 obs]v]s ( "t & space :o are 9 relative motion to "o ano!r2 :at "o sees z space ! o!r sees z p>tly "t1 because _! "t axes d n run q p>allel4 ,! natural "q "h1 ( c\rse1 is ,well1 :]e are _! "t axes8 ,if y "k :at to look =1 ( c\rse1 y ought to be able to p]ceive !m 9 j ! way y p]ceive ord9>y "t int]vals--) ! res]vation t !y are imag9>y1 aft] all1 j l y\r space axes1 & t y mu/ only expect to see !m 9 imag9ation4 ,if y look = a f\r? axis 9 ,euclidean ?ree-space to repres5t y\r "t axis1 y w ( c\rse n f9d x4 ,b y w by all means agree ) me t y\r "t runs 9 a def9ite direction2 & ?is x is t def9es y\r "t axis4 ,e9/e9 adds t if y & ,i are 9 relative motion1 my "t does n run 9 q ! same direction z y\rs4 ,h[ %all we prove x8 ,well1 h[ w\ld we prove x if he told u t our space axes did n run 9 precisely ! same direction8 ,( c\rse we c\ld n proce$ ?r\gh direct measures ^u ! axes !mselves2 we "k ^! are imag9>y4 ,:at we %\ld d w\ld be to /rike out1 ea* ( u1 a v long l9e inde$ 9 :at seem$ ! true horizontal direction2 & we %\ld hope t if we made !m long en\gh1 & measur$ !m accurately en\gh1 we %\ld be able to detect any div]g5ce t might exi/4 ,?is is precisely :at we mu/ d ) our "t axes if we wi% to v]ify ,e9/e9's /atem5t t !y are n precisely p>allel2 & :at bett] evid5ce c\ld we dem& ( ! tru? ( ?is /atem5t ?an ! evid5ce already pres5t$--t :5 we measure our respective "t compon5ts betwe5 two ev5ts1 we get diff]5t results8 ,,:at ,,x ,,all ,,leads ,,to ,! prec$+ *apt]s h be5 compil$ & writt5 ) a view to putt+ ! read] 9 a /ate ( m9d & 9 a /ate ( in=m$ness :i* %all enable him to d]ive pr(it f ! read+ ( ! actual compet+ essays :i* make up ! balance ( ! book4 ,= ?is purpose x has be5 pr(itable to take up 9 detail ! prelim9>ies ( ! ,special ,!ory ( ,relativity1 & to all[ ! ,g5]al ,!ory to g by default1 9 spite ( ! fact t x is ! latt] :i* con/itutes ,e9/e9's contribution ( importance to sci5ce4 ,! reason = ?is is precisely ! same z t = tak+ up ,euclidean geometry & ma/]+ x be=e proce$+ to ! /udy ( ,newtonian me*anics4 ,! fundam5tal ideas ( ! two !ories1 :ile by no means id5tical1 are 9 g5]al t]ms ! same2 & ! conditions surr\nd+ _! application to ! ,special ,!ory are s v mu* simpl] ?an ^? :i* confront u :5 we apply !m to ! m g5]al case1 t ?is may be tak5 z ! controll+ factor 9 a popul> pres5tation4 ,we _c omit ! ,g5]al ,!ory f consid]ation1 ( c\rse2 b we c omit x f our prelim9>y discussion1 & leave its developm5t to ! complete essays :i* foll[1 & :i* 9 almo/ e case give x ! l>g] half ( _! space :i* its l>g] cont5t dem&s4 ,9 ! process ( ! sl[ & difficult prep>ation ( ! lay m9d = ! assimilation ( an altoge!r new set ( fundam5tal ideas1 x is altoge!r desirable to give ! ,special ,!ory1 ) its simpl] applications ( ^! ideas1 a place out ( proportion to its importance 9 ,e9/e9's complet$ /ructure2 & ?is we h !re=e done4 ,! ,special ,!ory1 po/ulat+ ! relativity ( uni=m motion & d$uc+ ! consequ5ces ( t relativity1 is (t5 ref]r$ to z a special case ( ! ,g5]al ,!ory1 9 :i* ?is re/riction ( uni=mity is remov$4 ,?is is n /rictly speak+ correct4 ,! ,g5]al ,!ory1 :5 we h =mulat$ x1 w call our att5tion to some?+ :i* we really knew all ! "t1 b to :i* we *ose n to give he$--t 9 ! regions ( space to :i* we h access1 uni=m motion does n exi/4 ,all bodies 9 ^! regions are "u ! gravitational influ5ce ( ! o!r bodies !re91 & ?is influ5ce leads to accel]at$ motion4 ,no?+ 9 our univ]se c possibly travel at uni=m velocity2 ! int]f]5ce ( ! re/ ( ! bodies 9 ! univ]se prev5ts ?is4 ,obvi\sly1 we ought n to apply ! t]m special case to a case t nev] occurs4 ,nev]!less1 ?is case is ( extreme value to u 9 our m5tal processes4 ,_m ( ! motions ) :i* we are conc]n$ are s ne>ly at con/ant velocity t we f9d x conv5i5t to treat !m z ?\gh !y 7 uni=m1 ei!r ignor+ ! result+ error or correct+ = x at ! end ( our "w4 ,9 _m o!r cases we are able to le>n :at actually occurs "u accel]at$ motion by consid]+ :at w\ld h occurr$ "u uni=m motion 7 su* a ?+ possible4 ,sci5ce is full ( complications :i* we unravel 9 ?is fa%ion4 ,! physici/ deals ) gas pressures by assum+ temp]atures to be con/ant1 ?\gh he kn[s temp]ature nev] is con/ant2 & 9 turn he deals ) temp]atures by assum+ pressures to be con/ant4 ,aft] ?is1 he is able to pr$ict :at w happ5 :51 z 9 nature1 pressures & temp]atures are v>y+ simultane\sly4 ,by us+ z a *annel ( attack ! artificially simple case t nev] occurs1 we get a grip on ! complex case t gives u a true picture ( ! ph5om5on4 ,& because 9 actual nature we c come z close z we please to ?is artificial case1 by suppos+ ! v>iable factor to approa* con/ancy1 s :5 we assume x to be absolutely con/ant we speak ( ! result z ! limit+ case4 ,?is situation does n occur1 b is ! limit+ case = ^? t d occur4 ,:51 9 ! matt] ( motion1 we ab&on ! artificial1 limit+ case ( uni=m velocity & look into ! g5]al1 natural "o ( unre/rict$ motion1 we f9d t ! /ructure :i* we h built up to deal ) ! limit+ case provides u ) _m ( ! necess>y ideas & viewpo9ts4 ,?is is :at we expect--9 x lies ! value ( ! limit+ case4 ,we %all see t ! relativity ( "t & space1 e/abli%$ = ! limit+ case1 holds good 9 ! g5]al "o4 ,we %all see t ! idea ( ! f\r-dim5sional space-"t cont9uum z repres5t+ ! ext]nal _w p]si/s1 =m+ ! :ole backgr\nd ( ! ,g5]al ,!ory mu* m def9itely ?an 9 ! ,special ,!ory4 ,incid5tally we %all see t ! great] g5]ality ( ! case "u consid]ation w dem& a great] degree ( g5]ality 9 ! geometry ( ?is cont9uum1 a non-,euclideanism ( a mu* m :ole-he>t$ type ?an t ( ! ,special ,!ory4 ,b all ! revisions ( fundam5tal concepts :i* we h be5 at su* pa9s to make = ! sake ( ! ,special ,!ory w rema9 ) u 9 ! ,g5]al4 ,) ?is we may consid] our prelim9>y backgr\nd z e/abli%$1 & give our att5tion to ! essayi/s1 :o w try to take u m deeply into ! subject ?an we h yet gone1 )\t los+ u 9 its intricacies4 ,,vii ,,relativity ,! ,w9n+ ,essay 9 ! ,conte/ = ! ,eug5e ,higg9s #e1jjj ,prize ,,by ,,lyndon ,,bolton ,,s5ior ,,exam9]1 ,,briti% ,,pat5t ,,(fice ,,london ,! read] is probably acqua9t$ ) ! me?od ( specify+ positions ( po9ts 9 a plane by _! di/ances f two mutually p]p5dicul> l9es1 or if ! po9ts are 9 space by _! di/ances f ?ree mutually p]p5dicul> planes l adjac5t sides ( a flat-sid$ box4 ,! me?od is 9 fact 9 common use = exhibit+ relations betwe5 quantities by graphs or diagrams4 ,^! sets ( axes1 z !y are call$1 toge!r ) any scales us$ = measur+1 mu/ be suppos$ rigid1 o!rwise ! ev5ts or po9ts :i* !y are us$ to specify are indef9ite4 ,! l5g?s :i* locate any po9t ) ref]5ce to a set ( axes are call$ its coord9ates4 ,:5 su* sy/ems are us$ = physical purposes1 !y mu/ be supplem5t$ by clocks to enable ! times at :i* ev5ts occur to be det]m9$4 ,! clocks mu/ be syn*roniz$1 & mu/ g at ! same rate1 b x mu/ suffice "h to /ate t ?is is possible )\t indicat+ h[ ^! conditions c be atta9$4 ,a sy/em ( axes ) its clocks w h]e9aft] be call$ a ,frame ( ,ref]5ce1 & e obs]v] w be suppos$ to be provid$ ) su* a frame p>tak+ ( 8 motion4 ,all ! objects :i* p>take ( an obs]v]'s motion w be call$ 8 sy/em4 ,x is a "q :e!r among all possible frames ( ref]5ce any "o frame or class ( frames is m suit$ ?an ano!r = ! ma!matical /atem5t ( physical laws4 ,?is is = exp]i5ce to decide1 & a ,pr9ciple ( ,relativity is a /atem5t embody+ ! answ]4 ,,! ,,me*anical ,,pr9ciple ,,( ,,relativity ,x has be5 asc]ta9$ t all su* frames are equally suitable = ! ma!matical /atem5t ( g5]al me*anical laws1 provid$ t _! motion is rectil9e> & uni=m & )\t rotation4 ,?is fact is compreh5d$ 9 ! g5]al /atem5t t all unaccel]at$ frames ( ref]5ce are equival5t = ! /atem5t ( ! g5]al laws ( me*anics4 ,?is is ! me*anical pr9ciple ( relativity4 ,x is well recogniz$ h[ev] t ! laws ( dynamics z hi!rto /at$ involve ! assumptions t ! l5g?s ( rigid bodies are unaffect$ by ! motion ( ! frame ( ref]5ce1 & t measur$ times are likewise unaffect$2 t is to say t any l5g? measur$ on 8 own sy/em by ei!r ( two relatively mov+ obs]v]s appe>s ! same to bo? obs]v]s1 or t l5g?s ( objects & rates ( clocks d n alt] :atev] ! motion relative to an obs]v]4 ,^! assumptions seem s obvi\s t x is sc>cely p]ceiv$ t !y are assumptions at all4 ,yet ?is is ! case1 & z a matt] ( fact !y are bo? untrue4 ,,! ,,special ,,pr9ciple ,,( ,,relativity ,al?\gh all unaccel]at$ frames ( ref]5ce are equival5t = ! purposes ( me*anical laws1 ?is is n ! case = physical laws g5]ally z long z ! above suppositions are adh]$ to4 ,electromagnetic laws d alt] _! =m accord+ to ! motion ( ! frame ( ref]5ce2 t is to say1 if ^! suppositions are true1 electromagnetic ag5cies act 9 diff]5t ways accord+ to ! motion ( ! sy/em 9 :i* !y occur4 ,!re is no?+ a priori impossible 9 ?is1 b x does n agree ) exp]im5t4 ,! motion ( ea* locality on ! e>? is cont9ually *ang+ f h\r to h\r b no correspond+ *anges occur 9 electromagnetic actions4 ,x has h[ev] be5 asc]ta9$ t on disc>d+ ^! suppositions ! difficulty disappe>s1 & electromagnetic laws reta9 _! =m "u all circum/ances ( unaccel]at$ motion4 ,accord+ to ! !ory ( relativity1 ! correct view :i* replaces ^! suppositions is d$ucible f ! foll[+ po/ulates3 7#a7 ,by no exp]im5t conduct$ on 8 own sy/em c an obs]v] detect ! unaccel]at$ motion ( 8 sy/em4 7#b7 ,! measure ( ! velocity ( light 9 vacuo is unaffect$ by relative motion betwe5 ! obs]v] & ! s\rce ( light4 ,bo? ^! po/ulates are well e/abli%$ by exp]im5t4 ,! fir/ may be illu/rat$ by ! famili> difficulty ( det]m9+ :e!r a sl[ly mov+ tra9 "o happ5s to be sitt+ 91 or an adjac5t "o1 is 9 motion4 ,! pass5g] has ei!r to wait = bumps 7t is1 accel]ations7 or else he has to look out at "s adjac5t object :i* he kn[s to be fix$1 su* z a build+ 7t is1 he has to p]=m an exp]im5t on some?+ outside 8 sy/em71 be=e he c decide4 ,! second po/ulate is an obvi\s consequ5ce ( ! wave !ory ( light4 ,j z waves 9 wat]1 once />t$ by a %ip1 travel ?r\gh ! wat] ) a velocity indep5d5t ( ! %ip1 s waves 9 space travel onw>d ) a spe$ be>+ no relation to t ( ! body :i* orig9at$ !m4 ,! /atem5t h[ev] is bas$ on exp]im5t1 & c be prov$ indep5d5tly ( any !ory ( light4 ,x is n difficult to d$uce f ^! po/ulates c]ta9 rem>kable conclusions relat+ to ! sy/ems ( two obs]v]s1 ,a & ,b1 9 relative motion1 among !m ! foll[+3 7#a7 ,objects on ,b's sy/em appe> to ,a to be %ort] 9 ! direction ( relative motion ?an !y appe> to ,b4 7#b7 ,?is op9ion is reciprocal4 ,b ?9ks t ,a's measurem5ts on ,a's sy/em are too great4 7#c7 ,simil>ly = times3 ea* obs]v] ?9ks t ! o!r's clocks h a sl[] rate ?an 8 own1 s t ,b's durations ( "t appe> %ort] to ,b ?an to ,a1 & conv]sely4 7#d7 ,ev5ts :i* appe> simultane\s to ,a d n 9 g5]al appe> s to ,b1 & conv]sely4 7#e7 ,l5g?s at "r angles to ! direction ( motion are unaffect$4 7#f7 ,^! effects v>y ) ! ratio ( ! relative velocity to t ( light4 ,! great] ! relative velocity1 ! great] ! effects4 ,!y vani% if !re is no relative velocity4 7#g7 ,= ord9>y velocities ! effects are s small z to escape notice4 ,! rem>kable po9t h[ev] is _! occurr5ce r ?an _! magnitude4 7#h7 ,! obs]v]s simil>ly =m diff]5t e/imates ( ! velocities ( bodies on ea* o!r's sy/ems4 ,! velocity ( light h[ev] appe>s ! same to all obs]v]s4 ,tak+ into acc\nt ^! revis$ views ( l5g?s & times ! me*anical pr9ciple ( relativity may be ext5d$ to physical laws g5]ally z foll[s3 ,all unaccel]at$ frames ( ref]5ce are equival5t = ! /atem5t ( ! g5]al laws ( physics4 ,9 ?is =m ! /atem5t is call$ ! ,special1 or ,re/rict$1 ,pr9ciple ( ,relativity1 because x is re/rict$ to unaccel]at$ frames ( ref]5ce4 ,naturally ! laws ( classical me*anics n[ require "s modification1 s9ce ! suppositions ( unalt]able l5g?s & times no long] apply4 ,,! ,,f\r ,,dim5sional ,,cont9uum ,l5g?s & times !re=e h n ! absolute "* =m]ly attribut$ to !m4 ,z !y pres5t !mselves to u !y are relations betwe5 ! object & ! obs]v] :i* *ange z _! motion relative to him *anges4 ,"t c no long] be reg>d$ z some?+ indep5d5t ( position & motion1 & ! "q is :at is ! reality8 ,! only possible answ] is t objects mu/ be reg>d$ z exi/+ 9 f\r dim5sions1 ?ree ( ^! be+ ! ord9>y ones ( l5g?1 bread? & ?ickness1 & ! f\r?1 "t4 ,! t]m space is applicable only by analogy to su* a region2 x has be5 call$ a cont9uum1 & ! analogue ( a po9t 9 ord9>y ?ree-dim5sional space has be5 appropriately call$ an ev5t4 ,by dim5sion mu/ be und]/ood m]ely "o ( f\r indep5d5t quantities :i* locate an ev5t 9 ?is cont9uum4 ,9 ! nature ( ! case any cle> m5tal picture ( su* a cont9uum is impossible2 mank9d does n possess ! requisite faculties4 ,9 ?is respect ! ma!matician enjoys a great advantage4 ,n t he c picture ! ?+ m5tally any bett] ?an o!r p1 b 8 symbols enable him to ab/ract ! relevant prop]ties f x & to express !m 9 a =m suitable = exact treatm5t )\t ! necessity ( pictur+ any?+1 or tr\bl+ :e!r or n ! prop]ties are ^? on :i* o!rs rely = _! conceptions4 ,,gravitation ,,& ,,accel]ation ,! limitation ( /atem5ts ( g5]al law to uni=mly mov+ sy/ems is h>dly satisfactory4 ,! v concept ( g5]al law is oppos$ to ! notion ( limitation4 ,b ! difficulties ( =mulat+ a law s t ! /atem5t ( x %all hold good = all obs]v]s1 ^: sy/ems may be mov+ ) diff]5t & possibly v>iable accel]ations1 are v great4 ,accel]ations imply =ces :i* might be expect$ to upset ! =mulation ( any g5]al dynamical pr9ciples1 & besides1 ! behavior ( measur+ rods & clocks w\ld be s erratic z to r5d] unmean+ su* t]ms z rigidity & measur$ "t1 & !re=e to preclude ! use ( rigid scales1 or ( a rigid frame ( ref]5ce :i* is ! basis ( ! =ego+ inve/igation4 ,! foll[+ example tak5 f ,e9/e9 w make ?is cle>1 & also indicate a way out ( ! difficulty4 ,a rotat+ sy/em is *os51 b s9ce rotation is only a p>ticul> case ( accel]ation x w s]ve z an example ( ! me?od ( treat+ accel]at$ sy/ems g5]ally4 ,moreov]1 z x w be se51 ! attribution ( accel]ation to ! sy/em is simply a piece ( scaffold+ :i* c be disc>d$ :5 ! g5]al !ory has be5 fur!r develop$4 ,let u note ! exp]i5ces ( an obs]v] on a rotat+ disk :i* is isolat$ s t ! obs]v] has no direct means ( p]ceiv+ ! rotation4 ,he w !re=e ref] all ! occurr5ces on ! disk to a frame ( ref]5ce fix$ ) respect to x1 & p>tak+ ( its motion4 ,he w notice z he walks ab\t on ! disk t he himself & all ! objects on x1 :atev] _! con/itution or /ate1 are act$ ^u by a =ce direct$ away f a c]ta9 po9t ^u x & increas+ ) ! di/ance f t po9t4 ,?is po9t is actually ! c5t] ( rotation1 ?\gh ! obs]v] does n recognize x z su*4 ,! space on ! disk 9 fact pres5ts ! *>act]i/ic prop]ties ( a gravitational field4 ,! =ce diff]s f gravity z we "k x by ! fact t x is direct$ away f in/ead ( t[>d a c5t]1 & x obeys a diff]5t law ( di/ance2 b ?is does n affect ! *>act]i/ic prop]ties t x acts on all bodies alike1 & _c be scre5$ f "o body by ! int]position ( ano!r4 ,an obs]v] aw>e ( ! rotation ( ! disk w\ld say t ! =ce 0 c5trifugal =ce2 t is1 ! =ce due to in]tia :i* a body always ex]ts :5 x is accel]at$4 ,next suppose ! obs]v] to /& at ! po9t ( ! disk :]e he feels no =ce1 & to wat* someone else comp>+1 by repeat$ applications ( a small measur+ rod1 ! circumf]5ce ( a circle hav+ its c5t] at t po9t1 ) its diamet]4 ,! measur+ rod :5 laid along ! circumf]5ce is mov+ l5g?wise relatively to ! obs]v]1 & is !re=e subject to contraction by 8 reckon+4 ,:5 laid radially to measure ! diamet] ?is contraction does n occur4 ,! rod w !re=e require a great] proportional numb] ( applications to ! circumf]5ce ?an to ! diamet]1 & ! numb] repres5t+ ! ratio ( ! circumf]5ce ( ! circle to ! diamet] ?us measur$ w !re=e be great] ?an #c4adaei1 :i* is its normal value4 ,moreov] ! relative velocity decreases z ! c5t] is approa*$1 s t ! contraction ( ! measur+ rod is less :5 appli$ to a small] circle2 & ! ratio ( ! circumf]5ce to ! diamet]1 :ile /ill great] ?an ! normal1 w be ne>] to x ?an be=e1 & ! small] ! circle ! less ! diff]5ce f ! normal4 ,= circles ^: c5t]s are n at ! po9t ( z]o =ce ! confusion is /ill great]1 s9ce ! velocities relative to ! obs]v] ( po9ts on !m n[ *ange f po9t to po9t4 ,! :ole s*eme ( geometry z we "k x is ?us disorganiz$4 ,rigidity becomes an unmean+ t]m s9ce ! /&>ds by :i* alone rigidity c be te/$ are !mselves subject to alt]ation4 ,^! facts are express$ by ! /atem5t t ! obs]v]'s measur$ space is non-,euclidean2 t is to say1 9 ! region "u consid]ation measurem5ts d n con=m to ! sy/em ( ,euclid4 ,! same confusion arises 9 reg>d to clocks4 ,no two clocks w 9 g5]al g at ! same rate1 & ! same clock w alt] its rate :5 mov$ ab\t4 ,,! ,,g5]al ,,pr9ciple ,,( ,,relativity ,! region !re=e requires a space-"t geometry ( its own1 & be x not$ t ) ?is special geometry is associat$ a def9ite gravitational field1 & if ! gravitational field ceases to exi/1 = example if ! disk 7 br\ght to re/1 all ! irregul>ities ( measurem5t disappe>1 & ! geometry ( ! region becomes ,euclidean4 ,?is p>ticul> case illu/rates ! foll[+ propositions :i* =m ! basis ( ?is "p ( ! !ory ( relativity3 7#a7 ,associat$ ) e gravitational field is a sy/em ( geometry1 t is1 a /ructure ( measur$ space peculi> to t field4 7#b7 ,in]tial mass & gravitational mass are "o & ! same4 7#c7 ,s9ce 9 su* regions ord9>y me?ods ( measurem5t fail1 ow+ to ! indef9it5ess ( ! /&>ds1 ! sy/ems ( geometry mu/ be indep5d5t ( any p>ticul> measurem5ts4 7#d7 ,! geometry ( space 9 :i* no gravitational field exi/s 9 ,euclidean4 #a ,! connection betwe5 a gravitational field & its appropriate geometry sugge/$ by a case 9 :i* accel]ation 0 _! common cause is ?us assum$ to exi/ f :atev] cause ! gravitational field arises4 ,?is ( c\rse is pure hypo!sis1 to be te/$ by exp]im5tal trial ( ! results d]iv$ !refrom4 ,gravitational fields arise 9 ! pres5ce ( matt]4 ,matt] is !re=e presum$ to be accompani$ by a special geometry1 z ?\gh x imp>t$ "s peculi> k9k or twi/ to space :i* r5d]s ! me?ods ( ,euclid inapplicable1 or r we %\ld say t ! geometry ( ,euclid is ! p>ticul> =m :i* ! m g5]al geometry assumes :5 matt] is ei!r abs5t or s remote z to h no influ5ce4 ,! dropp+ ( ! notion ( accel]ation is aft] all n a v viol5t *ange 9 po9t ( view1 s9ce "u any circum/ances ! obs]v] is suppos$ to be unaw>e ( ! accel]ation4 ,all t he is aw>e ( is t a gravitational field & 8 geometry coexi/4 ,! prospect ( con/ruct+ a sy/em ( geometry :i* does n dep5d ^u measurem5t may n at fir/ sight seem hopeful4 ,nev]!less ?is has be5 done4 ,! sy/em consi/s 9 def9+ po9ts n by _! di/ances f l9es or planes 7= ?is w\ld involve measurem5t7 b by assign+ to !m arbitr>y numb]s :i* s]ve z labels be>+ no relation to measur$ di/ances1 v mu* z a h\se is locat$ 9 a t[n by its numb] & /reet4 ,if ?is label+ be done sy/ematically1 reg>d be+ _h to ! condition t ! label-numb]s ( po9ts :i* are close toge!r %\ld diff] f "o ano!r by inf9itesimal am\nts only1 x has be5 f\nd t a sy/em ( geometry c actually be work$ out4 ,p]haps ?is w appe> less artificial :5 ! fact is call$ to m9d t ev5 :5 /&>ds ( l5g? are available no m c be done to r5d] l5g?s ( objects am5able to calculation ?an to assign numb]s to !m1 & ?is is precisely :at is done 9 ! pres5t case4 ,?is sy/em ( label+ goes by ! "n ( ,gaussian coord9ates aft] ! ma!matician ,gauss :o propos$ x4 ,x is 9 t]ms ( ,gaussian coord9ates t physical laws mu/ be =mulat$ if !y are to h _! wide/ g5]ality1 & ! g5]al pr9ciple ( relativity is t all ,gaussian sy/ems are equival5t = ! /atem5t ( g5]al physical laws4 ,= ?is purpose ! label+ process is appli$ n to ord9>y space b to ! f\r dim5sional space-"t cont9uum4 ,! concept is some:at difficult & x may easily be aggravat$ into impossibility by anyone :o ?9ks t he is expect$ to visualize x4 ,=tunately ?is is n necess>y2 x is m]ely "o ( ^! irrelevancies to :i* ^? :o are unaccu/om$ to ?9k 9 symbols are liable4 ,x w n[ be se5 t among physical laws ! law ( gravitation /&s pre-em95t1 = x is gravitat+ matt] :i* det]m9es ! geometry1 & ! geometry det]m9es ! =m ( e o!r law4 ,! connection betwe5 ! geometry & gravitation is ! law ( gravitation4 ,?is law has be5 work$ out1 ) ! result t ,newton's law ( ! inv]se squ>e is f\nd to be approximate only1 b s closely approximate z to acc\nt = ne>ly all ! motions ( ! heav5ly bodies )9 ! limits ( obs]vation4 ,x has already be5 se5 t dep>ture f ! ,euclidean sy/em is int5sifi$ by rapidity ( motion1 & ! movem5ts ( ^! bodies are usually too sl[ = ?is dep>ture to be manife/4 ,9 ! case ( ! planet ,m]cury ! motion is suffici5tly rapid1 & an irregul>ity 9 its motion :i* long puzzl$ a/ronom]s has be5 expla9$ by ! m g5]al law4 ,ano!r d$uction is t light is subject to gravitation4 ,?is has giv5 rise to two pr$ictions1 "o ( :i* has be5 v]ifi$4 ,! v]ification ( ! o!r is z yet unc]ta91 ?\gh ! extreme difficulty ( ! necess>y obs]vations may acc\nt = ?is4 ,s9ce light is subject to gravitation x foll[s t ! con/ancy ( ! velocity ( light assum$ 9 ! e>li] "p ( ?is pap] does n obta9 9 a gravitational field4 ,!re is really no inconsi/5cy4 ,! velocity ( light is con/ant 9 ! abs5ce ( gravitation1 a condition :i* unaccel]at$ motion implies4 ,! special pr9ciple ( relativity is !re=e a limit+ case ( ! g5]al pr9ciple4 ,,viii ,,! ,,new ,,concepts ,,( ,,"t ,,& ,,space ,! ,essay 9 ,behalf ( ,:i* ! ,greate/ ,numb] ( ,diss5t+ ,op9ions ,h ,be5 ,record$ ,,by ,,montgom]y ,,francis ,,new ,,york ,we h all _h exp]i5ces1 on tra9s & boats1 illu/rat+ our inability to tell1 )\t look+ (f to "s ext]nal body1 :e!r we are at re/ or mov+ uni=mly2 & :5 we d s look1 to tell1 )\t ref]5ce to ! gr\nd or "s o!r po9t ext]nal to bo? sy/ems1 :e!r ours or ! o!r be ! seat ( motion4 ,uni=m motion mu/ be relative1 because we f9d n[h]e 9 ! univ]se a body 9 ! unique /ate ( absolute re/ f :i* alone absolute motion might be measur$4 ,true1 ! wave !ory ( light ) its homog5e\s space-fill+ e!r seem$ to provide a ref]5ce /&>d = ! concept ( absolute motion1 & = its measurem5t by exp]im5t ) light rays4 ,b :5 ,mi*elson & ,morley look$ = ?is absolute motion !y f\nd no trace ( x4 ,to ! physici/1 obs]vational /ud5t ( ! ext]nal _w1 no?+ exi/s save obs]vationally2 :at he c nev] obs]ve is n !re4 ,s3 ,i4 ,by no means :atev] may we reg>d uni=m /raight-l9e motion z o!r ?an relative4 ,z a fur!r direct consequ5ce ( ! ,mi*elson-,morley exp]im5t we h3 ,,ii4 ,light 9 a vacuum pres5ts ! same velocity1 ,c #ahf1ccj miles p] second1 to all obs]v]s :atev] _! velocity ( relative motion4 ,9 addition to be+ exp]im5tally e/abli%$1 ?is is necess>y to support ,i1 = if light w di/+ui% betwe5 our velocities1 its m$ium is necess>ily a univ]sal /&>d = absolute motion4 ,b x is contr>y to common s5se to suppose t if ,i pass y at #ajj miles p] h\r1 ! same light impulse c pass u bo? at ! same spe$1 ,c4 ,we feel1 in/9ctively1 t space & "t are n s con/itut$ z to make ?is possible4 ,b ! fact has be5 repeat$ly demon/rat$4 ,& :5 common s5se & fundam5tal concepts cla% ) facts1 x is n ! facts t mu/ yield4 ,we h surviv$ su* crises1 notably "o :]e we _h to *ange ! fundam5tal concept ( up-&-d[n2 if ano!r "o is "h1 says ,e9/e91 let u meet x4 ,?is ! ,special ,!ory ( ,relativity does4 ,x accepts ,po/ulates ,i & ,,ii above2 _! consequ5ces x d$uces & int]prets4 ,= ext5sive demon/ration ( ^! ,i lack space1 & ?is has be5 satisfactorily done by o!rs s x is n my *ief duty2 b cle>ly !y w be />tl+4 ,= ! v ray ( light :i* refuses to recognize our relative motion is ! m$ium ?r\gh :i* ,i mu/ obs]ve y\r sy/em & y m9e4 ,x turns out t ,i get diff]5t values = l5g?s & "t int]vals 9 y\r sy/em ?an y get1 & vice v]sa4 ,& we are bo? "r6 ,= me to accept y\r correction 7 = me to admit t y are at absolute re/ & ,i 9 absolute motion1 t y\r measure ( light velocity is "r & m9e wrong3 admissions b>r$ by ! po/ulates4 ,we h no?+ to correct2 we c only recognize ! reason = ! discrepancy2 & kn[+ our relative velocity1 ea* c calculate f 8 own results :at ! o!r's w be4 ,we f9d1 ( c\rse1 t at ord9>y velocities ! discrepancy is _m times too small = detection2 b at relative velocities at all comp>able ) t ( light x rises above ! obs]vational horizon4 ,to inquire ! true l5g? is mean+less4 ,*icago is ea/ ( ,d5v]1 we/ ( ,pittsburgh1 s\? ( ,milwaukee2 we d n consid] ?is contradictory1 or dem& ! true direction ( ,*icago4 ,e9/e9 f9ds t ! concept ( l5g?1 betwe5 po9ts 9 space or ev5ts 9 "t1 does n z we _h suppos$ repres5t an intr9sic prop]ty ( ! po9ts or ! ev5ts4 ,l direction1 x is m]ely a relation betwe5 ^! & ! obs]v]--a relation ^: value *anges ) ! obs]v]'s velocity relative to ! object4 ,if our ideas ( ! "p play$ 9 ! _w by "t & space d n p]mit u to believe ?is1 we mu/ alt] ^! ideas4 ,let u see h[ we may d ?is4 ,a ,,_w ,,( ,,po9ts ,to deal ) po9ts 9 a plane ! ma!matician draws two p]p5dicul> l9es1 & locates any po9t1 z ,p1 by measur+ its di/ances1 ,x & ,y1 f ^! coord9ate axes4 ,! directions ( 8 axes acquire = him a peculi> significance1 /&+ out above o!r directions2 he is apt to measure ! di/ances ,x-x & ,y-y betwe5 ! po9ts ,p & ,q 9 ^! directions1 in/ead ( measur+ ! s+le di/ance ,,pq4 ,we d ! same ?+ :5 we say t ! railroad /ation is five blocks nor? & two ea/4 ,! ma!matician visualizes himself z an obs]v]1 locat$ on 8 coord9ate framework4 ,= ano!r obs]v] on ano!r framework1 ! horizontal & v]tical di/ances ,x'-x' & ,y'-y' betwe5 ,p & ,q are diff]5t4 ,b = bo?1 ! di/ance f ,p direct to ,q is ! same4 ,9 ea* case ! "r triangle tells u t3 ,,pq sqrt7,x-x7#b 7,y-y7#b sqrt7,x'-x'7#b 7,y'-y'7#b ,imag9e an obs]v] s dom9at$ by 8 coord9ate sy/em t he kn[s no way ( relat+ ,p ) ,q save by _! horizontal & v]tical sep>ation4 ,8 :ole s*eme ( ?+s w\ld be %att]$ by ! sugge/ion t o!r obs]v]s on o!r ref]5ce frames f9d diff]5t horizontal & v]tical compon5ts4 ,we h to %[ him ! l9e ,,pq4 ,we h to conv9ce him t ?is l5g? is ! absolute prop]ty enjoy$ by 8 pair ( po9ts2 t horizontals & v]ticals are m]ely relations betwe5 ! po9ts & ! obs]v]1 result ( ! obs]v]'s hav+ analyz$ ! di/ance ,,pq into two compon5ts2 t diff]5t obs]v]s effect ?is decomposition diff]5tly2 t ?is seems n to make s5se to him only because ( 8 errone\s concept ( a fundam5tal diff]5ce betwe5 v]ticals & horizontals4 ,,! ,,f\r-,,dim5sional ,,_w ,,( ,,ev5ts ,we too h creat$ a di/9ction 9 our m9ds correspond+ to no suffici5t reality4 ,our m9ds seize on "t z inh]5tly sep>able f space4 ,we see ! _w made up ( ?+s 9 a cont9uum ( ?ree space dim5sions2 to make ?is dead _w live !re runs ?r\gh x a "o-dim5sional "t cont9uum1 impos$ f )\t1 unrelat$4 ,b did y ev] obs]ve any?+ sugge/+ ! pres5ce ( "t 9 ! abs5ce ( space1 or vice v]sa8 ,no2 ^! vessels ( ! univ]se always occur toge!r4 ,association ( ! space dim5sions into a manifold f :i* "t is exclud$ is purely a ph5om5on ( ! m9d4 ,! space cont9uum _c beg9 to exi/ until ! "t dim5sion is suppli$1 nor c "t exi/ )\t a place to exi/ 94 ,! ext]nal _w t we obs]ve is compos$1 n ( po9ts1 b ( ev5ts4 ,if a po9t lacks position 9 "t x does n exi/2 give x ?is position & x becomes an ev5t4 ,?is _w ( ev5ts is f\r-dim5sional--:i* means no?+ m t]rify+ ?an t y mu/ make f\r measures to locate an ev5t4 ,x does n mean1 at all1 t y mu/ visualize f\r mutually p]p5dicul> l9es 9 y\r accu/om$ ?ree-space or 9 a f\r-space analog\s to x4 ,if ?is _w ( f\r dim5sions seems to lack reality y w be able to exhibit no bett] reality = y\r old ideas4 ,"t belongs1 )\t "q2 & n z an aft]?\ght1 b z "p ( ! _w ( ev5ts4 ,to locate an ev5t we use f\r measures3 ,x1 ,y & ,z = space1 ,t = "t4 ,us+ ! same ref]5ce frame = "t & space1 we locate a second ev5t by ! measures x1 y1 z1 t4 ,m9k[ski %[$ t ! quantity sqrt7,x-x7#b 7,y-y7#b 7,z-z7#b - 7,,ct-,ct7#b is ! same = all obs]v]s1 no matt] h[ diff]5t _! x's1 y's1 z's & t's2 j z 9 ! plane ! quantity sqrt7,x-x7#b 7,y-y7#b is ! same = all obs]v]s1 no matt] h[ diff]5t _! x's & y's4 ,su* a quantity1 hav+ ! same value = all obs]v]s1 is absolute4 ,9 ! plane x repres5ts ! true1 absolute di/ance betwe5 ! po9ts--_! intr9sic prop]ty4 ,9 deal+ ) ev5ts x repres5ts ! true1 absolute int]val1 9 "t & space toge!r betwe5 ! ev5ts4 ,x is n space1 nor "t1 b a comb9ation ( ! two4 ,we h always brok5 x d[n into sep>ate space & "t compon5ts4 ,9 ?is we are z naive z ! plane obs]v] :o c\ld n visualize ! di/ance ,,pq until x 0 split into sep>ate horizontals & v]ticals4 ,he und]/ood ) difficulty t ano!r obs]v]1 employ+ a diff]5t ref]5ce frame because 9 diff]5t position1 w\ld make ! decomposition diff]5tly4 ,we und]/& ) difficulty t ano!r obs]v]1 employ+ a diff]5t ref]5ce frame because 9 uni=m motion relative to u1 w decompose ! int]val betwe5 ev5ts into "t & space compon5ts diff]5t f ours4 ,"t & space are relative to ! obs]v]2 only ! int]val repres5t+ space-"t is absolute4 ,s common s5se /&s reconcil$ to ! ,special ,!ory ( ,relativity4 ,,successive ,,/eps ,,t[>d ,,g5]ality ,is !n our labori\sly acquir$ geometry ( po9ts 9 a ?ree-dim5sional space to g into ! disc>d8 ,by no means4 ,jeans1 inve/igat+ ! equilibrium ( gase\s masses1 f\nd ! g5]al case too difficult = direct attack4 ,s he consid]$ ! case :]e ! masses involv$ are homog5e\s & incompressible4 ,?is nev] occurs2 b x ?r[s su* light on ! g5]al case z to po9t ! way t[>d attack on x4 ,euclidean geometry excludes motion1 save t eng9e]$ by ! obs]v]2 & !n ! "t is immat]ial4 ,"t does n ent] at all2 ! ?ree space dim5sions suffice4 ,?is simple case nev] occurs :]e matt] exi/s2 b its conclusions are ( value 9 deal+ ) m g5]al cases4 ,:5 we look into a _w alleg$ to be t ( ,euclid & f9d motion1 we may reta9 ! ,euclidean concept ( :at con/itutes ! _w & inv5t a ma*9]y to acc\nt = ! motion2 or we may ab&on ! ,euclidean _w1 z inadequate1 9 favor ( a m g5]al "o4 ,we h adopt$ ! second alt]native4 ,newton's laws tells u t a body free to move w d s1 proce$+ 9 a /raight l9e at uni=m velocity until int]f]$ )4 ,we d n ask1 nor does ! !ory tell u1 :5ce comes ! initial motion4 ,!re is no ma*9]y to produce x2 x is an inh]5t prop]ty ( ,newton's _w--assur$ by ! sup]position ( ! "t cont9uum ^u ,euclid's _w to make ,newton's1 accept$ )\t "q along ) t _w itself4 ,b ,newton saw t 8 _w ( uni=m motion1 l ,euclid's1 0 nev] realiz$4 ,9 ! neighborhood ( "o p>ticle a second is int]f]$ )1 =c$ to give up its uni=m motion & acquire a con/ant accel]ation4 ,?is ,newton expla9$ by employ+ ! fir/ ( ! alt]natives m5tion$ above4 ,he tells u t 9 connection ) all matt] !re exi/s a =ce :i* acts on o!r matt] 9 a c]ta9 way4 ,he does n display ! actual ma*9]y ?r\gh :i* ?is =ce works1 because he c\ld n discov] any ma*9]y2 he _h to /op ) 8 brilliant g5]alization ( ! obs]v$ facts4 ,& all 8 successors h fail$ to detect ! slighte/ trace ( a ma*9]y ( gravitation4 ,e9/e9 asks :e!r ?is is n because ! ma*9]y is abs5t--because gravitation1 l position 9 ,euclid's _w & motion 9 ,newton's1 is a fundam5tal prop]ty ( ! _w 9 :i* x occurs4 ,8 po9t ( attack "h lay 9 precise =mulation ( c]ta9 famili> facts t _h nev] be5 adequately appreciat$4 ,^! facts indicate t ev5 accel]at$ motion is relative1 9 spite ( its app>5tly real & absolute effects4 ,,gravitation ,,& ,,accel]ation ,an obs]v] 9 a clos$ comp>tm5t1 mov+ ) con/ant accel]ation ?r\gh empty space1 f9ds t ! bottom ( 8 cage cat*es up ) objects t he releases2 t x presses on 8 feet to give him ! s5sation ( weight1 etc4 ,x displays all ! effects t he w\ld expect if x 7 at re/ 9 a gravitational field4 ,on ! o!r h&1 if x 7 fall+ freely "u gravitational influ5ce1 its occupant w\ld s5se no weight1 objects releas$ w\ld n leave 8 h&1 ! reaction f 8 e motion w\ld *ange 8 e position 9 8 cage1 & he c\ld equally well assume himself at re/ 9 a region ( space free f gravitational action4 ,accel]at$ motion may always be int]pret$1 by ! obs]v] on ! sy/em1 z ord9>y =ce effects on 8 mov+ sy/em1 or z gravitational effects on 8 sy/em at re/4 ,an alt]native /atem5t ( ! ,special ,!ory is t ! obs]v$ ph5om5a ( uni=m motion may equally be acc\nt$ = by suppos+ ! object 9 motion & ! obs]v] ) 8 ref]5ce frame at re/1 or vice v]sa4 ,we may simil>ly /ate ! ,g5]al ,!ory3 ,! obs]v$ ph5om5a ( uni=mly accel]at$ motion may 9 e case be expla9$ on a basis ( /ation>y obs]v] & accel]at$ objective1 or ( /ation>y objective ) ! obs]v] & 8 ref]5ce sy/em 9 accel]at$ motion4 ,gravitation is "o ( ^! ph5om5a4 ,x foll[s t if ! obs]v] enjoy prop]ly accel]at$ axes 79 "t-space1 ( c\rse71 ! absolute "* ( ! _w ab\t him mu/ be su* z to pres5t to him ! ph5om5on ( gravitation4 ,x rema9s only to id5tify ! sort ( _w1 ( :i* gravitation z x is obs]v$ w\ld be a fundam5tal *>act]i/ic4 ,euclid's & ,newton's sy/ems /& z fir/ & second approximations to t _w4 ,! ,special ,relativity ,!ory con/itutes a correction ( ,newton1 presumably because x is a ?ird approximation4 ,we mu/ seek 9 x ^? features :i* we may mo/ hopefully c>ry along1 into ! /ill m g5]al case4 ,newton's sy/em reta9$ ! geometry ( ,euclid4 ,b ,m9k[ski's inv>iant expression tells u t ,e9/e9 has _h to ab&on ?is2 = 9 ,euclidean geometry ( f\r dim5sions ! inv>iant takes ! =m3 sqrt7,x-x7#b 7,y-y7#b 7,z-z7#b 7,t-t7#b11 analog\s to t ( two & ?ree dim5sions4 ,x is n ! pres5ce ( ! con/ant ,c 9 ,m9k[ski's =mula t c\nts2 ?is is m]ely an adju/m5t s t we may measure space 9 miles & "t 9 ! unit t corresponds to a mile4 ,x is ! m9us sign :]e ,euclidean geometry dem&s a plus t makes ,m9k[ski's cont9uum non-,euclidean4 ,! editor has told u :at ?is /atem5t means4 ,i ?9k he has made x cle> t :5 we speak ( ! geometry ( ! f\r-dim5sional _w1 we mu/ n read into ?is t]m ! re/rictions surr\nd+ ! k9d ( geometry we are be/ acqua9t$ )--t ( ! ?ree-dim5sional ,euclidean cont9uum4 ,s ,i ne$ only po9t out t if we are to make a f\r? 7& we hope1 f9al7 approximation to ! reality1 its geometry mu/ pres]ve ! g5]ality atta9$ by t ( ! ?ird /ep1 if x goes no fur!r4 ,,e9/e9',s ,,"t-,,space ,,_w ,e9/e9 accord+ly exam9$ ! possible non-,euclidean geometries ( f\r dim5sions1 9 se>* ( "o display+ fundam5tal *>act]i/ics :i*1 int]pret$ 9 t]ms ( space-"t1 w\ld lead to ! obs]v$ facts ( gravitation4 ,! ma!matics ( ?is inve/igation is t "p ( 8 "w :i*1 we are told1 b twelve m5 c foll[2 s we may only outl9e 8 conclusions4 ,if we assume t 9 ! neighborhood ( matt] ! _w ( space-"t is non-,euclidean1 & t its curvature or di/ortion or non-,euclideanism is ( a c]ta9 type already kn[n to ma!maticians2 t ! curvature ( ?is _w 9 ! neighborhood ( matt] increases ) ! mass1 & decreases z ! di/ance f ! matt] increases2 & t e p>ticle ( matt] t is n int]f]$ ) travels ?r\gh space-"t 9 ! mo/ direct pa? possible 9 t cont9uum2 !n ! obs]v$ facts ( gravitation are acc\nt$ = z an inh]5t geometric prop]ty ( ?is space-"t _w4 ,we usually say t ! pres5ce ( matt] di/orts ?is _w1 & t ?is di/ortion gives ! track ( p>ticles ?r\gh ! region affect$ its non-uni=m "*4 ,gravitation !n is n a =ce at all2 x is ! fundam5tal nature ( ?+s4 ,a body free to move ?r\gh ! _w mu/ foll[ "s def9ite pa?4 ,euclid says x w /& /ill2 ,newton t x w trav]se a /raight l9e 9 ?ree-space at uni=m "t-rate2 ,e9/e9 t x w move 9 a geodesic ?r\gh "t-space--9 e-day language1 t x w fall4 ,! num]ical consequ5ces ( ,e9/e9's !ory are1 )9 ! limits ( obs]vation1 ! same z ^? ( ,newton's = all bodies save "o--,m]cury4 ,?is planet %[s a small deviation f ! pa? pr$ict$ by ,newton's law2 ,e9/e9's !ory gives its motion exactly4 ,aga91 :5 mod]n rese>* %[$ t light mu/ be affect$ by gravitation1 ,e9/e9's !ory1 because ( ! extreme velocity ( light1 deviates f ,newton's1 :]e ! spe$ is less a det]m9+ factor2 & obs]vations ( />light deflect$ by ! sun dur+ ! eclipse 7 9 mu* bett] accord ) ,e9/e9's !ory ?an ,newton's4 ,moreov]1 ! ,special ,!ory pr$icts t mass is an obs]vational v>iable l l5g? & duration4 ,radioactive emanations h a velocity high en\gh to give appreciable results "h1 & ! pr$iction is v]ifi$1 t5d+ to support ! g5]al !ory by support+ its limit+ case4 ,we l always to unify our sci5ce2 & seldom1 aft] effect+ a unification1 are we =c$ to give x up4 ,e9/e9 = ! fir/ "t br+s me*anical1 electromagnetic & gravitational ph5om5a )9 "o /ructure4 ,?is is "o reason :y physici/s are s op5 m9d$ t[>d 8 !ory--!y want x to be true4 ,,! ,,layman',s ,,la/ ,,d\bt ,! f9al answ] to any s]ies ( que/ions is inevitably because ! _w is s con/ruct$4 ,! ?+s we are cont5t to leave on t basis are ^? to :i* we are accu/om$1 & :i* we !re=e ?9k we und]/&2 ^? = :i* ?is explanation leaves u unsatisfi$ are ^? :i* are new & unfamili>4 ,newton told u t ! _w ( ?ree-dim5sional space ) "o-dim5sional "t sup]pos$ 0 s con/ruct$ t bodies left to !mselves w\ld g on =ev] 9 a /raight l9e at con/ant spe$4 ,we ?9k we und]/& ?is1 b our und]/&+ consi/s m]ely ( ! unspok5 qu]y1 ,:y1 ( c\rse2 :at is !re to prev5t8 ,! ,greeks1 an intellig5t p1 look$ at ?is diff]5tly2 !y w\ld h met ,newton ) ! unanim\s dem& ,:y s2 :at is !re to keep !m go+8 ,s if1 9 seek+ an explanation ( any?+1 we come soon] ?an we _h expect$ to ! f9ality ,because ! _w is s con/ruct$1 let u n feel t we h be5 *eat$4 ,,ix ,,! ,,pr9ciple ,,( ,,relativity ,a ,/atem5t ( ,:at x is ,all ,ab\t1 9 ,ideas ( ,"o ,syllable ,,by ,,hugh ,,elliot ,,*islehur/1 ,,k5t1 ,,engl& ,! inv>iance ( ! laws ( nature 0 "o ( ! mo/ popul> !mes ( n9ete5? c5tury philosophy4 ,= x 0 n till la/ c5tury t g5]al acceptance 0 accord$ to ! doctr9e ( ! ,uni=mity ( ,law1 adumbrat$ 9 anci5t times by ,epicurus & ,lucretius4 ,x is n[ a c>d9al axiom ( sci5ce t ! same cause 9 ! same conditions is always foll[$ by ! same effect4 ,!re exi/s 9 nature no indet]m9ate elem5t2 all ?+s are gov]n$ by fix$ laws1 & ! discov]y ( ^! laws is ! ma9 bus9ess ( sci5ce4 ,x is necess>y to gu>d aga9/ read+ into ?is /atem5t an errone\s idea ( ! cont5t ( a law ( nature4 ,su* a law is ( c\rse n an enactm5t ( any sort2 & x is n ev5 to be ?\ght ( z an actual explanation ( ! h[ & :y ( ! ph5om5a ) :i* x has to d4 ,x really is no?+ b an expression ( our belief 9 ! pron\ncem5t ( ! prec$+ p>agraph1 t l conditions d produce l results4 ,x is a pr$iction bas$ on pa/ exp]i5ce1 & is ( value m]ely 9 t pa/ exp]i5ce leads u to cr$it its accuracy4 ,! composite essay beg9n+ on page #ai discusses ?is "q ( ! reality ( natural laws1 & %\ld be consult$ 9 connection ) ! pres5t contribution4--,editor4 ,?is great philosophic pr9ciple 0 d]iv$ ( c\rse f ! /udy ( natural sci5ce2 i4e41 f obs]vations & exp]im5ts conduct$ ^u ! e>?4 ,_! compreh5siv5ess is !re=e limit$ by ! fact t ! obs]v] is always 9 a /ate ( re/1 or ne>ly s1 z comp>$ ) ! e>?4 ,all obs]v]s ^u ! e>? are mov+ ?r\gh space at ! same velocity2 & x 0 possible to argue t ! uni=mity ( law might only hold good1 :5 exp]im5ts 7 conduct$ at ?is velocity4 ,an obs]v] mov+ at v diff]5t velocity might discov] t ! laws ( nature "u ^! new conditions 7 some:at diff]5t4 ,su* a view c\ld inde$ nev] be v plausible1 = motion is only a relative conception4 ,imag9e a univ]se consi/+ ( inf9ite empty space1 9 :i* !re is pois$ a s+le mat]ial body4 ,h[ %all we det]m9e :e!r ?is body is at re/1 or :e!r x is mov+ at high or l[ velocity ?r\gh space8 ,x is nev] gett+ ne>] to any?+ or f>!r f any?+1 s9ce !re is no o!r body = x to get ne>] to or f>!r f4 ,if we say x is mov+ at a uni=m velocity ( a ?\s& miles a second1 our /atem5t really has no significance4 ,we h no m reason = affirm+ t x is 9 motion ?an we h = affirm+ t x is at re/4 ,9 %ort1 !re is no su* ?+ z absolute motion2 ! conception ( motion only arises :5 !re are two or m bodies *ang+ _! position relatively to "o ano!r4 ,?is is :at is meant by ! relativity ( motion4 ,x seem$ !re=e improbable t ! laws ( nature w\ld be diff]5t if ! obs]v] 7 mov+ at high velocity2 = ! movem5t ( ! obs]v] is n an absolute quantity1 b m]ely a /atem5t ( 8 relation to o!r bodies1 & if !re 7 no o!r bodies1 ! /atem5t itself w\ld be mean+less4 ,,! ,,behavior ,,( ,,light ,n[ among ! e/abli%$ laws ( nature is t :i* specifies ! velocity ( light mov+ ?r\gh a vacuum4 ,if ! laws ( nature are inv>iable1 ?is velocity w always be ! same4 ,b consid] :at w\ld happ5 "u ! foll[+ circum/ances3 ,suppose t we are at re/1 & t an obs]v] on ano!r body flies pa/ u at #aej1jjj miles a second4 ,suppose t at ! mom5t he passes1 a piece ( fl9t project+ f him grazes a piece ( /eel project+ f u1 giv+ rise to a sp>k2 & t we bo? !reupon set ab\t to measure ! velocity ( ! light s produc$4 ,aft] "o second1 we %\ld f9d t ! light _h travel$ ab\t #ahf1jjj miles away1 & s9ce dur+ ?is second ! o!r obs]v] _h travel$ #aej1jjj miles1 we %\ld inf] t ! light travel+ 9 8 direction 0 only ab\t #cf1jjj miles ahead ( him4 ,we %\ld also inf] t he w\ld f9d ?is out by 8 exp]im5t1 & t he w\ld e/imate ! velocity ( light z only #cf1jjj miles a second 9 8 own direction1 & #ccf1jjj miles a second 9 ! opposite direction4 ,b if ?is is s1 !n t law ( nature :i* specifies ! velocity ( light is q diff]5t = him & = u3 ! laws ( nature mu/ be dep5d5t ^u ! obs]v]'s motion--a conclusion :i* appe>s incompatible ) ! idea ( ! relativity ( motion4 ,& x s happ5s t x is also contradictory to exp]im5tal conclusions4 ,exp]im5ts und]tak5 to settle ! po9t %[ t ea* obs]v] f9ds ! same velocity = ! light ( ! sp>k2 & aft] "o second1 ea* obs]v] f9ds t ! light has travel$ #ahf1jjj miles f himself4 ,b h[ is x possible t :5 x has travel$ #ahf1jjj miles 9 ! same direction z ! o!r obs]v] :o himself has mov$ #aej1jjj miles mean:ile1 he %\ld /ill ?9k x #ahf1jjj miles ahead ( him8 ,t is ! initial p>adox2 & s9ce !re has be5 no room = error 9 ! exp]im5ts1 we are =c$ to conclude t !re 0 some?+ wrong 9 ! assumptions & preconceptions ) :i* we />t$4 ,,space ,,& ,,"t ,!re c 9 fact be only "o int]pretation4 ,if we ea* f9d t ! light has mov$ ! same numb] ( miles 9 ! same numb] ( seconds1 !n we mu/ be mean+ some?+ diff]5t :5 we speak ( miles & seconds4 ,we are speak+ 9 diff]5t languages4 ,"s subsid5ce has occurr$ 9 ! f\ndations ( our sy/ems ( measurem5t4 ,we are ea* ref]r+ to "o & ! same objective fact2 b s9ce we describe x q diff]5tly1 & at fir/ sight incompatibly1 "s pr(\nd alt]ation mu/ h occurr$ 9 our p]ceptions--all unsuspect$ by ourselves4 ,x has be5 %[n precisely :at ?is alt]ation is4 ,a body mov+ at high velocity mu/ become flatt5$ 9 ! direction ( its motion2 all its measur+ app>atus1 :5 turn$ 9 t direction1 is %ort5$1 s t no h9t ( ! flatt5+ c be obta9$ f x4 ,fur!rmore1 ! /&>ds ( "t are l5g!n$ out1 & clocks g sl[]4 ,! ext5t ( ?is alt]ation 9 /&>ds ( space & "t is /at$ 9 ! equations ( ! s-call$ ,lor5tz trans=mation4 ,objection might be urg$ to ! above p>agraph on ! gr\nd t ! connection ( ! obs]v] ) ! v>iability ( measur$ l5g?s & times is n suffici5tly indicat$1 & t ?is v>iability !re=e might be tak5 z an intr9sic prop]ty ( ! obs]v$ body--:i* ( c\rse x is n4--,editor4 ,we are accu/om$ to describe space z be+ ( ?ree dim5sions1 & "t z be+ ( "o dim5sion4 ,z a matt] ( fact1 bo? space & "t are ideas1 & n imm$iate s5se-p]ceptions4 ,we p]ceive matt]2 we !n inf] a univ]sal cont9uum fill$ by x1 :i* we call space4 ,if we _h no k ( matt]1 we %\ld h no conception ( space4 ,simil>ly 9 ! case ( "t3 we p]ceive "o ev5t foll[+ ano!r1 & we !n inv5t a cont9uum :i* we call "t1 z an ab/raction bas$ on ! sequ5ce ( ev5ts4 ,we d n see space1 & we d n see "t4 ,!y are n real ?+s1 9 ! s5se t matt] is real1 & t ev5ts are real4 ,!y are products ( imag9ation3 useful en\gh 9 common life1 b mislead+ :5 we try to look on ! univ]se z a :ole1 free f ! artificial divisions & l&m>ks :i* we introduce into x = practical conv5i5ce4 ,h5ce x is p]haps n s surpris+ aft] all t 9 c]ta9 highly transc5d5tal inve/igations1 ^! artificial divisions %\ld cease to be a conv5i5ce1 & become a h9drance4 ,take = in/ance our conception ( "t4 ,x diff]s f our conception ( space 9 t x has only "o dim5sion4 ,9 space1 !re is a "r & left1 an up & d[n1 a be=e & aft]4 ,b 9 "t !re is only be=e & aft]4 ,:y %\ld !re be ?is limitation ( ! "t-factor8 ,m]ely because t is ! v]dict ( all our human exp]i5ce4 ,b is our human exp]i5ce bas$ on a suffici5tly broad f\ndation to enable u to say t1 "u all conditions & 9 all p>ts ( ! univ]se1 !re c be only "o "t-direction8 ,may n our belief 9 ! uni=mity ( "t be due to ! uni=mity ( ! motion ( all obs]v]s on ! e>?8 ,su* 9 fact is ! po/ulate ( relativity4 ,we n[ believe t1 at velocities v diff]5t f our own1 ! /&>d ( "t w\ld also be diff]5t f ours4 ,f our po9t ( view1 t diff]5t /&>d ( "t w\ld n be conf9$ to ! s+le direction =e & aft1 z we "k x1 b w\ld also h 9 x an elem5t ( :at we might call "r & left4 ,true1 x w\ld /ill be ( only "o dim5sion1 b its direction w\ld diff] f ! direction ( our "t4 ,x w\ld /ill run l a ?read ?r\gh ! univ]se1 b n 9 ! direction :i* we call /raight =w>d4 ,x w\ld h a slant 9 x1 & ! angle ( ! slant dep5ds ^u ! velocity ( motion4 ,x does n foll[ t because we are all travel+ 9 ! same direction d[n ! /ream ( "t1 !re=e t /ream c only fl[ 9 ! direction :i* we "k4 ,be=e & aft] are expressions :i*1 l "r & left1 dep5d ^u our p]sonal situation4 ,if we 7 diff]5tly situat$1 if to be precise we 7 mov+ at v high velocity1 we %\ld1 s to speak1 be fac+ 9 a new direction & be=e & aft] w\ld imply a diff]5t direction ( progress f t ) :i* we are n[ famili>4 ,,! ,,_w ,,( ,,reality ,b1 aft] all1 ! objective univ]se is ! same old univ]se h[ev] fa/ we are mov+ ab\t 9 x1 & :atev] way we are fac+4 ,^! details m]ely det]m9e ! way we divide x up into space & "t4 ,! univ]se is n affect$ by any arbitr>y l9es :i* we draw ?r\gh x = our p]sonal conv5i5ce4 ,= practical purposes1 we ascribe to x f\r dim5sions1 ?ree 9 space & "o 9 "t4 ,cle>ly if ! "t direction is alt]$1 all dim5sions bo? ( space & "t mu/ h diff]5t read+s4 ,if1 = in/ance1 ! "t direction slopes away to ! left1 z comp>$ ) ours1 !n space measurem5ts to "r & left mu/ be correspond+ly alt]$4 ,an analogy w simplify ! matt]4 ,suppose we desire to rea* a po9t t5 miles (f 9 a r\ghly nor!a/]ly direction4 ,we might d s by walk+ six miles due ea/ & !n eight miles due nor?4 ,we %\ld !n be precisely t5 miles f :]e we />t$4 ,b suppose our compass 7 out ( ord]1 s t its nor? pole po9t$ some:at to ! we/ ( nor?4 ,!n 9 ord] to get to our de/9ation1 we might h to walk sev5 miles 9 ! direction :i* we ?\ght 0 ea/1 & a little m ?an sev5 miles 9 ! direction :i* we ?\ght 0 nor?4 ,we %\ld !n rea* ! same po9t z be=e4 ,bo? obs]v]s h walk$ accord+ to _! lights1 fir/ due ea/ & !n due nor?1 & bo? h rea*$ ! same po9t3 ! "o obs]v] is c]ta9 t ! f9i%+ po9t is six miles ea/ ( ! />t+-po9t1 :ile ! o!r is sure x is sev5 miles4 ,n[ we on ! e>? are all us+ a compass :i* po9ts 9 ! same direction z reg>ds "t4 ,b o!r obs]v]s1 on bodies mov+ ) v diff]5t velocity1 h a compass 9 :i* ! "t-direction is displac$ z comp>$ ) ours4 ,h5ce our judgm5ts ( di/ances w n be alike4 ,9 our analogy1 ! nor!rly direction corresponds to "t1 & ! ea/]ly direction to space2 & s long z we use ! same compass we d n diff] 9 our measurem5ts ( di/ances4 ,b = any "o :o has a diff]5t notion ( ! "t-direction1 n only "t int]vals b space di/ances w be judg$ diff]5tly4 ,9 %ort1 ! univ]se is reg>d$ z a space-"t cont9uum ( f\r dim5sions4 ,a po9t 9 space-"t is call$ an ev5t--t :i* occurs at a specifi$ mom5t & at a specifi$ place4 ,! di/ance betwe5 two po9ts 9 space-"t is call$ _! int]val4 ,all obs]v]s w agree z to ! magnitude ( any int]val1 s9ce x is a prop]ty ( ! objective univ]se2 b !y w disagree z to its composition 9 space & "t sep>ately4 ,9 %ort1 space & "t are relative conceptions2 _! relativity is a necess>y consequ5ce ( ! relativity ( motion4 ,! p>adox nam$ at ! outset is ov]come2 = ! two obs]v]s measur+ ! velocity ( ! light produc$ z !y pass$ "o ano!r1 7 us+ diff]5t units ( space & "t4 ,& h5ce em]ges triumphant ! ,special ,pr9ciple ( ,relativity1 :i* /ates t ! laws ( nature are ! same = all obs]v]s1 :e!r !y are 9 a /ate ( re/ or ( uni=m motion 9 a /raight l9e4 ,,accel]at$ ,,motion ,uni=m motion 9 a /raight l9e is h[ev] a v special k9d ( motion4 ,our exp]i5ce 9 ord9>y life is ( motions t are nei!r uni=m nor 9 a /raight l9e2 bo? spe$ & direction ( motion are alt]+4 ,! mov+ body is !n said to und]go accel]ation3 :i* means ei!r t its spe$ is increas+ or dim9i%+1 or t its direction ( motion is *ang+1 or bo?4 ,if we rev]t to our =m] supposition ( a univ]se 9 :i* !re is only a s+le body 9 empty space1 we cle>ly _c say :e!r x has accel]ation any m ?an :e!r x is mov+1 !re be+ no outside /&>d ( comp>ison2 & ! ,g5]al ,pr9ciple ( ,relativity ass]ts ! inv>iance ( ! laws ( nature = all /ates ( motion ( ! obs]v]4 ,9 ?is case1 h[ev]1 a diff]5ce might be detect$ by an obs]v] on ! mov+ body itself4 ,x w\ld be manife/$ to him z ! action ( a =ce2 su* = in/ance z we feel :5 a tra9 9 :i* we are travel+ is increas+ or r$uc+ spe$1 or :51 )\t *ang+ spe$1 x is r\nd+ a corn]4 ,! =ce dies away z soon z ! velocity becomes uni=m4 ,?us accel]ation reveals itself to u "u ! guise ( action by a =ce4 ,=ce & accel]ation g toge!r1 & we may ei!r say t ! accel]ation is due to ! =ce1 or ! impression ( =ce to ! accel]ation4 ,n[ :5 we are travel+ ) accel]at$ motion1 we h q a diff]5t idea ( :at con/itutes a /raight l9e f t :i* we _h :5 at re/ or 9 uni=m motion4 ,if we are mov+ at uni=m velocity 9 an airplane & drop a /one to ! e>? x w appe> to u 9 ! airplane to fall 9 a /raight l9e d[nw>d1 :ile to an obs]v] on ! e>? x w appe> to describe a p>abola4 ,?is is due to ! fact t ! /one ga!rs spe$ z x falls2 x is subject to ! accel]ation associat$ ) gravity4 ,accel]ation oblit]ates ! fundam5tal diff]5ce betwe5 a /raight & curv$ l9e4 ,unless we "k :at is ! absolute motion ( ! /one1 & ! two obs]v]s1 we _c say :e!r ! l9e is really a /raight or a curv$ l9e4 ,s9ce absolute motion is an illegitimate conception1 x foll[s t !re is no su* ?+ z really /raight or really curv$4 ,^! are only appe>ances set up z a consequ5ce ( our relative motions ) respect to ! bodies conc]n$4 ,if !re 7 no su* ?+ z accel]ation--if ! /one fell to ! e>? at uni=m velocity--!n an obs]v] on ! e>? or any:]e else w\ld agree t x fell 9 a /raight l9e2 & /raight l9es w\ld always be /raight l9es4 ,"u ^! circum/ances1 ,euclidean geometry w\ld be absolutely true4 ,b if we are 9 a /ate ( accel]ation1 !n :at we ?9k are /raight l9es are really curv$ l9es1 & ,euclidean geometry1 bas$ on ! assumption t its l9es are /raight1 mu/ f\nd] :5 te/$ by m accurate measurem5ts4 ,& 9 po9t ( fact we are 9 a /ate ( accel]ation3 = we are be+ act$ ^u by a =ce--namely1 ! =ce ( gravitation4 ,:]ev] !re is matt]1 !re is gravitation2 :]ev] !re is gravitation !re is accel]ation2 :]ev] !re is accel]ation ,euclidean geometry is inaccurate4 ,h5ce 9 ! space surr\nd+ matt] a diff]5t geometry holds ! field2 & bodies 9 g5]al move ?r\gh su* space 9 curv$ l9es4 ,diff]5t p>ts ( space are ?us *>act]iz$ by diff]5t geometrical prop]ties4 ,all bodies 9 ! univ]se proce$ on _! e/abli%$ c\rses ?r\gh space & "t4 ,b :5 !y come to di/ort$ geometrical areas1 _! pa?s naturally seem to u diff]5t f :5 !y 7 mov+ ?r\gh less di/urb$ regions4 ,!y exhibit ! diff]5ce by acquir+ an accel]ation2 & we expla9 ! accel]ation by alleg+ ! exi/5ce ( a =ce1 :i* we call ! =ce ( gravitation4 ,b _! motions c 9 fact be p]fectly pr$ict$ if we "k ! geometry ( ! space ?r\gh :i* !y are travel+4 ,! pr$ictions s bas$ h 9 fact prov$ m accurate ?an ^? bas$ on ! law ( gravitation4 ,x ,,space1 ,,"t ,,& ,,gravitation ,an ,outl9e ( ,e9/e9's ,!ory ( ,g5]al ,relativity ,,by ,w4 ,,de ,,sitt] ,,pr(essor ,,( ,,a/ronomy ,,9 ,,! ,,univ]sity ,,( ,,leyd5 ,h5ce=? space by itself & "t by itself %all s9k to m]e %ad[s1 & only a union ( ! two %all pres]ve reality4 ,! prophecy conta9$ 9 ! above-quot$ words1 spok5 by ,m9k[ski at ! meet+ ( ,g]man ,natur=s*] und ,a]zte at ,cologne 9 #aijh1 has1 h[ev]1 only be5 completely fulfill$ by ,e9/e9's ,allgeme9e ,relativitts-!orie ( #aiae1 :i* incorporat$ gravitation into ! union4 ,9 ! foll[+ pages an attempt is made to set =?1 )\t us+ any te*nical language1 ! lead+ ideas ( t !ory3 ,i w conf9e myself to ! !ory z publi%$ by ,e9/e9 9 ,novemb]1 #aiae1 :i* =ms a consi/5t :ole1 complete 9 itself2 & ,i w n ref] to lat] developm5ts1 :i* are /ill m or less t5tative1 & n necess>y = ! und]/&+ ( ! !ory4 ,! ma!matics us$ by ,e9/e9 is ! s-call$ ,absolute ,diff]5tial ,calculus4 ,x is n m difficult or recondite ?an t us$ 9 o!r bran*es ( !oretical physics1 b x is some:at unfamili> to mo/ ( u1 because x is n g5]ally taught 9 ! regul> univ]sity c\rses4 ,i w1 h[ev]1 9 ?is essay ab/a9 f us+ any ma!matics at all1 at lea/1 ,i w n be us+ x op5ly4 ,x is ( c\rse unavoidable to use at lea/ ! results ( ! ma!matical reason+1 if n ! reason+ itself2 b s long z !y are n put into =mulas !y w1 x is hop$1 n look s =midable to ! read]4 ,ref]r+ to ! quot$ words ( ,m9k[ski1 we may ask :at is meant by reality4 ,physical sci5ce1 l common s5se1 takes = grant$ t !re is a reality beh9d ! ph5om5a1 :i* is indep5d5t ( ! p]son by :om1 & ! p>ticul> me?ods by :i* x is obs]v$1 & :i* is also !re :5 x is n obs]v$4 ,/rictly speak+1 all talk ab\t :at is n obs]v$ is metaphysics4 ,nev]!less ! physici/ unhesitat+ly believes t 8 laws are g5]al1 & t ! ph5om5a cont9ue to happ5 accord+ to !m :5 nobody is look+4 ,& s9ce x w\ld be impossible to prove t !y did n1 he is fully entitl$ to 8 belief4 ,! obs]v$ ph5om5a are ! effects ( ! action ( ?is reality1 ( :i* we assume ! exi/5ce1 on ! obs]v]'s s5ses--or app>atus1 :i* are ext5d$ & ref9$ s5se-organs4 ,! laws gov]n+ ! ph5om5a !re=e mu/ convey "s in=mation reg>d+ ?is reality4 ,we %all nev] by any means be able to "k any?+ else ab\t x b j ^! laws4 ,to all int5ts & purposes ! laws are ! reality1 if we elim9ate f !m all t ref]s to ! obs]v] alone4 ,:at ref]s to ! reality is call$ absolute1 & :at involves ref]5ce to ! obs]v] relative4 ,! elim9ation ( ! relative is "o ( ! ?+s ! !ory ( relativity has set out to d4 ,,! ,,ext]nal ,,_w ,,& ,,its ,,geometry ,to describe ! ph5om5a & d]ive laws f !m1 we locate !m 9 space & "t4 ,to d ?is we use geometry4 ,"h x is t ! "p contribut$ by ! obs]v] comes 94 ,!re are an inf9ite numb] ( geometries1 & a priori !re seems to be no reason to *oose "o r ?an ! o!r4 ,tak+ geometry ( two dim5sions z an example1 we c draw figures on a piece ( pap]1 & discuss _! prop]ties1 & we c also d s on ! %ell ( an egg4 ,b we _c draw ! same figures on ! egg z on ! pap]4 ,! ones w be di/ort$ z comp>$ ) ! o!rs3 ! two surfaces h a diff]5t geometry4 ,simil>ly x is n possible to draw an accurate map ( ! e>? on a %eet ( pap]1 because ! e>? is sph]ical & its repres5tation on ! flat pap] is always m or less di/ort$4 ,! e>? requires sph]ical geometry1 :i* diff]s f ! flat1 or ,euclidean1 geometry ( ! pap]4 ,up to a few ye>s ago ,euclidean 7i4e4 flat7 geometry ( ?ree dim5sions _h be5 exclusively us$ 9 physical !ories4 ,:y8 ,because x is ! true "o1 is ! "o answ] g5]ally giv54 ,n[ a /atem5t ab\t facts c be true or false1 b a ma!matical discipl9e is nei!r true nor false2 x c only be correct--i4e4 consi/5t 9 itself--or incorrect1 & ( c\rse x always is correct4 ,! ass]tion t a c]ta9 geometry is ! true "o c ?us only mean1 t x is ! geometry ( true space1 & ?is aga91 if x is to h any mean+ at all1 c only mean t x corresponds to ! physical reality4 ,leav+ aside ! "q :e!r ?is reality has any geometry at all1 we are confront$ ) ! m imm$iately practical consid]ation h[ we %all v]ify ! ass]t$ correspond5ce4 ,!re is no o!r way ?an by comp>+ ! conclusions d]iv$ f ! laws bas$ ^u our geometry1 ) obs]vations4 ,x ?us appe>s t ! only ju/ification = ! use ( ! ,euclidean geometry is its success 9 enabl+ u to draw an accurate map ( ! _w4 ,z soon z any o!r geometry is f\nd to be m successful1 t o!r mu/ be us$ 9 physical !ories1 & we may1 if we l1 call x ! true "o4 ,accurate obs]vations always consi/ ( measures1 det]m9+ ! position ( mat]ial bodies 9 space4 ,b ! positions *ange1 & = a complete description we also require measures ( "t4 ,an important rem>k mu/ be made "h4 ,nobody has ev] measur$ a pure space-di/ance1 nor a pure lapse ( "t4 ,! only ?+ t c be measur$ is ! di/ance f a body at a c]ta9 po9t ( space & a c]ta9 mom5t ( "t1 to a body 7ei!r ! same or ano!r7 at ano!r po9t & ano!r "t4 ,we c ev5 g fur!r & say t "t _c be measur$ at all4 ,we pr(ess to measure x by clocks4 ,b a clock really measures space1 & we d]ive ! "t f its space-measures by a fix$ rule4 ,?is rule dep5ds on ! laws ( motion ( ! me*anism ( ! clock4 ,?us f9ally "t is def9$ by ^! laws4 ,?is is s1 :e!r z a clock we use an ord9>y *ronomet]1 or ! rotat+ e>?1 or an atom emitt+ light-waves1 or any?+ else t may be sugge/$4 ,! physical laws1 ( c\rse1 mu/ be s adju/$ t all ^! devices give ! same "t4 ,ab\t ! reality ( "t1 if x has any1 we "k no?+4 ,all we "k ab\t "t is t we want x4 ,we _c adequately describe nature ) ! ?ree space-coord9ates alone1 we require a f\r? "o1 :i* we call "t4 ,we might ?us say ) "s reason t ! physical _w has f\r dim5sions4 ,b s long z x 0 f\nd possible adequately to describe all kn[n ph5om5a by a space ( ?ree dim5sions & an indep5d5t "t1 ! /atem5t did n convey any v important in=mation4 ,only aft] x _h be5 f\nd out t ! space-coord9ates & ! "t are n indep5d5t1 did x acquire a real mean+4 ,z is well kn[n ! obs]vation by :i* ?is 0 f\nd out is ! fam\s exp]im5t ( ,mi*elson & ,morley4 ,x l$ to ! special !ory ( relativity1 :i* is ! "o ref]r$ to by ,m9k[ski 9 #aijh4 ,9 x a geometry ( f\r dim5sions is us$1 n a m]e comb9ation ( a ?ree-dim5sional space & a "o-dim5sional "t1 b a cont9uum ( truly f\rfold ord]4 ,?is "t-space is n ,euclidean1 s9ce ! "t-compon5t & ! ?ree space-compon5ts are n on ! same foot+1 b its fundam5tal =mula has a great resemblance to t ( ,euclidean geometry4 ,we may call x pseudo-,euclidean4 ,?is !ory1 :i* we ne$ n expla9 "h1 0 v satisfactory s f> z ! laws ( electromagnetism1 & especially ! propagation ( light1 7 conc]n$1 b x did n include gravitation1 & me*anics g5]ally4 ,we !n _h ?is curi\s /ate ( affairs1 t physici/s actually believ$ 9 two diff]5t realities4 ,:5 !y 7 ?9k+ ( light !y believ$ 9 ,m9k[ski's "t-space2 :5 !y 7 ?9k+ ( gravitation !y believ$ 9 ! old ,euclidean space & indep5d5t "t4 ,?is1 ( c\rse1 c\ld n la/4 ,attempts 7 made s to alt] ,newton's law ( gravitation t x w\ld fit into ! f\r-dim5sional _w ( ! special relativity-!ory1 b ^! only succe$$ 9 mak+ ! law1 :i* _h be5 a model ( simplicity1 extremely complicat$1 &1 :at 0 worse1 x became ambigu\s4 ,x is ,e9/e9's great m]it to h p]ceiv$ t gravitation is ( su* fundam5tal importance1 t x mu/ n be fitt$ into a ready-made !ory1 b mu/ be wov5 into ! space-"t geometry f ! beg9n+4 ,& t he n only saw ! necessity ( do+ ?is1 b actually did x4 ,,gravitation ,,& ,,its ,,place ,,9 ,,! ,,univ]se ,to see ! necessity we mu/ g back to ,newton's sy/em ( me*anics4 ,newton did two ?+s 7among/ o!rs74 ,he canonis$ ,galileo's sy/em ( me*anics into 8 fam\s laws ( motion1 ! mo/ important ( :i* is ! law ( in]tia1 :i* says t3 a body1 t is n int]f]$ )1 moves 9 a /raight l9e ) con/ant velocity4 ,! velocity1 ( c\rse1 c be nil1 & ! body at re/4 ,?is is a p]fectly g5]al law1 ! same = all mat]ial bodies1 :atev] _! physical or *emical /atus4 ,newton took good c>e exactly to def9e :at he meant by uni=m motion 9 a /raight l9e1 & = ?is purpose he introduc$ ! absolute ,euclidean space & absolute "t z an ess5tial "p ( 8 sy/em ( laws at ! v beg9n+ ( 8 great "w4 ,! o!r ?+ ,newton did 0 to =mulate ! law ( gravitation4 ,gravitation 0 9 8 sy/em consid]$ z an int]f]5ce ) ! free1 or in]tial1 motion ( bodies1 & accord+ly requir$ a law ( its own4 ,b gravitation has ?is 9 common ) in]tia1 & 9 ?is x diff]s f all o!r int]f]5ces1 t x is p]fectly g5]al4 ,all mat]ial bodies are equally subject$ to x1 :atev] _! physical or *emical /atus may be4 ,b !re is m4 ,gravitation & in]tia are actually indi/+ui%able f ea* o!r1 & are measur$ by ! same numb]3 ! mass4 ,?is 0 already rem>k$ by ,newton himself1 & f 8 po9t ( view x 0 a mo/ wond]ful accid5tal co9cid5ce4 ,if an apple falls f ! tree1 t :i* makes x fall is its weight1 :i* is ! gravitational attraction by ! e>?1 dim9i%$ by ! c5trifugal =ce due to ! e>?'s rotation & ! apple's in]tia4 ,9 ,newton's sy/em ! gravitational attraction is a real =ce1 :]eas ! c5trifugal =ce is only fictiti\s4 ,b ! "o is z real z ! o!r4 ,! mo/ ref9$ exp]im5ts1 already begun by ,newton himself1 h n succe$$ 9 di/+ui%+ betwe5 !m4 ,_! id5tity is actually "o ( ! be/ e/abli%$ facts 9 exp]im5tal physics4 ,f ?is id5tity ( fictiti\s1 or in]tial1 & real1 or gravitational1 =ces x foll[s t locally a gravitational field c be artificially creat$ or de/roy$4 ,?us inside a clos$ room :i* is fall+ freely1 say a lift ( :i* ! cable has be5 brok51 bodies h no weight3 a balance c\ld be 9 equilibrium ) diff]5t weights 9 ! two scales4 ,hav+ ?us come to ! conclusion t gravitation is n an int]f]5ce1 b is id5tical ) in]tia1 we are tempt$ to re/ate ! law ( motion1 s z to include bo?1 ?us3 ,bodies :i* are n int]f]$ )--d n move 9 /raight l9es1 b--fall4 ,n[ ?is is exactly :at ,e9/e9 did4 ,only ! fall+ ( c\rse requires a precise ma!matical def9ition 7l ! uni=m motion 9 a /raight l9e71 & ! :ole gi/ ( 8 !ory is ! f9d+ ( t def9ition4 ,9 our e>?ly exp]i5ce ! fall+ nev] la/s long1 v soon some?+--! floor ( ! room1 or ! e>? itself--int]f]es4 ,b 9 free space bodies g on fall+ =ev]4 ,! motion ( ! planets is1 9 fact1 adequately describ$ z fall+1 s9ce x consi/s 9 no?+ else b obey+ ,newton's law ( gravitation toge!r ) 8 law ( in]tia4 ,a body v f> remov$ f all o!r matt] is n subject$ to gravitation1 consequ5tly x falls ) con/ant velocity 9 a /raight l9e accord+ to ! law ( in]tia4 ,! problem 0 ?us to f9d a ma!matical def9ition ( fall+1 :i* w\ld embrace ! uni=m /raight-l9e motion v f> f all matt] z well z ! complex pa?s ( ! planets ar\nd ! sun1 & ( an apple or a cannon-ball on e>?4 ,,gravitation ,,& ,,space-,,"t ,= ! def9ition ( ! uni=m rectil9e> motion ( pure in]tia ,newton's ,euclidean space & indep5d5t "t 7 suffici5t4 ,= ! mu* m complicat$ fall+ "u ! influ5ce ( gravitation & in]tia toge!r1 evid5tly a m complicat$ geometry w\ld be ne$$4 ,m9k[ski's pseudo-,euclidean "t-space also 0 insuffici5t4 ,e9/e9 accord+ly introduc$ a g5]al non-,euclidean f\r-dim5sional "t-space1 & enunciat$ 8 law ( motion ?us3 ,bodies :i* are n int]f]$ ) move 9 geodesics4 ,a geodesic 9 curv$ space is exactly ! same ?+ z a /raight l9e 9 flat space4 ,we only call x by its te*nical "n1 because ! "n /raight l9e w\ld rem9d u too mu* ( ! old ,euclidean space4 ,if ! curvature gets v small1 or z]o1 ! geodesic becomes v ne>ly1 or exactly1 a /raight l9e4 ,! problem has n[ become to assign to "t-space su* curvatures t ! geodesics w exactly repres5t ! tracks ( fall+ bodies4 ,space ( two dim5sions c j be flat1 l a %eet ( pap]1 or curv$1 l an egg4 ,b 9 geometry ( f\r dim5sions !re are sev]al /eps f p]fect flatness1 or pseudo-flatness1 to complete curvature4 ,n[ ! law gov]n+ ! curvature ( ,e9/e9's "t-space1 i4e41 ! law ( gravitation1 is simply t x c nev]1 outside matt]1 be curv$ m ?an j "o /ep beyond p]fect 7pseudo-7flatness4 ,s9ce ,i h promis$ n to use any ma!matics ,i c h>dly convey to ! read] an adequate idea ( ! difficulty ( ! problem1 nor d ju/ice to ! elegance & beauty ( ! solution4 ,x is1 9 fact1 little %ort ( miracul\s t ?is solution1 :i* 0 only adopt$ by ,e9/e9 because x 0 ! simple/ he c\ld f9d1 does s exactly co9cide 9 all its effects ) ,newton's law4 ,?us ! rem>kably accurate exp]im5tal v]ification ( ?is law c at once be transf]r$ to ! new law4 ,9 only "o in/ance d ! two laws diff] s mu* t ! diff]5ce c be obs]v$1 & 9 ?is case ! obs]vations confirm ! new law exactly4 ,?is is ! well kn[n case ( ! motion ( ! p]ihelion ( ,m]cury1 ^: disagreem5t ) ,newton's law _h puzzl$ a/ronom]s = m ?an half a c5tury4 ,s9ce ,e9/e9's "t-space includes ,m9k[ski's z a p>ticul> case1 x c d all t ! o!r 0 design$ to d = electro-magnetism & light4 ,b x does m4 ,! track ( a pulse ( light is also a geodesic1 & "t-space be+ curv$ 9 ! neighborhood ( matt]1 rays ( light are no long] /raight l9es4 ,a ray ( light f a />1 pass+ ne> ! sun1 w be b5t r\nd1 & ! /> consequ5tly w be se5 9 a diff]5t direction f :]e x w\ld be se5 if ! sun _h n be5 s ne>ly 9 ! way4 ,?is has be5 v]ifi$ by ! obs]vations ( ! eclipse ( ! sun ( #aiai ( ,may #bi4 ,!re is "o o!r new ph5om5on pr$ict$ by ! !ory1 :i* falls )9 ! rea* ( obs]vation ) our pres5t means4 ,gravitation *iefly affects ! "t-compon5t ( ! f\r-dim5sional cont9uum1 9 su* a way t natural clocks appe> to run sl[] 9 a /rong gravitational field ?an 9 a weak "o4 ,?us1 if we make ! hypo!sis--:i*1 ?\gh extremely probable1 is /ill a hypo!sis--t an atom emitt+ or absorb+ light-waves is a natural clock1 & ! fur!r hypo!sis--/ill v probable1 ?\gh less s ?an ! =m]--t !re is no?+ to int]f]e ) its p]fect runn+1 !n an atom on ! sun w give (f light-waves ( small] frequ5cy ?an a simil> atom 9 a t]re/rial laboratory emits4 ,op9ions z yet diff] z to :e!r ?is is confirm$ or contradict$ by obs]vations4 ,! great /r5g? & ! *>m ( ,e9/e9's !ory d h[ev] n lie 9 v]ifi$ pr$ictions1 nor 9 ! explanation ( small out/&+ discrepancies1 b 9 ! complete atta9m5t ( its orig9al aim3 ! id5tification ( gravitation & in]tia1 & 9 ! wide range ( =m]ly app>5tly unconnect$ subjects :i* x embraces1 & ! broad view ( nature :i* x af=ds4 ,outside matt]1 z has be5 expla9$1 ! law ( gravitation re/ricts ! curvature ( "t-space4 ,inside cont9u\s matt] ! curvature c be ( any arbitr>y k9d or am\nt2 ! law ( gravitation !n connects ?is curvature ) measurable prop]ties ( ! matt]1 su* z d5sity1 velocity1 /ress1 etc4 ,?us ^! prop]ties def9e ! curvature1 or1 if pref]r$1 ! curvature def9es ! prop]ties ( matt]1 i4e4 matt] itself4 ,f ^! def9itions ! laws ( cons]vation ( en]gy1 & ( cons]vation ( mom5tum1 c be d$uc$ by a purely ma!matical process4 ,?us ^! laws1 :i* at "o "t us$ to be consid]$ z ! mo/ fundam5tal ones ( me*anics1 n[ appe> z simple coroll>ies f ! law ( gravitation4 ,x mu/ be po9t$ out t su* ?+s z l5g?1 velocity1 en]gy1 mom5tum1 are n absolute1 b relative1 i4e4 !y are n attributes ( ! physical reality1 b relations betwe5 ?is reality & ! obs]v]4 ,consequ5tly ! laws ( cons]vation are n laws ( ! real _w1 l ! law ( gravitation1 b ( ! obs]v$ ph5om5a4 ,!re is1 h[ev] "o law :i*1 already be=e ! days ( relativity1 _h come to be consid]$ z ! mo/ fundam5tal ( all1 viz3 ! pr9ciple ( lea/ action4 ,n[ action is absolute4 ,accord+ly ?is pr9ciple reta9s its c5tral position 9 ,e9/e9's !ory4 ,x is ev5 m fundam5tal ?an ! law ( gravitation1 s9ce bo? ?is law1 & ! law ( motion1 c be d]iv$ f x4 ,! pr9ciple ( lea/ action1 s f> z we c see at pres5t1 appe>s to be ! law ( ! real _w4 ,,xi ,,! ,,pr9ciple ,,( ,,g5]al ,,relativity ,h[ ,e9/e91 to a ,degree ,nev] ,be=e ,equall$1 ,isolates ! ,ext]nal ,reality f ! ,obs]v]'s ,contribution ,,by ,e4 ,t4 ,,bell ,,univ]sity ,,( ,,wa%+ton ,,seattle ,e9/e9's g5]al relativity is ( su* va/ compass1 be+ coext5sive ) ! realm ( physical ev5ts1 t 9 any brief acc\nt a /rict selection f its num]\s aspects is prescrib$4 ,! old1 re/rict$ pr9ciple be+ conta9$ 9 ! g5]al1 we %all treat ! latt]1 its close relations ) gravitation1 & ! significance ( bo? = our k ( space & "t4 ,! ess5ce ( ,e9/e9's g5]alization is its f9al dis5tanglem5t ( t "p ( any physical ev5t :i* is contribut$ by ! obs]v] f t :i* is inh]5t 9 ! nature ( ?+s & indep5d5t ( all obs]v]s4 ,! argum5t turns ^u ! fact t an obs]v] mu/ describe any ev5t ) ref]5ce to "s framework f :i* he makes measurem5ts ( "t & di/ance4 ,?us1 suppose t at n9e o'clock a ball is toss$ across ! room4 ,at "o second pa/ n9e ! ball occupies a def9ite position :i* we c specify by giv+ ! ?ree di/ances f ! c5tre ( ! ball to ! nor? & we/ walls & ! floor4 ,9 ?is way1 ref9+ our measurem5ts1 we c give a precise description ( ! entire motion ( ! ball4 ,our f9al description w consi/ ( innum]able sep>ate /atem5ts1 ea* ( :i* conta9s f\r numb]s correspond+ to f\r measurem5ts1 & ( ^! "o w be = "t & ?ree = di/ances at ! "t indicat$4 ,imag9e n[ t a man 9 an automobile looks 9 & obs]ves ! mov+ ball4 ,suppose he records ! motion4 ,to d s1 he mu/ ref] to a timepiece & "s body ( ref]5ce4 ,say he selects 8 wri/-wat*1 ! floor ( 8 auto & two sides meet+ 9 a corn]4 ,fancy t j z he beg9s 8 s]ies ( obs]vations 8 auto />ts buck+ & ! ma9-spr+ ( 8 wat* breaks1 s t he mu/ measure seconds by ! crazy runn+-d[n ( 8 wat*1 & di/ances ) ref]5ce to ! sides ( 8 erratic auto4 ,despite ^! h&icaps he completes a set ( obs]vations1 ea* ( :i* consi/s ( a "t measur$ by 8 mad wat* & ?ree di/ances reckon$ f ! sides ( 8 buck+ ma*9e4 ,let u assume him to h be5 s absorb$ 9 8 exp]im5t t he notic$ nei!r ! disord]s ( 8 wat* nor ! motion ( 8 auto4 ,he gives u 8 sets ( measurem5ts4 ,we rem>k t 8 seconds are only small fractions ( ours1 also 8 nor?s & we/s are badly mix$4 ,if we int]pret 8 sets 9 t]ms ( our /ation>y walls & sob] clock we f9d ! curi\s p>adox t ! ball zigzagg$ across ! room l an intoxicat$ bee4 ,he ob/9ately argues t we "k no m ?an he ab\t h[ ! ball actually mov$4 ,= we got a smoo? description1 he ass]ts1 by *oos+ an artificially simple ref]5ce framework1 hav+ no necess>y relations :atev] to ! ball4 ,! crook$ pa? plott$ f 8 obs]vations proves1 he decl>es1 t ! ball 0 subject to v>y+ =ces ( :i* we 9 ! room suspect$ no?+4 ,he cont5ds t our room 0 be+ j>r$ by a sy/em ( =ces :i* exactly comp5sat$ & smoo!d out ! real jagg$ness ( pa? obs]v$ by himself4 ,b if we "k all ab\t 8 wat* & auto we c easily apply necess>y corrections to 8 measurem5ts1 &1 fitt+ ! correct$ set to our ref]5ce-framework ( walls & clock1 recov] our own smoo? description4 ,= consi/5cy we mu/ c>ry our readju/m5ts f>!r4 ,! pa? mapp$ f our measurem5ts is a curve4 ,p]haps ! curvature 0 introduc$ by "s peculi>ity ( our ref]5ce framework8 ,possibly our own room is be+ accel]at$ upw>d1 s t x makes ! ball's true pa?--:atev] t may be--appe> curv$ d[nw>d1 j z ! autoi/'s zigzags made ! pa? he mapp$ appe> jagg$4 ,tradition attributes ! d[nw>d curv+ to ! tug ( gravity4 ,?is =ce we say accel]ates ! ball d[nw>d1 produc+ ! curv$ pa?4 ,is ?is ! only possible explanation8 ,let u see4 ,,gravitation ,,& ,,accel]ation ,imag9e a man 9 a room out ( :i* he _c see4 ,he notices t :5 he releases any?+ x falls to ! floor ) a con/ant accel]ation4 ,fur!r he obs]ves t all 8 objects1 indep5d5tly ( _! *emical & physical prop]ties1 are affect$ 9 precisely ! same way4 ,n[1 he previ\sly has exp]im5t$ ) magnets1 & has rem>k$ t !y attract c]ta9 bodies 9 ess5tially ! same way t ! ?+s :i* he drops are attract$ to :atev] is b5ea? ! floor4 ,hav+ expla9$ magnetic attraction 9 t]ms ( =ces1 he makes 8 fir/ hypo!sis3 7,a7 ,he & 8 room are 9 a /rong field ( =ce1 :i* he designates gravitational4 ,?is =ce pulls all ?+s d[nw>d ) a con/ant accel]ation4 ,"h he notes a s+ul> di/9ction betwe5 magnetic & gravitational =ces3 magnets attract only a few k9ds ( matt]1 notably iron2 ! novel =ce1 if inde$ a =ce at all1 acts simil>ly ^u all k9ds ( matt]4 ,he makes ano!r hypo!sis3 7,b7 ,8 room & he are be+ accel]at$ upw>d4 ,ei!r 7,a7 or 7,b7 describes ! facts p]fectly4 ,by no exp]im5t c he discrim9ate betwe5 !m4 ,s he takes ! great /ep1 & =mulates ! ,equival5ce ,hypo!sis3 ,a gravitational field ( =ce is precisely equival5t 9 its effects to an artificial field ( =ce introduc$ by accel]at+ ! framework ( ref]5ce1 s t 9 any small region x is impossible to di/+ui% betwe5 !m by any exp]im5t :atev]4 ,next reconsid]+ 8 magnetic =ces1 he ext5ds ! equival5ce hypo!sis to cov] all manife/ations ( =ce3 ,! effects attribut$ to =ces ( any k9d :atev] c be describ$ equally well by say+ t our ref]5ce frameworks are accel]at$2 & moreov] !re is possible no exp]im5t :i* w discrim9ate betwe5 ! descriptions4 ,if ! accel]ations are null1 ! frameworks are at re/ or 9 uni=m motion relatively to "o ano!r4 ,?is special case is ! re/rict$ pr9ciple ( relativity1 :i* ass]ts t x is impossible exp]im5tally to detect a uni=m motion ?r\gh ! e!r4 ,be+ ?us sup]flu\s = descriptions ( natural ph5om5a1 ! e!r may be ab&on$1 at lea/ tempor>ily4 ,! old] physics s\ght ?is absolute e!r framework to :i* all motions c\ld be unambigu\sly ref]r$1 & fail$ to f9d x4 ,! mo/ exact+ exp]im5ts1 notably t ( ,mi*elson-,morley1 reveal$ no trace ( ! e>?'s suppos$ motion ?r\gh ! e!r4 ,fitzg]ald acc\nt$ = ! failure by assum+ t su* motion w\ld rema9 undetect$ if e mov+ body contract$ by an am\nt dep5d+ ^u its velocity 9 ! direction ( motion4 ,! contraction = ord9>y velocities is imp]ceptible4 ,only :5 z 9 ! case ( ! beta p>ticles1 ! velocity is an appreciable fraction ( ! velocity ( light1 is ! contraction reveal$4 ,?is contraction foll[s imm$iately f ,e9/e9's g5]alization con/ruct$ ^u ! equival5ce hypo!sis & ! re/rict$ relativity pr9ciple4 ,we %all see t ! contraction inevitably foll[s f ! actual geometry ( ! univ]se4 #b ,let u return = a mom5t to ! mov+ ball4 ,f\r measures1 ?ree ( di/ances & "o ( "t1 are requir$ 9 specify+ its position ) ref]5ce to "s framework at ea* po9t & at ea* in/ant4 ,all ( ^! measures c be summ$ up 9 "o comp5di\s /atem5t--! equations ( motion %[$ h[ 9 *ang+ f our room to 8 accel]at$ auto we f\nd a new summ>y1 trans=m$ equations1 :i* seem$ to indicate t ! ball _h trav]s$ a /rong1 v>iable field ( =ce4 ,is !re !n 9 ! *aos ( obs]vational disagreem5ts any?+ :i* is indep5d5t ( all obs]v]s8 ,!re is1 b x is hidd5 at ! v he>t ( nature4 ,,pa?s ,,?r\gh ,,! ,,_w ,,( ,,f\r ,,dim5sions ,to exhibit ?is1 we mu/ recall a famili> proposition ( geometry3 ! squ>e on ! longe/ side ( a "r-angl$ triangle is equal to ! sum ( ! squ>es on ! o!r two sides4 ,x has long be5 kn[n t f ?is alone all ! metrical prop]ties ( ,euclidean space--! space 9 :i* = #b1jjj ye>s we h imag9$ we 7 liv+--c be d$uc$4 ,metrical prop]ties are ^? dep5d+ ^u measurem5t4 ,n[1 9 ! geometry ( any space1 ,euclidean or n1 !re is a s+le proposition ( a simil> sort :i* tells u h[ to f9d ! mo/ direct di/ance betwe5 any two po9ts t are v close toge!r4 ,?is small di/ance is express$ 9 t]ms ( ! two sets ( di/ance measurem5ts by :i* ! end-po9ts are locat$1 j z two neighbor+ positions ( our ball 7 locat$ by two sets ( f\r measurem5ts ea*4 ,we say by analogy t two consecutive positions ( ! ball are sep>at$ by a small int]val ( "t-space4 ,f ! =mula = ! v small int]val ( "t-space we c calculate ma!matically all ! metrical prop]ties ( ! "t & space 9 :i* measurem5ts = ! ball's motion mu/ be made4 ,s 9 any geometry ma!matical analysis pr$icts infallibly ! tru? ab\t all facts dep5d+ ^u measurem5ts f ! simple =mula ( ! int]val betwe5 neighbor+ po9ts4 ,?us1 on a sph]e ! sum ( ! angles ( any triangle =m$ by arcs ( great circles exce$s #ahj1 & ?is foll[s f ! =mula = ! %orte/ 7geodesic7 di/ance betwe5 neighbor+ po9ts on ! sph]ical surface4 ,we saw t x takes f\r measurem5ts1 "o = "t & ?ree = di/ances1 to fix an elem5t>y ev5t1 viz41 ! position ( ! c5tre ( our ball at any in/ant4 ,a sy/em ( all possible su* sets ( f\r measurem5ts ea*1 con/itutes :at ma!maticians call a f\r-dim5sional space4 ,! /udy ( ! f\r-dim5sional "t-space geometry1 once its %orte/-di/ance proposition is kn[n1 reveals all ^? relations 9 nature :i* c be asc]ta9$ by measurem5ts1 t is1 exp]im5tally4 ,we h !n to f9d ?is indisp5sable proposition4 ,imag9e ! pa? tak5 by a p>ticle mov+ solely "u ! influ5ce ( gravitation4 ,?is be+ ! simple/ possible motion ( an actual p>ticle 9 ! real _w1 x is natural to guess t its pa? w be su* t ! p>ticle moves f "o po9t ( "t-space to ano!r by ! mo/ direct r\te4 ,?is 9 fact is v]ifi$ by =m+ ! equations ( ! free p>ticle's motion1 :i* turn out to be precisely ^? t specify a geodesic 7mo/ direct l9e7 jo9+ ! two po9ts4 ,on ! 7two-dim5sional7 surface ( a sph]e su* a l9e is ! position tak5 by a /r+ /ret*$ betwe5 two po9ts on ! surface1 & ?is is ! %orte/ di/ance on ! surface betwe5 !m4 ,b 9 ! "t-space geometry we f9d a rem>kable di/9ction3 ! int]val betwe5 any two po9ts ( ! pa? tak5 is ! longe/ possible1 & betwe5 any two po9ts !re is only "o longe/ pa?4 ,translat$ into ord9>y space & "t ?is m]ely ass]ts t ! "t tak5 betwe5 any two po9ts on ! natural pa? is ! longe/ possible4 ,recall n[ t :5 ! l9e-=mula = any k9d ( space is kn[n all ! metrical prop]ties ( t space are completely det]m9$1 & comb9e ) ?is :at we h j f\nd1 namely1 ! equations ( motion ( a p>ticle subject only to gravitation are ! same equations z ^? :i* fix ! l9e-=mula = ! f\r-dim5sional "t-space4 ,s9ce gravitation alone det]m9es ! motion ( ! p>ticle1 & s9ce ?is motion is completely describ$ by ! v equations :i* fix all ! metrical prop]ties ( "t-space1 x foll[s t ! metrical 7exp]im5tally det]m9able7 prop]ties ( "t-space are equival5t to ^? ( gravitation1 9 ! s5se t ea* set ( prop]ties implies ! o!r4 ,,! ,,univ]se ,,( ,,space-,,"t ,we h f\nd ! ?+ 9 nature :i* is indep5d5t ( all obs]v]s1 & x turns out to be ! v /ructure ( "t-space itself4 ,! motion ( ! free p>ticle obvi\sly is a ?+ uncondition$ by accid5ts ( obs]vation2 ! p>ticle "u ! influ5ce ( gravitation alone mu/ g a way ( its own4 ,& if "s obs]v] 9 an artificial field ( =ce produc$ by ! accel]ation ( 8 ref]5ce framework describes ! pa? z knott$1 he m]ely is foi/+ ecc5tricities ( 8 own motion ^u ! direct pa? ( ! p>ticle4 ,! conclusion is rational1 = we believe t "t-space exi/s indep5d5tly ( any man's way ( p]ceiv+ x4 ,incid5tally note t ?is space is t ( ! physical _w4 ,= only by measurem5ts ( di/ances & times c we become aw>e ( our ext5sion 9 "t & space4 ,if beyond ?is "t-space geometry ( measurem5ts !re is "s absolute geometry1 sci5ce c h no conc]n ) x1 = nev] c x be reveal$ by ! "o explor+ device we possess--measurem5t4 ,we h foll[$ a s+le p>ticle4 ,let u n[ =m a picture ( sev]al4 ,any ev5t c be analyz$ into a multitude ( co9cid5ces 9 "t-space4 ,= consid] two mov+ p>ticles--say electrons4 ,if !y collide !y bo? are 9 v approximately "o place at ! same "t4 ,we imag9e ! pa? ( an electron ?r\gh "t-space plott$ by a l9e 79 f\r-dim5sional space71 :i* w deviate f a mo/ direct 7geodesic7 pa? if ! electron is subject$ to =ces4 ,?is is ! _w-l9e ( ! electron4 ,if ! _w l9es ( sev]al electrons int]sect at "o po9t 9 "t-space1 ! int]section pictures ! fact ( _! co9cid5ce some:]e & some:52 = all _! _w-l9es hav+ a "t-space po9t 9 common1 at "s in/ant !y mu/ h be5 9 collision4 ,ea* po9t ( a _w-l9e pictures ! position at a c]ta9 place at a c]ta9 "t2 & x is ! int]sections ( _w-l9es :i* correspond to physical ev5ts4 ,( :at lies betwe5 ! int]sections we h no exp]im5tal k4 ,imag9e ! _w-l9es ( all ! electrons 9 ! univ]se ?read+ "t-space l ?reads 9 a jelly4 ,! int]sections ( ! tangle are a complete hi/ory ( all physical ev5ts4 ,n[ di/ort ! jelly4 ,cle>ly ! mutual ord] ( ! int]sections w be un*ang$1 b ! di/ances betwe5 !m w be %ort5$ or l5g!n$4 ,to a di/ortion ( ! jelly corresponds a special *oice 7by "s obs]v]7 ( a ref]5ce framework = describ+ ! ord] ( ev5ts4 ,he _c *ange ! natural sequ5ce ( ev5ts4 ,aga9 we h f\nd some?+ :i* is indep5d5t ( all obs]v]s4 ,we c n[ recapitulate our conclusions & /ate ! pr9ciple ( relativity 9 its mo/ g5]al =m4 7#a7 ,obs]v]s describe ev5ts by measures ( times & di/ances made ) reg>d to _! frameworks ( ref]5ce4 7#b7 ,! complete hi/ory ( any ev5t is summ>iz$ 9 a set ( equations giv+ ! positions ( all ! p>ticles involv$ at e in/ant4 7#c7 ,two possibilities arise4 7,a7 ,ei!r ^! equations are ! same 9 =m = all space-"t ref]5ce frameworks1 p]si/+ =mally un*ang$ = all %ifts ( ! ref]5ce s*eme2 or 7,b71 !y subsi/ only :5 "s special framework is us$1 alt]+ _! =m z !y are ref]r$ to diff]5t frameworks4 ,if 7,b7 holds1 we naturally assume t ! equations1 & ! ph5om5a :i* !y pr(ess to repres5t1 owe _! exi/5ce to "s peculi>ity ( ! ref]5ce framework4 ,!y d n1 !re=e1 describe any?+ :i* is inh]5t 9 ! nature ( ?+s1 b m]ely "s idiosyncrasy ( ! obs]v]'s way ( reg>d+ nature4 ,if 7,a7 holds1 !n obvi\sly ! equations describe "s real relation 9 nature :i* is indep5d5t ( all possible ways ( obs]v+ & record+ x4 7#d7 ,9 its mo/ g5]al =m ! pr9ciple ( relativity /ates t ^? relations1 & ^? alone1 :i* p]si/ un*ang$ 9 =m = all possible space-"t ref]5ce frameworks are ! inh]5t laws ( nature4 ,to f9d su* relations ,e9/e9 has appli$ a ma!matical me?od ( great p[]--! calculus ( t5sors--) extraord9>y success4 ,?is calculus ?re%es out ! laws ( nature1 sep>at+ ! obs]v]'s ecc5tricities f :at is indep5d5t ( him1 ) ! sup]b effici5cy ( a mod]n h>ve/]4 ,! residue is a physical geometry--or geometrical physics--( "t-space1 9 :i* x appe>s t ! times & spaces contribut$ by ! sev]al obs]v]s' ref]5ce frameworks are %ad[s ( _! own contriv+s2 :ile ! real1 endur+ univ]se is a f\rfold ord] ( "t & space indissolubly b\nd toge!r4 ,"o obs]v] sep>ates ?is "t-space into 8 own "t & space 9 "o way1 det]m9$ by 8 pa? ?r\gh ! _w ( ev5ts2 ano!r1 mov+ relatively to ! fir/1 sep>ates x diff]5tly1 & :at = "o is "t %ades into space = ano!r4 ,?is "t-space geometry is non-,euclidean4 ,x is w>p$ 7curv$71 ! am\nt ( w>p+ at any place be+ det]m9$ by ! int5sity ( ! gravitational field !re4 ,?us aga9 gravitation is root$ 9 ! nature ( ?+s4 ,9 ?is s5se x is n a =ce1 b a prop]ty ( space4 ,:]ev] !re is matt] !re is a gravitational field1 & h5ce a w>p+ ( space4 ,conv]sely1 z long ago imag9$ by ,clif=d1 :]ev] !re is a w>p+ ( space1 !re is matt]2 & matt] is resolv$ ultimately into wr9kles 9 "t-space4 ,to visualize a w>p$ space1 consid] a simple analogy4 ,a man walks away f a poli%$ globe2 8 image rec$es into ! mirror-space1 %ort5+ & ?9n+ z x goes1 & ?9n+ 79 ! direction ( motion7 fa/] ?an x %ort5s4 ,ev]y?+ ar\nd him exp]i5ces a l effect4 ,if he tries to discov] ?is by a footrule x automatically %ort5s fa/] z he turns x into ! horizontal position1 s 8 purpose eludes him4 ,! mirror-space is w>p$ 9 ! direction ( ! image's motion4 ,s is our own4 ,= all bodies1 z evid5c$ by ! ,fitzg]ald contraction1 %ort5 9 ! direction ( motion4 ,& j z ! image c nev] p5etrate ! mirror-space a great] di/ance ?an half its radius1 s probably "t-space is curv$ 9 su* a way t our univ]se1 l ! surface ( a sph]e1 is f9ite 9 ext5t1 b unb\nd$4 ,,xii ,,=ce ,,vs4 ,,geometry ,h[ ,e9/e9 ,has ,sub/itut$ ! ,second = ! ,fir/ 9 ,connection ,) ! ,cause ( ,gravitation ,,by ,,saul ,,du%man ,,g5]al ,,electric ,,laboratories ,,s*5ectady1 ,n4 ,y4 ,! !ory ( relativity repres5ts a mo/ /rik+ly orig9al conception ( "t & space1 :i* 0 sugge/$ by ,e9/e9 9 ord] to correlate ) all our pa/ exp]i5ce c]ta9 obs]vations made 9 rec5t ye>s4 ,x is !re=e extremely compreh5sive 9 its scope2 x dem&s f u a radical revision 9 our notions ( "t & space2 x ?r[s new light on ! nature ( mass & en]gy1 & f9ally1 x furni%es a totally new conception ( ! old problem ( gravitation4 ,! />t+ po9t ( ! !ory is ! famili> obs]vation t motion is always relative3 t is1 to def9e ! motion ( any object we mu/ always use "s po9t ( ref]5ce4 ,?us we speak ( ! velocity ( a tra9 z #dj miles p] h\r ) respect to ! e>?'s surface1 b w\ld f9d x impossible to det]m9e its absolute spe$1 or motion 9 space1 s9ce we "k ( no /> ^: position c be spok5 ( z absolutely fix$4 ,^! & simil> consid]ations h l$ to ! conclusion1 po9t$ out by ,newton & o!rs1 t x is impossible by any me*anical exp]im5ts on ! e>? to measure its velocity 9 space4 ,h[ev]1 ! results ( obs]vations on ! ph5om5a ( light & electricity l$ to ! revival ( ! same problem "u ano!r =m4 ,z well kn[n1 !re 0 evolv$ f ^! discov]ies1 ! !ory t light & electrical en]gy are ( ! same nature1 & are 9 ea* case manife/ations ( wave-di/urbances propagat$ ?r\gh a hypo!tical m$ium1 ! e!r1 ) a velocity ( #ahf1jjj miles p] second4 ,! problem !re=e arose z to :e!r ! e>? & all /ell> bodies move ?r\gh ?is e!r4 ,9 t case x ought to be possible to measure ! velocity ( ! e>? ) respect to ?is m$ium1 & "u ^! conditions we c\ld speak1 9 a s5se1 ( absolute motion4 ,a l>ge numb] ( exp]im5ts has be5 tri$ ) ?is end 9 view4 ,! mo/ fam\s ( ^!1 & ! "o :i* /imulat$ ! subsequ5t developm5t ( ! !ory ( relativity1 0 t c>ri$ out by ,mi*elson & ,morley 9 #ahhg4 ,to und]/& ! significance ( ?is exp]im5t we %all ref] briefly to an analog\s obs]vation :i* is q famili>4 ,does x take long] to swim to a po9t #a mile up a /ream & back or to a po9t #a mile across /ream & back8 ,! exp]i5c$ swimm] w answ] t ! up-&-d[n j\rney takes long]4 ,if we assume t ! swimm] has a spe$ ( #e miles an h\r 9 /ill wat] & t ! curr5t is #c miles an h\r1 we f9d t1 :ile x requires five-eigh?s h\r to make ! up-&-d[n j\rney1 x takes only "o-half h\r = ! trip across /ream & back4 ,! ratio betwe5 ! times requir$ = ! two j\rneys is ?us five-f\r?s1 & if ?is is writt5 9 ! =m frac#asqrt#a - 7frac#ce7b x %[s h[ ! result dep5ds ^u ! squ>e ( ! ratio ( ! spe$s ( ! swimm] & ! curr5t4 ,n[ ! e>? is mov+ 9 its orbit ab\t ! sun ) a velocity ( #ah miles p] second4 ,if ! e>? moves ?r\gh ! e!r & a light-beam passes f "o mirror to ano!r & back aga91 ! "t tak5 = ?is j\rney ought to be long] :5 ! light-pa? is 9 ! direction ( ! e>?'s motion ?an :5 x is at "r angles to ?is direction4 ,= we c consid] ! light z a swimm] hav+ a spe$ ( #ahf1jjj miles p] second & travell+ 9 a /ream ^: curr5t is #ah miles p] second4 ,:5 ,mi*elson & ,morley tri$ ! exp]im5t !y c\ld n obs]ve any diff]5ce 9 ! velocity ( light 9 ! two directions4 ,! exp]im5t has s9ce be5 repeat$ "u v>i\s conditions1 b always ) negative results4 ,e9/e9's contribution to sci5ce consi/s 9 int]pret+ ?is result z be+ 9 accord ) ,newton's ideas on me*anical relativity 9 t x demon/rates ! impossibility ( measur+ absolute motion1 n only by me*anical1 b also by optical or electrical exp]im5ts4 ,consequ5tly ! velocity ( light mu/ be reg>d$ z con/ant & indep5d5t ( ! motion ( ei!r s\rce or obs]v]4 ,,! ,,relativity ,,( ,,uni=m ,,motion ,let u consid] "s ( ! consequ5ces :i* foll[ f ?is pr9ciple4 ,an obs]v] travell+ ) say "o-half ! velocity ( light 9 ! same direction z a ray ( light w\ld f9d t ! latt] has ! usual velocity ( #ahf1jjj miles p] second4 ,simil>ly an obs]v] travell+ 9 ! opposite direction to t ( ! light-ray1 ) "o-half ! velocity ( light1 w\ld obta9 ! same result4 ,e9/e9 has %[n t ^! conclusions c be valid only if ! units ( "t & space us$ by ! two obs]v]s dep5d ^u _! relative motions4 ,a c>eful calculation %[s t ! unit ( l5g? us$ by ei!r obs]v] appe>s to ! o!r obs]v] contract$ :5 plac$ 9 ! direction ( _! relative motion 7b n1 :5 plac$ at "r angles to ?is direction71 & ! unit ( "t us$ by ei!r obs]v] appe>s to ! o!r too great4 ,moreov]1 ! ratio ( ! units ( l5g? or ( "t v>ies ) ! squ>e ( ! relative spe$ ( ! two obs]v]s1 accord+ to a relation :i* is simil> to t m5tion$ above = ! swimm] 9 ! curr5t4 ,?is relation %[s t z ! relative spe$ approa*es t ( light ! discrepancy betwe5 ! units increases4 ,?us1 = an obs]v] mov+ pa/ our e>? ) a velocity :i* is n9e-t5?s t ( light1 a met] /ick on ! e>? w\ld be #dd c5timet]s z measur$ by him1 :ile a second on our clocks w\ld be ab\t two & a half seconds z m>k$ by 8 clock4 ,simil>ly1 :at he calls a met] l5g? w\ld1 = u1 be only #dd c5timet]s & he w\ld appe> to u to be liv+ ab\t two & a half times sl[] ?an we are4 ,ea* obs]v] is p]fectly consi/5t 9 8 measurem5ts ( "t & space z long z he conf9es 8 obs]vations to 8 own sy/em1 b :5 he tries to make obs]vations on ano!r sy/em mov+ pa/ 81 he f9ds t ! results :i* he obta9s d n agree ) ^? obta9$ by ! o!r obs]v]4 ,x is n surpris+ t 9 accordance ) ?is conclusion x also foll[s t ! mass ( a body mu/ increase ) its velocity4 ,= l[ velocities ! increase is s small t we _c ev] hope to measure x1 b z ! velocity ( light is approa*$ ! diff]5ce becomes m & m appreciable & a body hav+ ! velocity ( light w\ld possess inf9ite mass1 :i* simply means t su* a velocity _c be atta9$ by any mat]ial object4 ,?is conclusion has be5 exp]im5tally confirm$ by obs]vations on ! mass ( ! extremely small negatively *>g$ p>ticles :i* are emitt$ by radioactive elem5ts4 ,"s ( ^! p>ticles are eject$ ) velocities :i* are ov] n9e-t5?s t ( light1 & measurem5ts %[ t ! increase 9 mass is 9 accord ) ?is !ory4 ,! relativity !ory also ?r[s new light on ! nature ( mass itself4 ,accord+ to ?is view1 mass & en]gy are equival5t4 ,! absolute de/ruction ( #a gram ( any sub/ance1 if possible1 w\ld yield an am\nt ( en]gy :i* is "o hundr$ million times z mu* z t obta9$ by burn+ ! same mass ( coal4 ,conv]sely1 en]gy *anges are accompani$ by *anges 9 mass4 ,! latt] are ord9>ily s inappreciably small z to escape our mo/ ref9$ me?ods ( measurem5ts1 b 9 ! case ( ! radioactive elem5ts we actually obs]ve ?is ph5om5on4 ,f ?is /&po9t1 also1 ! laws ( cons]vation ( en]gy & ( mass are %[n to be intimately relat$4 ,,univ]sal ,,relativity ,s f> we h dealt ) :at has be5 designat$ z ! special !ory ( relativity4 ,?is1 z we h se51 applies to uni=m motion only4 ,9 ext5d+ ! !ory to include non-uni=m or accel]at$ motion1 ,e9/e9 has at ! same "t d$uc$ a law ( gravitation :i* is mu* m g5]al ?an t ( ,newton4 ,a body fall+ t[>ds ! e>? increases 9 velocity z x falls4 ,! motion is said to be accel]at$4 ,we ascribe ?is increase 9 velocity to a gravitational =ce ex]t$ by ! e>? on all objects4 ,z %[n by ,newton1 ?is =ce acts betwe5 all p>ticles ( matt] 9 ! univ]se1 & v>ies inv]sely z ! squ>e ( ! di/ance1 & directly z ! product ( ! masses4 ,( c\rse1 we h _h a numb] ( !ories ( gravitation1 & none ( !m h prov5 successful4 ,e9/e91 h[ev]1 0 ! fir/ "o to sugge/ a conception ( gravitation :i* has prov5 extremely significant4 ,he po9ts out t a gravitational =ce is non-exi/5t = a p]son fall+ freely ) ! accel]ation due to gravity4 ,= ?is p]son !re is no s5sation ( weight1 & if he 7 9 a clos$ box :i* is also fall+ ) ! same accel]ation1 he w\ld be unable to decide z to :e!r 8 sy/em 7 fall+ or situat$ 9 int]planet>y space :]e !re is no gravitational field4 ,fur!rmore1 if he 7 to c>ry out any optical or electrical exp]im5ts 9 ?is box he w\ld obs]ve ! same results z an exp]im5t] on ! e>?4 ,a ray ( light w\ld travel 9 a /raight l9e s f> z ?is obs]v] c p]ceive1 :ile an ext]nal obs]v] w\ld1 ( c\rse1 judge diff]5tly4 ,e9/e9 %[s t ?is is equally true = all k9ds ( accel]ation includ+ t due to rotation4 ,9 ! case ( a rotat+ body !re exi/s a c5trifugal =ce :i* t5ds to make objects on ! surface fly outw>ds1 b = an ext]nal obs]v] ?is =ce does n exi/ any m ?an gravity exi/s = ! obs]v] fall+ freely4 ,?us we c draw ! g5]al conclusion t a gravitational field or any o!r field ( =ce may be elim9at$ by *oos+ an obs]v] mov+ ) ! prop] accel]ation4 ,= ?is obs]v]1 h[ev]1 ! laws ( optics & electricity mu/ be j z valid z = an obs]v] on ! e>?4 ,9 po/ulat+ ?is equival5ce hypo!sis ,e9/e9 m]ely makes use ( ! v famili> obs]vation t1 indep5d5tly ( ! nature ( ! mat]ial1 all bodies possess ! same accel]ation 9 a giv5 field ( =ce4 ,! problem :i* ,e9/e9 n[ sets out to solve is t ( det]m9+ ! law :i* %all describe ! motion ( any sy/em 9 a field ( =ce 9 su* a g5]al mann] z to leave unalt]$ ! fundam5tal relations ( electricity & optics4 ,9 connection ) ! solution ( ?is problem he f9ds x necess>y to disc>d ! limitations plac$ on u by ord9>y or ,euclidean geometry4 ,9 ?is mann] geometrical concepts z well z ^? ( =ce are completely robb$ ( all notions ( absolut5ess1 & ! goal ( a g5]al !ory ( relativity is atta9$4 ,,! ,,geometry ,,( ,,gravitation ,let u consid] a circul> disc rotat+ ) a uni=m p]iph]al spe$4 ,accord+ to ! d$uctions f ! special !ory ( relativity1 an obs]v] situat$ ne> ! edge ( ?is disc1 b n rotat+ ) x1 w obs]ve t units ( l5g? measur$ along ! circumf]5ce ( ! disc are contract$4 ,on ! o!r h&1 measurem5ts along ! diamet]1 :i* is at "r angles to ! direction ( motion ( ! circumf]5ce1 w %[ no contraction :atev]1 &1 consequ5tly ! obs]v] w f9d t ! ratio ( circumf]5ce to diamet] has n ! well kn[n value #c4adaei 444 b exce$s ?is value1 ! diff]5ce be+ great] & great] z ! p]iph]al spe$ approa*es t ( light4 ,t is1 ! laws ( ord9>y geometry no long] hold true4 ,h[ev]1 we "k o!r cases 9 :i* ! ord9>y or ,euclidean geometry is n applicable4 ,?us suppose t on ! surface ( a sph]e we describe a s]ies ( conc5tric circles4 ,s9ce ! surface is curv$1 we are n surpris$ at f9d+ t ! circumf]5ce ( any "o ( ^! circles is less ?an #c4adaei 444 times ! di/ance across ! circle z measur$ on ! surface ( ! sph]e4 ,:at ?is means1 !re=e1 is t we _c use ,euclidean geometry to describe measurem5ts on ! surface ( a sph]e1 & e s*oolboy kn[s ?is f comp>+ ,m]cator's projection ( ! e>?'s surface ) ! actual repres5tation on a globe4 ,:5 we come to ?9k ( x1 ! reason we realize all ?is is because our s5se ( ?ree dim5sions enables u to diff]5tiate flat surfaces f ^? t are curv$4 ,let u1 h[ev]1 imag9e a two-dim5sional be+ liv+ on ! surface ( a l>ge sph]e4 ,s long z 8 measurem5ts are conf9$ to relatively small areas he w f9d x possible to describe all 8 measurem5ts 9 t]ms ( ,euclidean geometry4 ,z1 h[ev]1 8 area ( op]ation increases he w beg9 to obs]ve great] & great] discrepancies4 ,be+ unfamili> ) ! exi/5ce ( su* a ?ree-dim5sional object z a sph]e1 & !re=e n realiz+ t he is on ! surface ( "o1 our intellig5t two-dim5sional be+ w conclude t ! di/urbance 9 8 geometry is due to ! action ( a =ce1 & by means ( plausible assumptions on ! law ( ?is =ce he w reconcile 8 obs]vations ) ! laws ( plane geometry4 ,n[ s9ce an accel]ation 9 a gravitational field is id5tical ) t due to c5trifugal =ce produc$ by rotation1 we conclud$ t ! geometry 9 a gravitational field mu/ also be non-,euclidean4 ,t is1 space 9 ! neighborhood ( matt] is di/ort$ or curv$4 ,! curvature ( space be>s ! same relation to ?ree dim5sions t ! curvature ( a sph]ical surface be>s to two dim5sions1 & t is :y we d n p]ceive x1 any m ?an ! intellig5t two-dim5sional be+ w\ld be aw>e ( ! di/ortion ( 8 space 7or surface74 ,fur!rmore1 l ?is be+1 we h assum$ ! exi/5ce ( a gravitational =ce to acc\nt = discrepancies 9 our geometrical measurem5ts4 ,! id5tification 9 ?is mann] ( gravitational effects ) geometrical curvature ( space enables ,e9/e9 to d]ive a g5]al law = ! pa? ( any p>ticle 9 a gravitational field1 ) respect bo? to space & to "t4 ,fur!rmore1 ! law expresses ?is motion 9 t]ms :i* are indep5d5t ( ! relative motion & position ( ! obs]v]1 & satisfies ! condition t ! fundam5tal laws ( physics be equally valid = all obs]v]s4 ,! solution ( ! problem involv$ ! use ( a new k9d ( high] calculus1 elaborat$ by two ,italian ma!maticians1 ,ricci & ,levi-,civita4 ,! result is a law ( motion :i* is extremely g5]al 9 its validity4 ,= l[ velocities x approximates to ,newton's solution1 & 9 ! abs5ce ( a gravitational field x leads to ! same conclusions z ! special !ory ( relativity4 ,!re are ?ree d$uctions f ?is law :i* h ar\s$ a great deal ( int]e/1 & ! confirmation ( two ( ^! by actual obs]vation mu/ be reg>d$ z /rik+ pro( ( ,e9/e9's !ory4 ,,xiii ,,an ,,introduction ,,to ,,relativity ,a ,treatm5t 9 ,:i* ! ,ma!matical ,connections ( ,e9/e9's ,"w are ,br\ght ,out ,m ,/rongly & ,m ,successfully ,?an ,usual 9 a ,popul> ,explanation ,,by ,,h>old ,t4 ,,davis1 ,,univ]sity ,,( ,,wiscons91 ,madison1 ,wis4 ,"o ( ! fir/ que/ions :i* appe>s 9 philosophy is ?is3 ,:at is ! great reality t und]lies space & "t & ! ph5om5a ( ! physical univ]se8 ,kant1 ! philosoph]1 dismiss$ x z a subjective problem1 affirm+ t space & "t are a priori concepts beyond :i* we c say no m4 ,!n ! _w came ^u "s />tl+ facts4 ,9 #aije a pap] appe>$ by ,pr(essor ,alb]t ,e9/e9 :i* ass]t$ t ! explanation ( c]ta9 rem>kable discov]ies 9 physics gave u a new conception ( ?is /range f\r-dim5sional manifold 9 :i* we live4 ,?us1 ! great diff]5ce betwe5 ! space & "t ( philosophy & ! new k is ! objective reality ( ! latt]4 ,x re/s ^u an amaz+ sequ5ce ( physical facts1 & ! g5]aliz$ !ory1 :i* appe>$ sev]al ye>s lat]1 f\nd$ z x is ^u ! ab/ruse diff]5tial calculus ( ,riemann1 ,*ri/(fel1 ,ricci & ,levi-,civita1 em]ges f its maze ( =mulas ) ! pr$iction ( real ph5om5a to be s\ght = ! 9 ! _w ( facts4 ,we %all1 !re=e1 approa* ! subject f ?is objective po9t ( view4 ,let u g to ! realm ( actual physical ev5ts & see h[ ! ideas ( relativity gradually unfold$ !mselves f ! fir/ crude wond]+s ( sci5ce to ! /ately rese>*es t fir/ discov]$ ! great ocean ( e!r & !n p5etrat$ 9 su* a m>vel\s mann] into "s ( its mo/ my/]i\s prop]ties4 ,,! ,,electromagnetic ,,!ory ,,( ,,light ,suppose t we g out on a summ] night & look into ! d>k dep?s ( ! sky4 ,a ?\s& bright specks are fla%+ !re1 blue1 r$1 yell[ aga9/ ! d>k velvet ( space4 ,& z we look we mu/ all be impress$ by ! fact t su* remote objects z ! />s c be kn[n to u at all4 ,h[ is x t light1 t curi\s ?+ :i* falls ^u ! optic n]ve & transmits its pictures to ! bra91 c ev] rea* u ?r\gh ! black regions ( int]/ell> space8 ,t is ! "q :i* has = its answ] ! electromagnetic !ory ( light4 ,! fir/ !ory to be advanc$ 0 ,newton's corpuscul> !ory :i* suppos$ t ! />s are s5d+ (f into space little pellets ( matt] s inf9itesimally small t !y c move at ! rate ( #ahf1jjj miles a second )\t injur+ ev5 s delicate a ?+ z ! eye :5 !y /rike aga9/ x4 ,b 9 #ahja1 :5 ,?omas ,"y made ! v important discov]y ( int]f]5ce1 ?is _h to give way to ! wave !ory1 fir/ propos$ by ,huygh5s 9 ! #ag? c5tury4 ,! fir/ great d$uction f ?is1 ( c\rse1 0 ! lum9if]\s e!r1 because a wave )\t "s m$ium = its propagation 0 q un?9kable4 ,c]ta9 peculi> prop]ties ( ! e!r 7 at once evid5t1 s9ce we d$uce t x mu/ fill all space & at ! same "t be s extremely t5u\s t x w n ret>d to any noticeable degree ! motion ?r\gh x ( mat]ial bodies l ! planets4 ,b h[ light 0 propagat$ ?r\gh ! e!r /ill rema9$ a p]plex+ problem & v>i\s !ories 7 propos$1 mo/ prom95t among !m be+ ! ela/ic solid !ory :i* tri$ to ascribe to e!r ! prop]ties ( an ela/ic body4 ,?is !ory1 h[ev]1 laid itself op5 to s]i\s objection on ! gr\nd t no longitud9al waves _h be5 detect$ 9 ! e!r1 s t x began to appe> t fur!r insight into ! nature ( light _h to be s\ght = 9 ano!r direction4 ,?is 0 soon =?com+ = 9 #ahfd a new !ory 0 propos$ by ,james ,cl]k ,maxwell :i* seem$ to solve all ( ! difficulties4 ,maxwell _h be5 work+ ) ! facts d]iv$ f a /udy ( electrical & magnetic ph5om5a & _h %[n t electromagnetic di/urbances 7 propagat$ ?r\gh ! e!r at a velocity id5tical ) t ( light4 ,?is1 ( c\rse1 might h be5 m]ely a /range co9cid5ce1 b ,maxwell w5t fur!r & demon/rat$ ! int]e/+ fact t an oscillat+ electric *>ge %\ld give rise to a wave t w\ld behave 9 a mann] id5tical ) all ( ! kn[n prop]ties ( a light wave4 ,"o p>ticul>ly impressive ass]tion 0 t ^! waves1 consi/+ ( an alt]nat+ electric field accompani$ by an alt]nat+ magnetic field at "r angles to x1 & h5ce call$ electromagnetic waves1 w\ld advance 9 a direction p]p5dicul> to ! alt]nat+ fields4 ,?is satisfi$ ! fir/ ess5tial prop]ty ( light rays1 i4e41 t !y mu/ be transv]se waves1 & ! ease ) :i* x expla9$ all ( ! fundam5tal ph5om5a ( optics & pr$ict$ a mo/ /rik+ int]relation betwe5 ! electrical & optical prop]ties ( mat]ial bodies1 gave x at once a prom95t place among ! v>i\s !ories4 ,! electromagnetic !ory1 h[ev]1 _h to wait until #ahhh = v]ification :5 ,he9ri* ,h]tz1 9 a s]ies ( brilliant exp]im5ts1 succe$$ 9 produc+ electromagnetic waves 9 ! laboratory & 9 %[+ t !y possess$ all ( ! prop]ties pr$ict$ by ,maxwell4 ,^! waves mov$ ) ! velocity ( light3 !y c\ld be reflect$1 refract$1 & pol>iz$3 !y exhibit$ ! ph5om5on ( int]f]5ce &1 9 %ort1 c\ld n be di/+ui%$ f light waves except = _! diff]5ce 9 wave l5g?4 ,,! ,,mi*elson-,,morley ,,exp]im5t ,) ! f9al e/abli%m5t ( ! electromagnetic !ory ( light z a fact ( physics1 we h at la/ end[$ ! e!r ) an actual sub/antiality4 ,! empty void is no long] empty1 b a great ocean ( e!r ?r\gh :i* ! planets & ! suns turn )\t ev] be+ aw>e t x is !re4 ,9 #ahha ,a4 ,a4 ,mi*elson und]took an exp]im5t1 orig9ally sugge/$ by ,maxwell1 to det]m9e ! relative motion ( our e>? to ! e!r ocean & six ye>s lat] he repeat$ x ) ! assi/ance ( ,e4 ,w4 ,morley4 ,! exp]im5t is n[ kn[n z ! ,mi*elson-,morley exp]im5t & s9ce x is ! great physical fact ^u :i* ! !ory ( relativity re/s1 x w be well = u to exam9e x 9 detail4 ,s9ce we c sc>cely ?9k t our e>? is privileg$ 9 ! univ]se & t x is at re/ ) respect to ?is great e!r ocean t fills space1 we propose to discov] h[ fa/ we are actually mov+4 ,b ! />tl+ fact is t ! exp]im5t devis$ = ?is purpose fail$ to detect any motion :atev] ( ! e>? relative to ! e!r4 #c ,! explanation ( ?is v curi\s fact 0 giv5 by bo? ,h4 ,a4 ,lor5tz & ,g4 ,f4 ,fitzg]ald 9 :at is n[ widely kn[n "u ! "n ( ! contraction hypo!sis4 ,x is no?+ m nor less ?an ?is3 ,e solid body und]goes a slight *ange 9 dim5sions1 ( ! ord] ( 7v#b_/;c#b71 :5 x moves ) a velocity v ?r\gh ! e!r4 ,! reason :y ! exp]im5t fail$1 !n1 0 n because ! e>? 0 n mov+ ?r\gh ! e!r1 b because ! in/rum5ts ) :i* ! exp]im5t 0 be+ conduct$ _h %runk j en\gh to negative ! effect t 0 be+ look$ =4 #d ,,! ,,lor5tz ,,trans=mation ,we c n at ?is po9t =ebe> introduc+ a little ma!matics to fur!r emphasize ! !ory & ! v logical nature ( ?is contraction hypo!sis4 ,let u suppose t we 7 on a _w t 0 absolutely motionless ) respect to ! e!r & 7 look+ at a ray ( light4 ,! magnetic & electric fields :i* =m ! ray c be describ$ by means ( f\r ma!matical expressions :i* h come to be> ! "n ( ,maxwell's field equations4 ,n[ suppose t we ask ourselves ! "q3 ,h[ mu/ ^! equations be *ang$ s t !y w apply to a ray ( light :i* is be+ obs]v$ by p on a _w t is mov+ ) a velocity v ?r\gh ! e!r8 ,! answ] is imm$iate4 ,f ! ,mi*elson-,morley exp]im5t we "k t we c n tell h[ fa/ or h[ sl[ly we are mov+ ) respect to ! e!r4 ,?is means t no matt] :at _w we may be ^u1 ! =m ( ! ,maxwell field equations w always be ! same1 ev5 ?\gh ! second set ( axes 7or frame ( ref]5ce7 may be mov+ ) high velocity ) respect to ! fir/4 ,/>t+ f ?is hypo!sis 7call$ 9 te*nical language ! cov>iance ( ! equations ) respect to a trans=mation ( coord9ates71 ,lor5tz f\nd t ! trans=mation :i* leaves ! field equations un*ang$ 9 =m 0 ! foll[+3 x' k7x - vt71 y' y1 z' z1 t' k7t - vx_/c7 :]e k is z on page #ib4 ,& :at1 n[1 c be d$uc$ f ^! v simple look+ equations8 ,9 ! fir/ place we see t ! space ( x'1 y'1 z'1 t' is n our ord9>y concept ( space at all1 b a space 9 :i* "t is all tangl$ up ) l5g?4 ,to put x m concretely1 we may d$uce f !m ! int]e/+ fact t :5ev] an aviator moves ) respect to our e>?1 8 %ape *anges1 & if he 7 to comp>e 8 wat* ) "o on ! e>?1 he w\ld f9d t 8 "t _h *ang$ also4 ,a sph]e w\ld flatt5 into an ellipse1 a met] /ick w\ld %ort5 up1 a wat* w\ld sl[ d[n & all because1 z ,h4 ,m9k[ski has %[n u f ^! v equations1 we are really liv+ 9 a physical _w q diff]5t f ! _w ( ,euclid's geometry 9 :i* we are accu/om$ to ?9k we live4 ,a v>iety ( objections has v naturally be5 made to ?is r radical hypo!sis 9 an attempt to discr$it ! entire !ory1 b x is easily se5 t any result obta9$ ?r\gh ! field equations mu/ necess>ily be 9 con=mity ) ! !ory ( contraction1 s9ce ?is !ory is only ! physical int]pretation ( t trans=mation :i* leaves ! field equations unalt]$4 ,inde$1 x is ev5 possible to po/ulate ! ,lor5tz trans=mation toge!r ) ! assumption t ea* elem5t ( *>ge is a c5t] ( uni=mly div]g+ tubes ( /ra9 & d]ive ! ,maxwell field equations f ?is1 :i* %[s f ano!r po9t ( view ! truly fundam5tal nature ( ! trans=mation4 ,,! ,,fir/ ,,!ory ,,( ,,relativity ,! :ole "q ( ! e!r _h arriv$ at ?is v int]e/+ po9t :5 ,pr(essor ,e9/e9 9 #aije /at$ ! !ory ( relativity4 ,he _h notic$ t ! equations ( dynamics z =mulat$ by ,newton did n admit ! ,lor5tz trans=mation1 b only ! simple ,galilean trans=mation3 x' x - vt1 y' y1 z' z1 t' t14 ,"h1 inde$1 0 a curi\s situation4 ,two physical pr9ciples1 t ( dynamics & t ( electromagnetism1 7 coexi/5t & yet ea* "o admitt$ a diff]5t trans=mation :5 ! sy/em ( ref]5ce 0 transf]r$ to axes mov+ ) con/ant velocity ) respect to ! e!r4 ,n[ ! electromagnetic equations & _! trans=mation _h be5 %[n to be 9 accord ) exp]im5tal fact1 :]eas x _h long be5 felt t ,newton's equations 7 only a fir/ approximation to ! tru?4 ,= example1 ! elliptic orbit ( a planet _h be5 obs]v$ by ,lev]ri] to exhibit a disquiet+ t5d5cy to rotate 9 ! direction ( motion4 ,?is precession1 :i* 9 ! case ( ,m]cury 0 z l>ge z #dc'' p] c5tury1 c\ld n be acc\nt$ = 9 any way by ! ord9>y ,newtonian laws & 01 consequ5tly1 a v celebrat$ case ( discordance 9 gravitational a/ronomy4 ,) ?is example cle>ly be=e him1 ,e9/e9 took ! great /ep & said t ! laws ( dynamics & all o!r physical laws _h to be remade s t !y1 also1 admit ! ,lor5tz trans=mation4 ,t is to say1 ,! laws ( physical ph5om5a1 or r ! ma!matical expressions = ^! laws1 are cov>iant 7un*ang$ 9 =m7 :5 we apply ! ,lor5tz trans=mation to !m4 ,! d$uctions f ! ,mi*elson-,morley exp]im5t n[ seem to h rea*$ _! ultimate conclusion4 ,"o discordant fact 9 ?is new !ory rema9$1 h[ev]4 ,t same precession ( ! p]ihelion ( ,m]cury :i* _h fir/ lead ,e9/e9 to 8 !ory rema9$ unsettl$4 ,:5 ! new approximations 7 appli$ to ! =mula ( orbital motion1 a precession 01 inde$1 obta9$1 b ! comput$ value fell consid]ably bel[ t ( ! obs]v$ #dc'' p] c5tury4 ,,! ,,inclusion ,,( ,,gravitation ,) ! idea ( inve/igat+ ! problem f ! v bottom1 ,e9/e9 n[ und]took a broad] & m d>+ po9t ( view4 ,9 ! fir/ place he said t !re is no app>5t reason 9 ! great s*eme ( _w ev5ts :y any "o special sy/em ( coord9ates %\ld be fundam5tal to ! description ( ph5om5a1 j z 9 ! special !ory a ray ( light w\ld appe> ! same :e!r view$ f a fix$ sy/em or a sy/em mov+ ) con/ant velocity ) respect to ! e!r4 ,?is makes ! v broad assumption t no matt] :at sy/em ( coord9ates we may use1 ! ma!matical expressions = ! laws ( nature mu/ be ! same4 ,9 ,e9/e9's own words1 !n1 ! fir/ pr9ciple ( ?is m g5]al !ory ( relativity mu/ be ! foll[+3 ,! g5]al laws ( nature are express$ ?r\gh equations :i* hold = all sy/ems ( coord9ates1 t is1 !y are cov>iant ) respect to arbitr>y sub/itutions4 #e ,b ?is 0 n en\gh to include gravitation s ,e9/e9 next =mulat$ :at he 0 pleas$ to call 8 equival5ce hypo!sis4 ,?is is be/ illu/rat$ by an example4 ,suppose t we are m\nt+ 9 an elevator & wi% to inve/igate ! _w ( ev5ts f our mov+ plat=m4 ,we m\nt m & m rapidly1 t is ) con/ant accel]ation1 & we appe> to be 9 a /rong gravitational field due to our own in]tia4 ,suppose1 on ! o!r h&1 t ! elevator desc5ds ) an accel]ation equal to t ( gravity4 ,we w\ld n[ feel c]ta9 t we 7 9 empty space because our own relative accel]ation has entirely de/roy$ t ( ! e>?'s gravitational field & all objects plac$ ^u scales 9 an elevator w\ld app>5tly be )\t weight4 ,apply+ ?is idea1 !n1 ,e9/e9 decid$ to d away ) gravitation entirely by ref]r+ all ev5ts 9 a gravitational field to a new set ( axes :i* %\ld move ) con/ant accel]ation ) respect to ! fir/4 ,9 o!r words we are go+ to deal ) a sy/em mov+ ) uni=m accel]ation ) respect to ! e!r1 j z we consid]$ a sy/em mov+ ) uni=m velocity 9 ! special !ory4 ,! next /ep 9 ! con/ruction ( ?is complicat$ !ory is to r$uce ^! two hypo!ses to ! language ( ma!matics & ?is 0 accompli%$ by ,e9/e9 ) ! help ( ,m4 ,grossmann by means ( ! !ory ( t5sors4 ,on acc\nt ( ! v great intricacy ( ! details1 we mu/ cont5t ourselves ) ! m]e /atem5t t ?is really involv$ ! g5]alization ( ! fam\s expressions kn[n z ,laplace's & ,poisson's equations1 on ! explicit assumption t ^! two equations w\ld /ill describe ! gravitational field :5 we are cont5t to use a fir/ approximation to ! tru?4 ,! set ( t5 diff]5tial equations :i* ,e9/e9 got z a result ( 8 g5]alization he call$ 8 field equations ( gravitation4 #f ,,xiv ,,new ,,concepts ,,= ,,old ,:at ! ,_w ,looks ,l ,aft] ,e9/e9 ,has ,_h ,8 ,way ,) ,x ,,by ,,john ,g4 ,mc,h,a,r,d,y1 ,,comm&] ,r4,n41 ,,london ,! new-creat$ _w1 :i* fame 9 heav5 ,long _h =etold1 a fabric wond]ful1 ,( absolute p]fection4 ,e9/e9's ,!ory ( ,relativity has l$ to det]m9+ a key law ( nature--! law ( gravitation--:i* is also ! basic law ( me*anics4 ,?us x embraces a :ole realm ( physics1 & promises1 ?r\gh ! rese>*es ( ,pr(essor ,weyl1 to embrace ano!r realm--electro-dynamics4 ,its limitations are n yet rea*$1 = ,e9/e9 has already po/ulat$ !refrom a !ory ( a f9ite1 yet unb\nd$1 univ]se4 ,?is essay1 h[ev]1 is ma9ly conc]n$ ) me*anics1 & electrical =ces are n consid]$4 ,to h syn!sis$ ,newton's two great pr9ciples--8 law ( motion & law ( gravitation--int]pret+ 9 ! process ! empirical law ( equality ( gravitational & in]tial mass1 is alone an imm5se a*ievem5t2 b ,e9/e9's rese>*es h op5$ up a new _w to ! physici/ & philosoph] :i* is ( great] importance4 ,he has giv5 u a vision ( ! immat]ial _w1 a geometrical or ma!matical vision1 :i* is m satisfy+ ?an ! e!r conceptions hi!rto pres5t$4 ,! fabric ( 8 vision is n baseless4 ,x is ?is fabric we %all consid]1 t\*+ on c]ta9 aspects ( ! ,e9/e9 !ory 9 ! endeavor to pres5t an image 9 m9iature ( 8 edifice ( ?\ght & to %[ ! firmness ( its f\ndations4 ,t !y are well & truly laid 0 demon/rat$ by ! v]ification1 f obs]vations made dur+ ! sol> eclipse 9 #aiai1 ( ,e9/e9's pr$iction ( ! displacem5t ( a wave ( light 9 a gravitational field1 %[+ light to h ! prop]ty ( weight4 ,! physical _w is %[n by ,e9/e9 to be a _w ( relations4 ,und]ly+ x !re is an absolute _w ( :i* physical ph5om5a are ! manife/ation4 ,give me matt] & motion1 says ,desc>tes1 & ,i w con/ruct ! _w4 ,give me a _w 9 :i* !re are ord]$ relations1 says ! ,relativi/1 & ,i w %[ y ! behavior ( matt] !re9 7me*anics74 ,we fir/ view ?is und]ly+ _w z an ab/raction1 ab/ract+ en]gy 7b\nd z 9 matt] & electrons1 free z 9 light71 & its attribute =ce4 ,?is ab/raction we w call ! ,_w-,frame4 ,lat]1 we w /udy ! und]ly+ _w 9 connection ) en]gy1 & w call ?is absolute _w ! ,_w-,fabric4 ,! connection betwe5 ! geometrical "* ( ! ,_w-,frame & ! geometrical *>act]s ( ! ,_w-,fabric is ! key to ! law ( gravitation4 ,,! ,,_w-,,frame ,?is is our conception ( a _w1 if su* 7 possible1 entirely free f ! influ5ce ( en]gy4 ,we may conceive ( x z an amorph\s immat]ial some?+ conta9+ po9t-ev5ts 7a po9t-ev5t be+ an in/ant ( "t at a po9t 9 space--a conception1 n a def9ition74 ,^! po9t-ev5ts h a f\rfold ord] & def9ite relation 9 ?is ,frame1 i4e4 !y c be specifi$ by f\r v>iables or coord9ates 9 ref]5ce to "s base call$ a ref]5ce sy/em1 ) respect to :i* !y are =w>d or backw>d1 "r or left1 above or bel[1 soon] or lat]4 ,?is %[s ! ,_w-,frame to be f\r-dim5sional4 ,?us an aggregate ( po9t-ev5ts 7or an ev5t1 :i* implies limit$ ext5sion 9 space & limit$ duration 9 "t7 #g w\ld h :at we famili>ly describe z l5g?1 bread?1 height & "t4 ,to express ^! metrical prop]ties mo/ simply we mu/ *oose a f\r-dim5sional ref]5ce sy/em hav+ a p>ticul> =m--rectil9e> axes 7,c>tesian coord9ates71 & a p>ticul> motion--uni=m & rectil9e>1 i4e4 unaccel]at$1 & non-rotat+ ) respect to ! pa? ( a light ray4 ,we call ?is an in]tial sy/em because ,newton's ,law ( ,in]tia holds = su* a sy/em alone4 ,?is sy/em indicates h[ obs]v]s p>tition ! ,_w-,frame into space & "t4 ,x re/ricts obs]v]s to uni=m rectil9e> motion1 & obs]vations to bodies & light-pulses 9 su* motion4 ,?us gravitational & o!r =ces are disc\nt$1 & we obta9 ,_w-,frame conditions not)/&+ ! fact t obs]v]s are 9 ! pres5ce ( en]gy4 ,n[ ! sep>ation betwe5 po9t-ev5ts :i* h a def9ite relation to ea* o!r mu/ be absolute4 ,! sep>ation betwe5 two po9ts 9 a plane is def9$ by ! unique di/ance betwe5 !m 7! /raight l9e jo9+ !m74 ,betwe5 po9t-ev5ts ! analogue ( ?is unique di/ance1 :i* we call ! sep>ation-int]val 7to indicate its "t-l & space-l nature71 is also unique4 ,its unique & absolute "* give x great importance z !reby x is ! same = all obs]v]s reg>dless ( _! ref]5ce sy/em4 ,if1 9 place ( ! r cumb]some expression ,x-x to indicate ! diff]5ce betwe5 ! x-coord9ates ( two po9ts1 we employ ! m compact expression dx2 if = ! b5efit ( read]s :o h a little algebra b no analysis we /ate explicitly t ?is expression is a s+le symbol = a s+le quantity1 & has no?+ to d ) any product ( two quantities d & x2 & if we ext5d ?is notation to all our coord9ates3 !n x is cle> f previ\s essays t ! di/ance ,s betwe5 two po9ts 9 a plane ref]r$ to a rectil9e> sy/em ,,ox1 ,,oy1 is giv5 by ! simple equation ,s#b 7dx7#b 7dy7#b4 ,e9/e9 & ,m9k[ski %[ t ! value = ! sep>ation int]val ,omega1 ! analogue ( ,s1 ref]r$ to an in]tial sy/em is giv5 by ! equation ,omega#b 7dx7#b 7dy7#b 7dz7#b - 7dt7#b11 :i* is se5 to be a modifi$ ext5sion to f\r dim5sions ( ! equation = ,s4 ,we mu/ measure t 9 ! same units z x1 y1 z4 ,by tak+ ! con/ant velocity ( light 7#cjj1jjj kilometres p] second7 z unit velocity1 we c measure 9 l5g? or "t indiscrim9ately4 #h ,we w analyse briefly ?is equation z x epitomizes ! ,special ,!ory ( ,relativity4 ,if ! ,_w-,frame _h be5 ,euclidean ! equation w\ld h be5 ,omega#b 7dx7#b 7dy7#b 7dz7#b 7dt7#b b ?is w\ld n satisfy ! trans=mation equations :i* result$ f ! ,special ,!ory4 ,^! trans=mation equations arose directly f a reconciliation betwe5 two obs]v$ facts2 7a7 ! obs]v$ agreem5t ( all natural ph5om5a ) ! ,re/rict$ ,pr9ciple ( ,relativity--a pr9ciple :i* %[s t absolute rectil9e> motion _c be e/abli%$--7z reg>ds me*anics ?is 0 recogniz$ by ,newton2 ! ,mi*elson-,morley & o!r exp]im5ts %[$ ?is pr9ciple also appli$ to optical & electro-dynamical ph5om5a72 & 7b7 ! obs]v$ disagreem5t ( optical & electro-dynamical ph5om5a 7notably ! con/ancy ( light velocity7 ) ! laws ( dynamics z giv5 by classical me*anics1 e4g41 9 reg>d to ! comp\nd+ ( relative velocities4 ,e9/e9 effect$ ?is reconciliation by detect+ a flaw 9 classical me*anics4 ,he %[$ t by reg>d+ space & "t measurem5ts z relative to ! obs]v]--n absolute z ,newton def9$ !m--!re 0 no?+ incompatible betwe5 ! ,pr9ciple ( ,relativity & ! laws ( dynamics s modifi$4 ,newton's def9itions 7 f\nd$ on conception4 ,e9/e9's recognition ( ! relativity ( space & "t is bas$ on obs]vation4 ,equation 7#a7 %[s t ! geometry ( ! ,_w-,frame ref]r$ to an in]tial sy/em is semi-,euclidean 7hyp]bolic71 & t space & "t measurem5ts are relative to ! obs]v]'s in]tial ref]5ce sy/em4 ,! equation %[s t ! ,_w-,frame has a c]ta9 geometrical "* :i* we di/+ui% z f\r-dim5sional flatness4 ,x is ev]y:]e alike 7homaloidal74 ,its flat "* is %[n by ! /raight l9e nature ( ! sep>ation-int]val & ( ! sy/em to :i* x is mo/ simply ref]r$4 ,?us we h f\nd two absolute features 9 ! ,_w-,frame--7#a7 ,its geometrical "*--flatness2 7#b7 ,! sep>ation-int]val--:i* c be express$ 9 t]ms ( measurable v>iables call$ space & "t p>titions1 ?is p>tition+ be+ dep5d5t on ! obs]v]'s motion4 ,we are n[ 9 a position to explore ! ,_w-,fabric4 ,already we see t1 /udi$ "u in]tial conditions 7free ( =ce71 x agrees ) ! ,_w-,frame4 ,,! ,,_w-,,fabric ,! ,g5]al ,!ory ( relativity is l>gely conc]n$ ) ! inve/igation ( ! ,_w-,fabric4 ,consid] ! ,_w-,frame to be di/urb$4 ,we may reg>d ?is di/urbance1 :i* manife/s itself 9 physical ph5om5a1 z en]gy1 or m correctly action4 ,:5 en]gy is ?w>t$ 9 its natural fl[1 =ce is manife/$1 ) :i* are associat$ non-uni=m motions su* z accel]ations & rotations4 ,?is di/urb$ ,_w-,frame we di/+ui% z ! ,_w-,fabric4 ,x is f\nd to h v>i\s non-,euclidean *>act]s diff]+ f ! simple flat "* ( ! ,_w-,frame accord+ to ! degree ( di/urbance 7action7 9 ! region4 ,di/urbance gives ! fabric a geometrical "* ( curvature2 ! m consid]able ! di/urbance1 ! great] ! curvature4 ,?us an empty region 7n conta9+ en]gy1 b "u its influ5ce7 has less curvature ?an a region 9 :i* free en]gy ab\nds4 ,our problem1 aft] %[+ ! relativity ( =ce 7especially gravitational =ce71 is to det]m9e ! law und]ly+ ! fabric's geometrical "*2 to asc]ta9 h[ ! degree ( curvature is relat$ to ! en]gy influ5c+ a region1 & h[ ! curvature ( "o region is l9k$ by diff]5tial equations to t ( neighbor+ regions4 ,su* a law w be se5 to be ! law ( gravitation4 ,we /udy ! ,_w-,fabric by consid]+ tracks on :i* mat]ial p>ticles & light-pulses progress2 we f9d su* tracks regulat$ & def9$ by ! ,fabric's curvature1 & n1 z hi!rto suppos$1 by attractive =ce inh]5t 9 matt]4 ,z a track is measurable by summ+ ! sep>ation-int]vals betwe5 ne>-by po9t-ev5ts on x1 all obs]v]s w agree :i* is ! unique track betwe5 two di/ant po9t-ev5ts4 ,e9/e9 po/ulates t freely progress+ bodies w foll[ unique tracks1 :i* are !re=e call$ natural tracks 7geodesics74 ,if mat]ial bodies are prev5t$ f foll[+ natural tracks by contact ) matt] or o!r causes1 ! ph5om5on ( gravitational =ce is manife/$ relative to !m4 ,:5ev] ! natural fl[ ( en]gy is int]rupt$ =ce is born4 ,= example1 :5 ! pi/on int]rupts ! fl[ ( /eam1 or golf ball fl[ ( club1 =ce results--! int]ruption is mutual1 & ! =ce relative to bo?4 ,likewise :5 ! e>? int]rupts ! natural track ( a p>ticle 7or obs]v]7 gravitational =ce is manife/$ relative to bo?4 ,s long z a body moves freely no =ce is appreciat$ by x4 ,a fall+ aviator 7neglect+ air resi/ance7 w n appreciate any gravitational =ce4 ,he foll[s a natural track1 !reby free+ himself f ! =ce exp]i5c$ 9 contact ) matt]4 ,he acquires an accel]at+ motion ) respect to an in]tial sy/em4 ,by acquir+ a p>ticul> accel]at+ motion an obs]v] c annul any =ce exp]i5c$ 9 any small region :]e ! field ( =ce c be consid]$ con/ant4 ,?us ,e9/e91 int]pret+ ! equality ( gravitational & in]tial mass1 %[$ t ! same quality manife/s itself accord+ to circum/ances z weight or z in]tia1 & t all =ce is purely relative & may be treat$ z "o ph5om5on 7an int]ruption 9 en]gy fl[74 ,?is ,pr9ciple ( ,equival5ce %[s t small portions ( ! ,_w-,fabric1 obs]v$ f a freely mov+ p>ticle 7free ( =ce71 c\ld be treat$ z small portions ( ! ,_w-,frame4 #i ,if su* obs]vations 7 practicable1 we c\ld det]m9e ! ,fabric curvature by ref]r+ po9t-ev5t measurem5ts to equation 7#a74 ,we _c obs]ve f unique tracks b we c obs]ve !m f our re/ra9$ situation4 ,_! importance is n[ app>5t1 because1 by trac+ !m ov] a region1 we are trac+ some?+ absolute 9 ! ,fabric--its geometrical "*4 ,we /udy ?is curvature by explor+ sep>ation-int]vals on ! tracks ( freely mov+ bodies1 relat+ ^! sep>ation-int]vals to actual measurem5ts 9 t]ms ( space & "t compon5ts dep5d+ on ! obs]v]'s ref]5ce sy/em4 ,! law ( curvature mu/ be ! law ( gravitation4 ,to illu/rate ! l9es on :i* ,e9/e9 proce$$ to survey ! ,_w-,fabric f ! e>? we w consid] a simil> b m simple problem--! survey ( ! sea-surface curvature f an air%ip4 ,we /udy ?is curvature by explor+ small di/ances on ! tracks ( %ips 7:i* we mu/ suppose c only move uni=mly on unique tracks--arcs ( great circles71 relat+ su* di/ances to actual measurem5ts 9 t]ms ( l5g? & bread? compon5ts dep5d+ on ! obs]v]'s ref]5ce sy/em4 ,?is two-dim5sional surface problem c be ext5d$ to ! f\r-dim5sional ,fabric "o4 ,we consid] ! surface to be cov]$ by two arbitr>ily drawn int]sect+ s]ies ( curves3 curves 9 "o s]ies n int]sect+ ea* o!r1 vide figure4 ,?is ,gaussian sy/em ( coord9ates is appropriate only :5 ! small] ! surface consid]$1 ! m ne>ly x approximates to ,euclidean conditions4 ,x admits ( def9+ any po9t on ! surface by two numb]s indicat+ ! curves int]sect+ at t po9t4 ,p is def9$ by x#a1 x#b4 ,p#a 7v ne> ,p7 is def9$ by x#a dx#a1 x#b dx#b4 ,! equation = ! m9ute di/ance s betwe5 two adjac5t po9ts 9 su* a sy/em is giv5 by ! g5]al =mula s#b g#aa;dx#ab g#ab;dx#a;dx#b g#bb;dx#bb14 ,! g's may be con/ants or functions ( x#a1 x#b4 ,_! value is dep5d5t on ! obs]v]'s ref]5ce sy/em & on ! geometrical "* ( ! surface obs]v$4 ,! curves be+ arbitr>y1 ! =mula is appropriate = any ref]5ce sy/em1 or ev5 if ! obs]v] does n "k exactly :at 8 ref]5ce sy/em is4 7,! ,fabric obs]v] does n "k :at 8 space & "t p>tition+ actually is because he is 9 a gravitational field74 ,x is ! g's :i* disclose ! geometry ( an obs]v]'s p>titions1 & _! values also conta9 a reflection ( ! "* ( ! region obs]v$4 ,we f9d s by direct exploration ) a mov+ %ip 7,omega is f\nd by direct exploration ) a freely mov+ p>ticle72 dx#a1 dx#b are ! obs]v$ l5g? & bread? measurem5t diff]5ces :i* we h to relate to s4 ,by mak+ suffici5t obs]vations 9 a small area & ref]r+ !m to ! g5]al =mula we c f9d ! values ( ! g's = ! obs]v]'s p>ticul> ref]5ce sy/em4 ,diff]5t values = g's w be f\nd if ! obs]v] *anges 8 ref]5ce sy/em1 b !re is a limitation to ! values s obta9able ow+ to ! "p play$ by ! surface itself1 :i* is diffid5tly express+ its intr9sic geometrical "* 9 ! g's 9 ea* obs]vation4 ,,e9/e9',s ,,results ,?us we approa* ! absolute "* ( ! surface ?r\gh ! relative nature ( ! obs]v]'s ref]5ce sy/em4 ,!re is a relation%ip common to all values ( ! g's t belong to ! same curvature4 ,?is relation%ip is express$ by a diff]5tial equation4 ,x is ?is equation ( curvature t ! air%ip's obs]v] mu/ f9d4 ,e9/e9's problem 0 simil>1 b he 0 conc]n$ ) f\r dim5sions1 :i* entail$ a g5]al =mula ) t5 g's1 & he _h to f9d a set ( diff]5tial equations ( ! second ord] to det]m9e ! law ( ,fabric curvature4 ,he divid$ ! ,fabric into regions3 ,i4 ,_w-,frame--beyond influ5ce ( en]gy4 ,,ii4 ,empty region--free ( en]gy1 b "u its influ5ce4 ,,iii4 ,region conta9+ free en]gy only4 ,ea* region has a *>act]i/ic curvature4 ,by means ( an absolute diff]5tial calculus--a wond]ful ma!matical scaffold+ erect$ by ,riemann1 ,*ri/(fel & o!rs--involv+ ! !ory ( t5sors1 he succe$$ 9 f9d+ su* a set ( equations4 ,he kept ! foll[+ po9ts 9 view3 7#a7 ,! equations mu/ n only give ! "* ( region ,,ii1 b mu/ satisfy ! special case ( region ,i2 7#b7 ,!y mu/ be indep5d5t ( any p>tition+ sy/em1 because ! ,g5]al ,!ory ( ,relativity dem&s t a law ( nature be 9 a =m appropriate = all obs]v]s :atev] _! position & motion2 7#c7 ,!y mu/ be conc]n$ ) en]gy :i* is cons]v$1 n mass :i* ! ,special ,!ory %[$ dep5d5t on velocity4 ,?is set ( diff]5tial equations :i* %[s h[ ! curvature ( ! ,fabric at any po9t l9ks to ! curvature at neighbor+ po9ts is ! law ( gravitation1 a law :i* has be5 sev]ely te/$ by ! practical obs]vation ( ! sol> eclipse already ref]r$ to4 ,at a fir/ approximation ^! equations deg5]ate into ,newton's ,law4 ,at a second approximation !y acc\nt = ! motion ( ! p]ihelion ( ,m]cury1 :i* _h hi!rto baffl$ a/ronom]s4 ,all ! laws ( me*anics are d$ucible f ?is law ( ,_w-,fabric curvature1 i4e4 cons]vation ( en]gy 7:i* includes cons]vation ( mass s9ce we re-def9e mass z en]gy7 & cons]vation ( mom5tum 7re-def9$ by a relativi/74 ,x mu/ be not$ t ?is law & ! ,g5]al ,!ory %[ t ! velocity ( light is n absolutely con/ant1 b1 l ev]y?+ else1 a light-pulse is affect$ by ! ,fabric curvature 9 a gravitational field4 ,9 conclusion we w contra/ "s conspicu\s diff]5ces 9 ! old _w view ( classical me*anics & ! new view pres5t$ by ,e9/e94 #a4 ,a ?ree-dim5sional e!r m$ium ) v>i\sly conceiv$ prop]ties :i* communicat$ ! suppos$ inh]5t attractive =ce 9 matt] 9 "s unexpla9$ way1 & transmitt$ electromagnetic waves1 has be5 replac$ by a f\r-dim5sional ext]nal ,_w-,fabric1 ! geometrical "* ( :i* controls ! motion ( matt] 7en]gy7 & acc\nts = all me*anical laws4 #b4 ,aft] sep>at+ ! obs]v]'s subjective %>e 9 def9itions f nature's %>e 9 ! ?+s def9$1 space1 "t1 & =ce1 hi!rto reg>d$ z absolute1 h be5 %[n to be purely relative & dep5d5t on ! obs]v]'s track4 ,mass has also prov$ to be relative to velocity unless re-def9$ z en]gy4 ,z classical me*anics bases all def9itions on space1 "t1 & mass units1 ! relativity ( su* def9$ quantities is n[ app>5t4 #c4 ,newton's laws ( motion1 8 law ( gravitation1 & ! laws ( cons]vation1 hi!rto reg>d$ z unrelat$1 are n[ syn!sis$ 9 a basic law ( me*anics4 ,e9/e9 has n di/urb$ ! electric !ory ( matt]1 & bo? ! old & new physics h 9 common ! ,pr9ciple ( ,lea/ ,action4 ,we obta9 a glimpse ( ?is pr9ciple 9 ! unique tracks pursu$ by freely mov+ bodies1 :i* may be reg>d$ z tracks ( lea/ ef=t1 =ce only be+ manife/$ z an expression ( ! ,fabric's res5tm5t :5 bodies dep>t f ^! natural tracks4 ,e9/e9 has approa*$ ne>] to ! tru? 9 reg>d to ! laws und]ly+ nature1 &1 z always1 ?is means a simplification4 ,8 !ory1 :i* entails a readju/m5t ( su* fundam5tal conceptions z space & "t1 op5s up fre% fields to sci5tific inve/igation & to philosophic ?\ght4 ,x reveals a bridge unit+ ! doma9s ( physics & philosophy1 & x h]alds a new era 9 ! hi/ory ( sci5ce4 ,,xv ,,! ,,new ,,_w ,a ,univ]se 9 ,:i* ,geometry ,takes ! ,place ( ,physics1 & ,curvature ,t ( ,=ce ,,by ,,george ,,fr$]ick ,,hem5s1 ,m4,c41 ,b4,,sc41 ,,london ,x is famili> k t ! l9e1 ! surface & ord9>y ,euclidean space are to be reg>d$ z spaces ( "o1 two & ?ree dim5sions respectively & read]s ( ?is j\rnal are aw>e t a hypo!tical space ( f\r dim5sions has be5 closely inve/igat$4 ,! mo/ conv5i5t space to /udy is ! surface or two-space1 s9ce we c reg>d x z emb$d$ 9 a ?ree-space4 ,if a surface is curv$ x is g5]ally impossible to draw a /raight l9e on x1 = z we see cle>ly1 ! /raighte/ l9e is *ang+ its direction at e po9t4 ,to describe ?is prop]ty accurately x is necess>y to ascribe to ea* po9t a magnitude :i* expresses :at happ5s to ! direction ( a %ort l9e 9 ! region :5 displac$ a %ort di/ance p>allel to itself4 ,?is is call$ ! direction-def9+ magnitude4 ,diff]5t sets ( values ( ?is magnitude relate to surfaces ( diff]5t curvatures4 ,a second fundam5tal prop]ty has rec5tly be5 po9t$ out4 ,!re is inh]5t 9 e "p ( a space a measure ( l5g? peculi> to t p>ticul> region & :i* 9 g5]al v>ies f region to region4 ,to describe ?is v>iation accurately x is necess>y to ascribe to ea* po9t ano!r magnitude call$ ! l5g?-def9+ magnitude1 :i* expresses ! *ange f ea* po9t to ! next ( ! unit ( l5g?4 ,^! two magnitudes def9e ! surface completely4 ,simil>ly1 a space ( any numb] ( dim5sions is def9$ completely by a simil> pair ( magnitudes4 ,a space is ! field ( su* a magnitude-pair & ! nature ( ^! magnitudes def9es ! dim5sions ( ! space4 ,! f\r-space usually describ$ is ! ,euclidean memb] ( an inf9ity ( f\r-spaces4 ,:5 we look into a mirror we see a space diff]+ f ord9>y space 9 t "r & left are int]*ang$ & ?is is describ$ ma!matically by say+ t if we locate po9ts z usual by specify+ ?ree di/ances ,x#a1 ,x#b1 ,x#c ( ! po9t f ?ree mutually p]p5dicul> planes1 !n a po9t ,x#a1 ,x#b1 ,x#c1 9 actual space corresponds ) a po9t ,x#a1 ,x#b1 -,x#c 9 ! mirror$ space3 9 o!r words ! mirror$ space is d]iv$ f ! real space by multiply+ ! ,x#c coord9ates by -#a4 ,if we 7 to multiply by sqrt-#a in/ead ( -#a we %\ld d]ive a diff]5t space2 9 ?is case1 h[ev]1 we h no mirror to %[ u :at x looks l4 ,su* a space is said to h "o negative dim5sion & x has ! peculi> prop]ty t 9 ! figure d]iv$ f ! "r triangle ( ord9>y space ! squ>e ( ! hypot5use equals ! diff]5ce & n ! sum ( ! squ>es ( ! o!r two sides1 s t ! l5g? ( a l9e may sometimes h to be repres5t$ by ! squ>e-root ( a negative numb]1 a complex numb]4 ,9 consid]+ :at at fir/ sight may appe> to be fanta/ic /atem5ts made by ?is !ory1 x mu/ be borne 9 m9d t all our k ( ! ext]nal univ]se comes ?r\gh our s5se-impressions1 & our mo/ confid5t /atem5ts ab\t ext]nal ?+s are really ( ! nature ( inf]5ces f ^! s5se-impressions &1 be+ inf]5ces1 liable to be wrong4 ,s t if ! !ory says t a /one ly+ on ! gr\nd is n a simple ?ree-dim5sional object1 & t its sub/ance is n ! same z its sub/ance a mom5t be=e1 ! matt] is "o = due consid]ation & n imm$iate disbelief4 ,! idea t ! univ]se ext5ds 9 "t z well z 9 space is n new1 & fiction-writ]s h famili>iz$ u ) wond]ful ma*9es 9 :i* travell]s j\rney 9 "t & are pres5t at v>i\s /ages ( ! _w's hi/ory4 ,?is conception ( ! univ]se1 to :i* ! "n space-"t is usually appli$1 is adopt$ by ! new !ory & assign$ ! /atus ( a physical reality4 ,,! ,,_w ,,geometry ,! fundam5tal cre$ ( ! new !ory is t ! space-"t univ]se con/itutes a true f\r-dim5sional space ( "o negative dim5sion1 ?is dim5sion be+ "t4 ,! v>iations f po9t to po9t ( ! direction-def9+ & l5g?-def9+ magnitudes g5]ate ! geometrical prop]ties ( curvature1 etc41 & ^! are cognis$ by ! human m9d z physical ph5om5a3 our s5se-impressions are no?+ m nor less ?an p]ceptions ( ! geometry ( a f\rspace4 ,s in/ead ( inf]r+ f our s5se-impressions ! exi/5ce ( matt]1 motion & ! l z we are accu/om$ to d1 we %\ld ) equal ju/ice inf] ! exi/5ce ( a geometrical f\rspace4 ,?us x becomes necess>y to prep>e a diction>y 9 :i* ! famili> ?+s ( our _w are id5tifi$ ) ^? geometrical prop]ties ( ! f\r-space :i* really con/itute !m1 & 9 s do+ p>ts ( our geometrical k assume ! guise ( new physical k4 ,?r\gh ! f\rspace our consci\sness travels1 cognis+ a *ang+ ?ree-dim5sional section ( x z x goes & ?us giv+ rise to "t4 ,x becomes aw>e t ! f\rspace is pleat$ or fold$ along l9es all runn+ r\ghly 9 ! same direction1 & possibly because ?is is ! easie/ direction to foll[1 x travels along ! l9es4 ,! direction ( ?is motion is ! negative dim5sion4 ,?us consci\sness is always aw>e ( ! ne>ly con/ant =ms ( ! cross-sections ( ! pleats along :i* x travels4 ,^! unv>y+ =ms con/itute matt]3 matt] is ! =m ( a section ?r\gh a uni=m pleat ( ! f\rspace--a ?ree-dim5sional aspect ( a f\r-dim5sional curvature2 s t 9 /rict accuracy we %\ld say t a /one is ! %ape or =m ( a *ang+ section ( a f\r-dim5sional object1 ! complete object be+ a long fold 9 ! f\rspace4 ,! physical int]pretation ( ?is cons]vation ( =m ( ! cross-section is t matt] is cons]v$4 ,x is ?us se5 t ! consci\s m9d1 by foll[+ ^! pleats1 has s det]m9$ "t t ! law ( ! cons]vation ( matt] mu/ hold4 ,! ma!matical treatm5t ( ! subject makes x cle> t practically all o!r physical laws simil>ly foll[ z a direct result ( ?is *oice ( "t4 ,! type ( ord] prevail+ 9 ! physical univ]se1 ! laws ( gravitation1 heat1 motion & ! re/ are n directly impos$ by "s ext]nal p[]1 b are app>5tly *os5 by m9d itself4 ,9 ! neighborhood ( ^! pleats ! f\rspace is /ill curv$1 b to a small] degree4 ,?is we cognise z en]gy or z a field ( =ce4 ,?us en]gy is se5 to be ! same k9d ( ?+ z matt] & w\ld !re=e be expect$ to h weight4 ,?is 0 exp]im5tally demon/rat$ 9 #aiai :5 light 0 9 effect actually weigh$4 ,conv]sely1 matt] consi/s ( en]gy2 & x is calculat$ t "o lit] ( wat] conta9s suffici5t en]gy to develop a million horsep[] = ab\t f\r ye>s4 ,x is n[ believ$ t ! sun's en]gy is d]iv$ f ! dis9tegration ( ! matt] ( :i* x is made4 ,! me?od ( e/abli%+ ^! id5tifications w be cle> f ! foll[+3 ,we already knew t matt] is made up ( electrons & t radiant en]gy is electromagnetic & be=e ! adv5t ( ?is !ory x 0 reg>d$ z c]ta9 t practically all obs]v$ physical ph5om5a except gravitation 7 manife/ations ( ! electromagnetic field4 ,! new !ory has confirm$ ?is belief4 ,x is f\nd t ! gravitational & electromagnetic conditions ( ! univ]se are completely def9$ if to ea* po9t ( space-"t a gravitational & an electric pot5tial are ascrib$4 ,^! are magnitudes ( ! same nature z ! direction-def9+ & l5g?-def9+ magnitudes :i* mu/ necess>ily be associat$ ) e po9t ( space-"t if x is a true space1 & !y are !re=e id5tifi$ ) ^!4 ,by p]=m+ ord9>y ma!matical op]ations on ^! magnitudes /atem5ts ( fact clo!d 9 ma!matical =m are obta9$1 :i* are to be int]pret$ on ! "o h& z physical laws & on ! o!r z geometrical prop]ties ( ! f\rspace4 ,ne>ly all our physical laws are d]ivable ma!matically 9 ?is way1 s t an ext5sive id5tification is effect$ :i* has be5 fruitful ( results4 ,x has be5 m5tion$ t a slight curvature is sometimes cognis$ z =ce & z ?is id5tification appe>$ orig9ally z a po/ulate its hi/ory is int]e/+4 ,,! ,,g5esis ,,( ,,! ,,!ory ,an exp]im5t by ,mi*elson & ,morley 7#ahhg71 on :i* ! :ole !ory is bas$1 made x appe> t if a man measures ! velocity at :i* light passes him he w get ! same result :e!r he is /ation>y1 ru%+ to meet ! light1 or mov+ 9 ! same direction z ! light4 ,! solution 0 provid$ by ,e9/e9 9 #aije4 ,he sugge/$ t s9ce we "k ! results ( ^! det]m9ations ought n to agree1 some?+ mu/ h happ5$ to ! clocks & measur+-rods us$ 9 measur+ ! velocity s t ! /&>ds ( l5g? & "t 7 n ! same 9 ! ?ree cases1 ! alt]ations be+ exactly su* z to make ! velocity ( light con/ant4 ,?is solution is univ]sally accept$ z true & is ! fundam5tal po/ulate4 ,?us ! l5g? ( a /ick & ! rate at :i* "t passes w *ange z ! velocity ( ! p]son obs]v+ ^! ?+s *anges4 ,if a man measur$ ! l5g? ( an a]oplane go+ pa/ him at #afa1jjj miles p] second x w\ld measure only half ! l5g? obs]v$ :5 /ation>y4 ,if ! a]oplane 7 go+ ) ! velocity ( light1 its l5g? w\ld vani% ?\gh its bread? & height w\ld be unalt]$4 ,simil>ly1 if ( two tw9 bro!rs "o 7 cont9ually mov+ ) ref]5ce to ! o!r _! ages w\ld gradually div]ge1 = "t w\ld g at diff]5t rates = ! two4 ,if "o mov$ ) ! velocity ( light1 "t w\ld /& /ill = him :ile = ! o!r x w\ld g on z usual4 ,to get actually y\ng] x w\ld be necess>y to move quick] ?an light :i* is believ$ to be impossible4 ,! velocity ( light is assum$ to be ! greate/ velocity occurr+ 9 nature4 ,evid5tly !n if ! di/ance 9 space & ! int]val 9 "t sep>at+ two giv5 ev5ts1 su* z ! fir+ ( a gun & ! bur/+ ( ! %ell1 are measur$ by two obs]v]s 9 uni=m relative motion1 _! e/imates w n agree4 ,consid] n[ ! simple problem ( measur+ ! di/ance betwe5 two po9ts on an ord9>y draw+-bo>d4 ,if we draw two p]p5dicul> axes1 we c def9e ?is di/ance by specify+ ! l5g?s ( ! projections on ! two axes ( ! l9e jo9+ ! po9ts4 ,if we *oose two diff]5t axes ! projections w n be ! same b w def9e ! same l5g?4 ,simil>ly1 9 a ,euclidean f\r-space ! di/ance betwe5 two po9ts w be def9$ by ! projections on ! f\r axes1 b if ^! axes be rotat$ slightly1 ! projections w be diff]5t1 b w def9e ! same l5g?4 ,n[1 return+ to ! two obs]v]s j m5tion$1 x 0 notic$ by ,m9k[ski 9 #aijh t if ! space measurem5ts betwe5 ! two ev5ts are split into ! usual ?ree compon5ts1 & if ! "t measurem5ts are multipli$ by sqrt-#a1 ! diff]5ce betwe5 ! two sets ( measurem5ts is exactly ! same z w\ld h occurr$ _h ^! two ev5ts be5 po9ts 9 a ,euclidean f\rspace1 & two diff]5t obs]vations made ( _! di/ance ap>t us+ two sets ( axes incl9$ to ea* o!r4 ,! velocity ( light is made equal to #a 9 ?is calculation by a suitable *oice ( units4 ,?is discov]y ?rew a vivid light on ! problem ( space-"t1 %[+ t x is probably a true f\r-space ( "o negative dim5sion1 a simple d]ivative ( ! mu*-discuss$ & n[ famili> ,euclidean f\r-space4 ,al?\gh ?is discov]y gave a trem5d\s impetus to ! progress ( ! !ory1 x is probable t x holds a deep] significance n yet reveal$4 ,x is probably a /atem5t ( ! /uff ( :i* ! f\r-space is made1 & p]haps also ( h[ x is made2 b ! problem rema9s unsolv$4 ,x ?us becomes pla9 t our two obs]v]s are m]ely look+ at ! same ?+ f diff]5t viewpo9ts4 ,ea* has j z mu* "r z ! o!r to reg>d himself z be+ at re/ 9 ord9>y space 7?is is ! po/ulate ( ! relativity ( uni=m motion7 & to reg>d 8 "t direction z a /raight l9e 9 ! f\r-space4 ,! diff]5ce is m]ely t ! two "t axes are incl9$ to ea* o!r4 ,if1 h[ev]1 "o 7 mov+ ) an accel]ation ) ref]5ce to ! o!r 8 pa? 9 ! f\r-space w appe> curv$ to ! o!r1 ?\gh he himself1 s9ce he reg>ds x z 8 "t axis1 w /ill assume x to be /raight4 ,if !re is a body mov+ 9 :at "o obs]v] sees to be a /raight l9e1 ! o!r w1 ( c\rse1 9 g5]al see x z curv$1 & foll[+ ! usual cu/om1 s9ce ?is body1 )\t app>5t reason1 deviates f ! /raight pa?1 w say !re mu/ be "s =ce act+ on x4 ,?us ! curvature ( 8 "t axis1 due to 8 accel]at$ motion1 makes x appe> t !re is r\nd him a field ( =ce1 :i* causes freely mov+ bodies to deviate f ! /raight pa?4 ,n[ if space-"t is itself inh]5tly curv$ x is n g5]ally possible = any l9e 9 x to be /raight any m ?an x is possible = any l9e on ! surface ( a sph]e to be /raight4 ,h5ce1 all axes mu/ be curv$1 & all obs]v]s1 :atev] _! /ates ( motion1 mu/ exp]i5ce fields ( =ce :i* are ( ! same nature z ^? due to motion only4 ,! extra =ce exp]i5c$ :5 a lift beg9s to rise is an example ( =ce due to pure motion3 gravitation is ! simil> =ce due to an inh]5t curvature ( ! f\r-space1 & x 0 ! po/ulate t ^! =ces 7 simil> t made possible ,e9/e9's solution ( ! g5]al problem ( gravitation4 ,,! ,,"t ,,diagram ,! correlation ( "t ) its geometrical analogue is ( absorb+ int]e/4 ,repres5t+ velocity by ! common me?od ( plott+ a curve %[+ positions at v>i\s times & m>k+ di/ances horizontally & times v]tically1 ! velocity ( light be+ #a1 ,,mm' & ,,nn' w bo? repres5t ?is velocity4 ,s9ce ?is is assum$ to be ! greate/ velocity occurr+ 9 nature1 all o!r possible velocities are repres5t$ by l9es fall+ )9 ! upp] & l[] ,v's4 ,n[ ?is diagram correctly repres5ts two dim5sions ( ,m9k[ski's ,euclidean f\r-space s1 transmut+ to real b flat f\r-space by multiply+ times by sqrt-#a1 x is se5 t !re is a region outside :i* no effect c be propagat$ f ,o s9ce t w\ld involve ! exi/5ce ( a velocity great] ?an t ( light4 ,?is region repres5ts ! future ( ,o4 ,simil>ly1 ,o c only be affect$ by ev5ts )9 ! region d]iv$ f ! d[nw>d-op5+ ,v1 :i* !re=e repres5ts ! pa/ ( ,o4 ,! region betwe5 ! two repres5ts ev5ts :i* may be ei!r simultane\s ) ,o or n1 accord+ to ! velocity ( ! obs]v] at ,o4 ,?us 9 ?is !ory an ev5t dictat$ by free-w1 c\ld affect po9ts 9 its future region1 b n 9 any o!r1 :i* agrees ) exp]i5ce & %[s t ! !ory is n ess5tially det]m9i/4 ,if free-w is really free1 ! future is n yet det]m9$1 & ! f\rspace mu/ be 9 "s way =m$ by ! w z "t progresses4 ,! tra9s ( ?\ght inspir$ by ,e9/e9's po/ulates h already c>ri$ u to a p9nacle ( k unprec$5t$ 9 ! hi/ory ( man4 ,on e h&1 z we look out ^u ! univ]se f our new & l(ty /&po9t1 unexpect$ & en?rall+ vi/as op5 up be=e u1 & we f9d ourselves confront+ nature ) an insight su* z no man has ev] be=e d>$ aspire to4 ,x is completely un?9kable t ?is !ory c ev] be swept aside4 ,ap>t f exp]im5tal v]ifications :i*1 9 po9t ( fact1 l5d x ! /ronge/ support1 no "o c\ld "w ?r\gh ! !ory )\t feel+ t "h1 9 tru?1 ! inn] work+s ( ! univ]se 7 laid b>e be=e him4 ,! h>mony ) nature is f> too complete = any d\bt to arise ( its tru?4 ,,xvi ,,! ,,que/ ,,( ,,! ,,absolute ,mod]n ,developm5ts 9 ,!oretical ,physics1 & ! ,climax ,suppli$ by ,e9/e9 ,,by ,,dr4 ,,francis ,d4 ,,murnaghan1 ,,johns ,,hopk9s ,,univ]sity ,,baltimore ,we %all discuss ! m important aspects ( ! !ory popul>ly kn[n z ! ,e9/e9 ,!ory ( ,gravitation & %all try to %[ cle>ly t ?is !ory is a natural outcome ( ideas long held by physici/s 9 g5]al4 ,^! ideas are3 7a7 ,! impossibility ( action at a di/ance2 9 o!r words we f9d an in/9ctive repugnance to admit t "o body c affect ano!r1 remote f x1 in/antane\sly & )\t ! exi/5ce ( an int]v5+ m$ium4 7b7 ,! indep5d5ce ( natural1 i4e41 physical1 laws ( _! ma!matical mode ( expression4 ,?us1 :5 an equation is writt5 d[n z ! expression ( a physical law x mu/ be satisfi$1 no matt] :at units we *oose 9 ord] to measure ! quantities occurr+ 9 ! equation4 ,z our physics tea*] us$ to say ! expression ( ! law mu/ h 9 e t]m ! same dim5sions4 ,m ?an ?is ! *oice ( ! quantities us$ to express ! law--if !re be a *oice op5--mu/ h no effect on its correctness4 ,z we 7 told--all physical laws are capable ( expression z relations betwe5 vectors or else z relations betwe5 magnitudes ( ! same dim5sions4 ,we %all hope to make ?is cle>] 9 its prop] place 9 ! essay1 z its obvi\s g5]alization is ,e9/e9's c>d9al pr9ciple ( relativity4 ,! measurem5ts :i* an exp]im5tal physici/ makes are always ! expression ( a co9cid5ce ( two po9ts 9 space at ! same "t4 ,if we ask su* an exp]im5t] :at he means by a po9t 9 space he tells u t1 = him1 ! t]m has no mean+ until he has a mat]ial body ) ref]5ce to :i* he c locate ! po9t by measurem5ts2 9 g5]al x requires ?ree measurem5ts & he expresses ?is by say+ t space has ?ree dim5sions4 ,he measures 8 di/ance1 z a rule1 p>allel to ?ree mutually p]p5dicul> l9es fix$ 9 ! mat]ial body--a ,c>tesian ref]5ce-frame s-call$4 ,s t a po9t 9 space is equival5t to a giv5 mat]ial ref]5ce-frame & ?ree numb]s or coord9ates4 ,if1 = any reason1 we pref] to use a new mat]ial ref]5ce-frame ! coord9ates or measurem5ts w *ange &1 if we "k ! relative positions ( ! two mat]ial ref]5ce-frames1 !re is a def9ite relation betwe5 ! two sets ( ?ree coord9ates :i* is t]m$ a trans=mation ( coord9ates4 ,b :i* p>ticul> mat]ial ref]5ce-frame %all we use8 ,! fir/ *oice w\ld1 we ?9k1 be t atta*$ to ! e>?4 ,b1 ev5 yet1 we are 9 d\bt z !re are numb]less ,c>tesian frameworks atta*$ to ! e>? 7z to any mat]ial body7 & x is "h t our idea 7b7 beg9s to function4 ,we say x mu/ be immat]ial :i* ( ^! ,c>tesian frames we use4 ,9 ea* frame a vector has ?ree compon5ts & :5 we *ange f "o frame to ano!r ! compon5ts *ange 9 su* a way t if two vectors h _! ?ree compon5ts equal 9 "o framework !y w be equal 9 any o!r atta*$ to ! same mat]ial sy/em4 ,s our idea 7b71 :i* says t our physical equations mu/ be vector equations1 is equival5t to say+ t ! *oice ( ! framework atta*$ to any giv5 mat]ial body c h no effect on ! mode ( expression ( a natural law4 ,%all we c>ry ov] our idea 7b7 to answ] ! next "q3 ,to :i* mat]ial body %all we atta* our framework8 ,to ?is "q ,newton gave "o answ] & ,e9/e9 ano!r4 ,we %all fir/ consid] ,newton's position & !n we may hope to see cle>ly :]e ! new !ory div]ges f ! classical or ,newtonian me*anics4 ,newton's answ] 0 t !re is a p>ticul> mat]ial frame ) ref]5ce to :i* ! laws ( me*anics h a rem>kably simple =m commonly kn[n z ,newton's laws ( motion & s x is pref]able to use ?is framework :i* is call$ an absolute frame4 ,:at is ! ess5tial peculi>ity ( an absolute frame8 ,newton 0 ess5tially an empirici/ ( ,bacon's s*ool & he obs]v$ ! foll[+ facts4 ,let u suppose we h a framework ( ref]5ce atta*$ to ! e>?4 ,!n a small p>ticle ( matt] "u ! gravitational influ5ce ( surr\nd+ bodies1 includ+ ! e>?1 takes on a c]ta9 accel]ation ,a#a4 ,n[ suppose ! surr\nd+ bodies remov$ 7s9ce we _c remove ! e>? we %all h to view ! exp]im5t z an ab/raction71 & ano!r set introduc$2 ! p>ticle1 be+ aga9 at its orig9al position1 w beg9 to move ) an accel]ation ,a#b4 ,if bo? sets ( surr\nd+ bodies are pres5t simultane\sly ! p>ticle beg9s to move ) an accel]ation :i* is approximately b n q ! sum ( ,a#a & ,a#b4 ,newton po/ulat$ !re !re is a c]ta9 absolute ref]5ce frame 9 :i* ! approximation w\ld be an equality2 & s ! accel]ation1 relative to ! mat]ial frame1 furni%es a conv5i5t measure ( ! effect ( ! surr\nd+ bodies--:i* effect we call _! gravitational =ce4 ,notice t if ! effect ( ! surr\nd+ bodies is small ! accel]ation is small & s we obta9 z a limit+ case1 ,newton's law ( in]tia :i* says t a body subject to no =ces has no accel]ation2 a law :i*1 z ,po9c> ju/ly obs]v$1 c nev] be subject$ to exp]im5tal ju/ification4 ,! natural que/ions !n arise3 :i* is ! absolute & privileg$ ref]5ce-frame & h[ mu/ ! simple laws be modifi$ :5 we use a frame m conv5i5t = u--"o atta*$ to ! e>? let u say8 ,! absolute frame is "o atta*$ to ! fix$ />s2 & to ! absolute or real =ce def9$ z above1 we mu/ add c]ta9 t]ms1 usually call$ c5trifugal =ces4 ,^! are ref]r$ to z fictiti\s =ces because1 z x is expla9$1 !y are due to ! motion ( ! ref]5ce-frame ) respect to ! absolute frame & 9 no way dep5d on ! di/ribution ( ! surr\nd+ bodies4 ,gravitational =ce & c5trifugal =ces h 9 common ! rem>kable prop]ty t !y dep5d 9 no way on ! mat]ial ( ! attract$ body nor on its *emical /ate2 !y act on all matt] & are 9 ?is way diff]5t f o!r =ces met ) 9 nature1 su* z magnetic or electric =ces4 ,fur!r ,newton f\nd t he c\ld pr$ict ! facts ( obs]vation accurately on ! hypo!sis t two small p>ticles ( matt] attract$ ea* o!r1 9 ! direction ( ! l9e jo9+ !m1 ) a =ce v>y+ inv]sely z ! squ>e ( ! di/ance betwe5 !m4 ,?is law is an action at a di/ance law & s is oppos$ to ! idea 7a74 ,we h tacitly suppos$ t ! space 9 :i* we make our measurem5ts is t made famili> to u by ! /udy ( ,euclid's elem5ts4 ,! *>act]i/ic prop]ty ( ?is space is t /at$ by ! !orem ( ,py?agoras t ! di/ance betwe5 two po9ts is f\nd by extract+ ! squ>e root ( ! sum ( ! squ>es ( ! diff]5ces ( ! ,c>tesian coord9ates ( ! two po9ts4 ,ma!maticians h long recogniz$ ! possibility ( o!r types ( space & ,e9/e9 has foll[$ _! lead4 ,he ab&ons ! empirici/ me?od & :5 ask$ :at he means by a po9t 9 space replies t to him a po9t 9 space is equival5t to f\r numb]s h[ obta9$ x is unnecess>y to "k a priori2 9 c]ta9 special cases !y may be ! ?ree ,c>tesian coord9ates ( ! exp]im5t] 7measur$ ) ref]5ce to a def9ite mat]ial framework7 toge!r ) ! "t4 ,accord+ly he says 8 space is ( f\r dim5sions4 ,betwe5 any two po9ts we may ins]t a sequ5ce ( sets ( f\r numb]s1 v>y+ cont9u\sly f ! fir/ set to ! second1 ?us =m+ :at we call a curve jo9+ ! two po9ts4 ,n[ we def9e ! l5g? ( ?is curve 9 a mann] :i* involves all ! po9ts on x & /ipulate t ?is l5g? has a physical reality1 i4e41 accord+ to our idea 7b7 its value is indep5d5t ( ! p>ticul> *oice ( coord9ates we make 9 describ+ ! space4 ,among all ! jo9+ curves !re w be "o ) ! prop]ty ( hav+ ! smalle/ l5g?2 ?is is call$ a geodesic & corresponds to ! /raight l9e 9 ,euclidean space4 ,we mu/ n[1 = lack ( an a priori description ( ! actual significance ( our coord9ates1 ext5d ! idea ( vector s t we may speak ( ! compon5ts ( a vector no matt] :at our coord9ates may actually signify4 ,9 ?is way are introduc$ :at are kn[n z t5sors2 if two t5sors are equal1 i4e41 h all _! compon5ts equal1 9 any "o set ( coord9ates !y are equal 9 any o!r & ! fundam5tal dem& ( ! new physics is t all physical equations :i* are n m]ely ! expression ( equality ( magnitudes mu/ /ate ! equality ( t5sors4 ,9 ?is way no "o sy/em ( coord9ates is privileg$ above any o!r & ! laws ( physics are express$ 9 a =m indep5d5t ( ! actual coord9ates *os52 !y are writt51 z we may say1 9 an absolute =m4 ,,! ,,gravitational ,,hypo!sis ,e9/e9 flatly d5ies ,newton's hypo!sis t !re is an absolute sy/em 7&1 inde$1 _m o!rs be=e him _h f\nd x difficult to admit t s insignificant a "p ( ! univ]se z our fix$ /> sy/em %\ld h su* a privileg$ position z t accord$ to x 9 ! ,newtonian ,me*anics74 ,9 any sy/em1 he says1 we h no reason to di/+ui% betwe5 ! s-call$ real gravitational =ce & ! s-call$ fictiti\s c5trifugal =ces--if we wi% s to express x gravitational =ce is fictiti\s =ce4 #aj ,a p>ticle mov+ 9 ! neighborhood ( mat]ial bodies moves accord+ to a law ( in]tia--a physical law expressible1 !re=e1 9 a mann] q indep5d5t ( ! *oice ( coord9ates4 ,! law ( in]tia is t a p>ticle left to itself moves along ! geodesics or %orte/ l9es 9 ! space4 ,if ! p>ticle is remote f o!r bodies ! space has ! ,euclidean "* & we h ,newton's law ( in]tia2 o!rwise ! p>ticle is 9 a space ( a non-,euclidean "* 7! space be+ always ! f\r-dim5sional space7 & ! pa? ( ! p>ticle is along a geodesic 9 t space4 ,e9/e91 9 ord] to make ! !ory m concrete1 makes a c]ta9 /ipulation z to ! nature ( ! gravitational space :i* /ipulation is express$1 z are all physical laws1 by means ( a t5sor equation--& ?is is sometimes call$ 8 law ( gravitation4 ,p]haps x w be well1 9 exemplification1 to expla9 :y light rays1 :i* pass close to ! sun1 %\ld be b5t accord+ to ! new !ory4 ,x is assum$ t light rays travel along c]ta9 geodesics kn[n z m9imal geodesics4 ,! sun has an int5se gravitational field ne> x--or1 z we n[ say1 ! dep>ture ( ! f\r-dim5sional space f ! ,euclidean is v m>k$ = po9ts ne> ! sun--b = po9ts s remote z ! e>? ?is dep>ture is s small z to be negligible4 ,h5ce ! =m ( ! geodesics ne> ! sun is diff]5t f t ne> ! e>?4 ,if ! space surr\nd+ ! sun 7 ,euclidean ! actual pa?s ( ! light rays w\ld appe> diff]5t f geodesics or /raight-l9es4 ,h5ce ,e9/e9 speaks ( ! curvature ( ! light rays due to ! gravitational field ( ! sun2 b we mu/ n be misl$ by a phrase4 ,light always travels along geodesics 7or /raight l9es--! only def9ition we h ( a /raight l9e is t x is a geodesic72 b1 ow+ to ! di/ortion ( ! space !y trav]se1 due to ! sun1 ^! geodesics rea* u ) a direction diff]5t f t !y w\ld h if !y did n pass ?r\gh ! m>k$ly non-,euclidean space ne> ! sun4 ,! consid]ation ( ! fundam5tal f\r-dim5sional space z be+ non-,euclidean :]e matt] is pres5t gives a possibility ( an answ] to ! _w old "q3 ,is space f9ite or inf9ite8 ,is "t et]nal or f9ite8 ,! fasc9at+ possibility arises t ! space may be l ! two-dim5sional surface ( a sph]e :i* to a limit$ exp]i5ce seems inf9ite 9 ext5t & flat or ,euclidean 9 "*4 ,a new ,columbus n[ asks u to consid] o!r possibilities 9 :i* we %\ld h a f9ite univ]se--f9ite n only z to space measurem5t b z to "t 7= ! space may be su* t all ( ! f\r coord9ates ( its po9ts are b\nd$ 9 magnitude74 ,h[ev]1 al?\gh ,e9/e9 speaks ( ! possibility ( a f9ite univ]se1 we d n1 p]sonally1 ?9k 8 argum5t conv9c+4 ,po9ts on a sph]e may be locat$ by ! ,c>tesian coord9ates ( _! /]eographic projections on ! equatorial plane & ^! coord9ates1 :i* might well be ^? actually measur$1 are n b\nd$4 ,,! ,,special ,,relativity ,,!ory ,9 our acc\nt ( ! ,e9/e9 !ory we h n foll[$ its hi/orical ord] ( developm5t = two reasons4 ,fir/ly1 ! e>li] ,special ,relativity ,!ory prop]ly belongs to a s*ool ( ?\ght diametrically oppos$ to t furni%+ ! ,g5]al ,!ory ( ,relativity &1 secondly1 ! latt] _c be obta9$ f ! =m] by ! process ( g5]alization z commonly und]/ood4 ,e9/e91 :5 propos+ ! e>li] !ory1 adopt$ ! position ( ! empirici/ s t to him ! phrase1 a po9t 9 space1 _h no mean+ )\t a mat]ial framework ( ref]5ce 9 :i* to measure space di/ances4 ,:5 he came to inve/igate :at is meant by "t & :5 he ask$ ! "q :at is meant by ! /atem5t t two remote ev5ts are simultane\s8 x became evid5t t "s mode ( communication betwe5 ! two places is necess>y2 ! mode adopt$ 0 t by means ( light-signals4 ,! fundam5tal hypo!sis 0 !n made t ! velocity ( su* signals is indep5d5t ( ! velocity ( _! s\rce 7"s hypo!sis is necess>y if we wi% to comp>e ! "t associat$ ) ev5ts1 :5 "o mat]ial ref]5ce-sy/em is us$1 & ! correspond+ "t :5 ano!r 9 motion relative to ! fir/ is adopt$74 ,x develops t "t & space measurem5ts are inextricably int]wov52 !re is no su* ?+ z ! l5g? ( a body or ! duration ( an ev5t b r ^! are relative to ! ref]5ce-sy/em4 #aa ,m9k[ski introduc$ ! idea ( ! space ( ev5ts--( f\r dim5sions--b ?is space 0 suppos$ ,euclidean l ! ?ree-dim5sional space ( 8 pr$ecessors4 ,to ,e9/e9 belongs ! cr$it ( tak+ f ?is repres5tation a purely =mal ma!matical "* & ( insi/+ t ! real space--^: di/ances h a physical significance--is ! f\r-dim5sional space4 ,b we _c insi/ too /rongly on ! fact t 9 ! gravitational space ( ! g5]al !ory !re is no po/ulate ( ! con/ancy ( velocity ( a light-signal & accord+ly no me?od ( assign+ a "t to ev5ts correspond+ to t adopt$ 9 ! special !ory4 ,9 ?is latt] !ory att5tion 0 conf9$ to mat]ial sy/ems mov+ ) uni=m velocity ) respect to ea* o!r & x develop$ t ! velocity ( light 0 ! ultimate velocity fa/] ?an :i* no sy/em c\ld move--a result surpris+ & a priori r repugnant4 ,x is m]ely a consequ5ce ( our mode ( comp>+ times ( ev5ts2 if "s o!r me?od--?\ght transf]5ce1 let u say--7 possible ! velocity ( ?is w\ld be ! limit+ velocity4 ,9 conclusion we %\ld rem>k t ! po/ulat$ equival5ce ( gravitational & c5trifugal =ces dem&s t any?+ possess$ ( in]tia w be act$ ^u by a gravitational field & ?is leads to a possible id5tification ( matt] & en]gy4 ,fur!r our guid+ idea 7a7 w prompt u to say1 foll[+ ! example ( ,f>aday 9 8 electrical rese>*es1 t ! geodesics ( a gravitational space h a physical exi/5ce z di/9ct f a m]e ma!matical "o4 ,! f\r-dim5sional space we may call ! e!r1 & s re/ore ?is be>] ( physical =ces to ! position x lo/ :51 z a ?ree-dim5sional idea 9 ! ,special ,relativity ,!ory1 x _h to be> an id5tical relation to a multitude ( relatively mov+ mat]ial sy/ems4 ,! reason = our seem+ly p>adoxical title = an essay on ,relativity w be cle> :5 x is rememb]$ t 9 ! new !ory we consid] ^? space-"t prop]ties :i* are absolute or devoid ( ref]5ce to any p>ticul> mat]ial ref]5ce-frame4 ,nev]!less1 al?\gh ! g5]al *>act]i/ics ( ! !ory are ?us describ$1 )\t ref]5ce to exp]im5t1 :5 ! !ory is to be te/$ x is necess>y to /ate :at ! f\r coord9ates discuss$ actually are--h[ !y are det]m9$ by measurem5t4 ,x is our op9ion t mu* rema9s to be done to place ?is portion ( ! subject on a satisfactory basis4 ,= example1 9 ! d]ivation ( ! nature ( ! gravitational space1 surr\nd+ a s+le attract+ body1 mo/ ( ! acc\nts use ,c>tesian coord9ates z if ! space 7 ,euclidean & /ep f ^! to pol> coord9ates by ! =mul famili> 9 ,euclidean geometry4 ,b ^! details are1 p]haps1 l matt]s ( elegance1 if we %all be all[$ to give ,e9/e9's quotation f ,boltzmann1 to be left to ! tailor & ! cobbl]4 ,,xvii ,,! ,,physical ,,side ,,( ,,relativity ,! ,imm$iate ,contacts ,betwe5 ,e9/e9's ,!ories & ,curr5t ,physics & ,a/ronomy ,,by ,,pr(essor ,,william ,h4 ,,pick]+ ,,h>v>d ,,college ,,obs]vatory1 ,,m&eville1 ,,jamaica ,! ,!ory ( ,relativity w be treat$ fir/ f ! physical side1 leav+ ! ?ree a/ronomical te/s to :i* x has be5 put to be discuss$ lat]4 ,!re is "o a/ronomical fact h[ev] t mu/ be m5tion$ 9 ?is connection1 & ?is is ! discov]y ( ! ab]ration ( light by ,bradley 9 #agbf4 ,x is f\nd t e /> 9 ! heav5s app>5tly describes a small annual ellipse1 ^: major axis is #da'' 9 l5g?4 ,?is ,bradley %[$ to be due to a comb9ation ( ! velocity ( ! e>? 9 its orbit1 & ! velocity ( light2 & x is s expla9$ 9 all ! elem5t>y text-books on a/ronomy4 ,x implies a /ation>y e!r ?r\gh :i* ! e>? is mov+4 ,! importance ( ?is /atem5t w appe> pres5tly4 ,! subject is usually illu/rat$ by suppos+ a man to g out 9 a ra9/orm c>ry+ a v]tical tube4 ,if ! ra9 is fall+ v]tically1 & ! man /&s /ill1 ! sides ( ! tube w n be wet1 save by an occasional drop1 b if ! tube is mov$1 x mu/ !n be incl9$ =w>d 9 ord] to keep x dry4 ,! angle ( incl9ation1 :i* corresponds to ab]ration1 w dep5d on ! relative velocity ( ! tube1 correspond+ to ! e>?1 & ! ra9 drops :i* correspond to ! waves ( light4 ,if ?ree l9es are dropp$ ^u a po9t 9 space1 ea* l9e be+ p]p5dicul> to ! plane conta9+ ! o!r two1 we h :at is kn[n z a sy/em ( coord9ates4 ,e9/e9's orig9al !ory ( relativity1 :i* he n[ designates z ! special !ory1 dep5ds on two pr9ciples4 ,! fir/ is t ,e law ( nature :i* holds good ) respect to a coord9ate sy/em ,k mu/ also hold good = any o!r sy/em ,k'1 provid$ t ,k & ,k' are 9 uni=m movem5t ( translation4 ,! second pr9ciple is t ,light 9 a vacuum has a def9ite & con/ant velocity1 indep5d5t ( ! velocity ( its s\rce4 ,^! two s5t5ces may be consid]$ z au?oritative1 be+ quot$ 9 ,e9/e9's own words4#a ,! fir/ ( ^! pr9ciples ne$ n greatly surprise u4 ,! second is n well express$1 because x is ambigu\s4 ,he does n say h[ ! fir/ velocity is measur$1 :e!r relatively to ! e!r or relatively to ! obs]v]4 ,9 fact ?is is ! v gi/ ( ! :ole matt]1 z we %all pres5tly see4 ,9 ! case ( s\nd ! velocity is con/ant ) reg>d to ! m$ium1 ! air1 9 ! case ( light x is suppos$ to be con/ant ) reg>d to ! obs]v]4 ,x rea*es him ) a con/ant velocity1 no matt] h[ he moves4 ,9 ord] to und]/& ?is /atem5t cle>ly let u consid] ! app5d$ tabul> diagram4 ,on a calm day imag9e a s\rce ( s\nd at ,s 9 l9e a4 ,?is may be ei!r a gun or a bell4 ,imag9e an obs]v] #a1ajj feet di/ant1 locat$ at ,o4 ,! velocity ( s\nd 9 air is #a1ajj feet p] second4 ,?is velocity we w take z unity1 z indicat$ 9 ! ?ird column1 & ! velocity ) :i* ! s\nd rea*es ! obs]v] is also #a1 z %[n 9 ! f\r?4 ,x w rea* him 9 a unit int]val ( #a second1 z %[n 9 ! fif?4 ,if ! bell is /ruck1 x w give its normal pit* or frequ5cy1 :i* we w also call unity1 9 ! six? column4 ,n[ imag9e case b :]e ! obs]v] is on a tra9 advanc+ t[>d ,s4 ,:5 he is #a1ajj feet di/ant1 ! gun is fir$1 b z he is advanc+ t[>d x1 he he>s x at ,o 9 r less ?an a second1 z %[n 9 ! fif? column4 ,! velocity ( ! s\nd ) reg>d to him is r m ?an unity1 z %[n 9 ! f\r? column4 ,if ! bell is s\nd$1 ! pit*1 t is ! frequ5cy1 is rais$1 because he receives m s\nd waves p] second ?an be=e4 ,9 case c ! obs]v] is /ation>y1 b ! s\rce ( s\nd is rec$+4 ,at a di/ance ( #a1ajj feet ! gun is fir$1 & ! obs]v] he>s x aft] an int]val ( j "o second1 z 9 case a4 ,! velocities ) reg>d to ! obs]v] & ?r\gh ! m$ium are also unity4 ,if ! bell is /ruck ! pit* is l[]$1 s9ce he receives few] s\nd waves p] second1 ! rev]se ( case b4 ,velocity ,s\rce 9 to ,int]val ,frequ5cy ,obs]v] ,m$ium ,obs]v] ,air a ,s #a #a #a #a ,o b ,s #a #a #a- #a ,o c ,s #a #a #a #a- ,o d ,s #a #a #a- #a ,o ,e!r ,a ,s #a #a #a #a ,o ,b ,s #a- #a #a #a ,o ,c ,s #a #a #a #a- ,o ,d ,s #a - #a #a #a ,o ,9 case d imag9e ! s\rce & ! obs]v] #a1ajj feet ap>t1 & advanc+ on ! same tra94 ,:5 ! gun is fir$1 ! velocity ( ! s\nd waves w be great] ) reg>d to ! obs]v]1 & he w he> ! s\nd 9 less ?an a second1 z 9 case b4 ,:5 ! bell is /ruck x w h ! normal pit*1 ! same z 9 case a4 ,we f9d !re=e t = s\nd ! velocity ) reg>d to ! m$ium is always unity1 :ile ! velocity ) reg>d to ! obs]v]1 & ! int]val elaps$1 dep5d only on ! motion ( ! obs]v] himself1 & are indep5d5t ( ! motion ( ! s\rce4 ,! frequ5cy ( ! vibrations1 on ! o!r h&1 dep5ds only on ! relative motion ( ! obs]v] & ! s\rce1 b is indep5d5t ( _! common motion 9 any direction4 ,fur!r1 x makes no diff]5ce :e!r ! s\rce & ! obs]v] are mov+ on a tra91 or :e!r !y are /ation>y1 & a uni=m w9d is bl[+ pa/ !m4 ,9 ! case ( light waves we %all f9d a v diff]5t /ate ( affairs1 al?\gh ! rules = frequ5cy are ! same z !y are = s\nd4 ,9 case ,a we h ! normal conditions1 :]e bo? ! s\rce & obs]v]s are /ation>y4 ,9 case ,b we h a repres5tation ( ! ,mi*elson-,morley exp]im5t z supplem5t$ by t ( ,majorana1#b :]e ! s\rce is /ation>y & ! obs]v] advances4 ,unlike ! case ( s\nd1 ! int]val elaps$1 z %[n by ! exp]im5t1 is n[ ! same z 9 case ,a1 & s9ce ! di/ance to ! obs]v] is less1 ! velocity ( light ) respect to ! e!r mu/ also be less ?an unity4 ,s9ce ! obs]v] is advanc+ aga9/ ! light1 ?is w p]mit ! velocity ( light ) reg>d to ! obs]v] to rema9 unity1 9 con=mity ) ! second pr9ciple ( relativity4 ,comp>e ) case b = s\nd4 ,z ,jeans expresses x1 ,! velocity ( light 9 all directions is ! same1 :atev] ! motion ( ! obs]v]4#c ,t is to say x appe>s to be ! same to him1 h[ev] he moves4 ,case ,c repres5ts ,e9/e9's /atem5t1 z confirm$ by ,majorana's exp]im5t4 ,x does n diff] f case c = s\nd4 ,case ,d is m complex1 b accept+ ! /atem5t above t ! velocity is con/ant ) reg>d to ! obs]v]1 we see t ! velocity ?r\gh ! m$ium mu/ be less1 & t ! int]val elaps$ w be con/ant1 z 9 case ,b4 ,c\ld we use ! bright] />s & planets z s\rces ( light1 sev]al ( ^! cases c\ld be fur!r te/$4 ,?is br+s u at once to /atem5ts t contradict our common s5se4 ,= in/ance1 ,jeans says no matt] :at ! velocity ( ! obs]v] is1 ! light surface1 z obs]v$ by t obs]v]1 is inv>iably a sph]e hav+ t obs]v] z c5t]4#c ,t is to say ! light surface1 or wave front1 is a contract+1 n an exp&+1 sph]e4 ,?is1 if confirm$1 w\ld g a long way t[>d mak+ our univ]se a subjective r ?an an objective ph5om5on4 ,aga9 imag9e a fla% ( light1 su* z an explosion1 to occur :5 an obs]v] is 9 a giv5 position4 ,x makes no diff]5ce h[ ! obs]v] may move :ile ! light is approa*+ him1 :e!r sev]al miles =w>d or backw>d1 ! light w rea* him 9 exactly ! same "t1 z is %[n by ,mi*elson's exp]im5t4 ,or if two obs]v]s are at ! same spot :5 ! explosion occurs1 & "o moves =w>d1 & ! o!r backw>d1 !y w bo? see ! explosion at exactly ! same in/ant4 ,?is s\nds ridicul\s1 b n only is x :at ,jeans says1 b x is ! logical int]pretation ( ,e9/e9's second pr9ciple1 if ,e9/e9 means by velocity1 velocity ) reg>d to ! obs]v]4 ,if he means velocity ) reg>d to ! m$ium1 !n ! case is exactly ! same z t ( s\nd 9 air1 & ,mi*elson's exp]im5t z well z ! ,maxwell-,lor5tz !ory ( light are contradict$4 ,?is !ory is n[ univ]sally accept$1 & ,mi*elson's exp]im5t has be5 c>efully repeat$ by o!r obs]v]s1 & fully confirm$4 ,?is is ! v he>t ( ! relativity "q4 ,if we /ate ! matt] objectively x comes to ?is4 ,! velocity ( light ) reg>d to ! e!r is a v>iable quantity1 dep5d+ m]ely on :]e ! obs]v] *ooses to g4 ,z ,edd+ton well says1 ^! relations to ! e!r h no effect on ! ph5om5a & c be disreg>d$--a /ep :i* appe>s to dive/ ! e!r ( ! la/ remnants ( sub/antiality4#d ,! only way ( avoid+ ?is app>5t absurdity seems to be to consid] t ! e!r moves ) ! e>?4 ,mi*elson's result w\ld !n be fully expla9$4 ,( c\rse ?is c only be true = a few miles above ! e>?'s surface4 ,beyond t ! e!r mu/ ei!r be /ation>y or move ) ! sun4 ,! velocity ( light ) reg>d to ! e!r w\ld !n be a con/ant1 j z ! velocity ( s\nd is con/ant ) reg>d to ! air4 ,?is w\ld contradict ,e9/e9's second pr9ciple z x is g5]ally und]/ood4 ,! tr\ble ) ?is sugge/ion is t x fails to acc\nt = ab]ration1 :i*1 z already expla9$1 appe>s to require t ! e>? %\ld be mov+ ?r\gh ! e!r4 ,to meet ?is em]g5cy w\ld involve "s modification ( ! undulatory !ory ( light1 :i* app>5tly w\ld n be impossible1 b has n yet be5 made4 ,9 #aiae ,e9/e9 br\ght out an ext5sion ( 8 fir/ pr9ciple4 ,?is he calls ! g5]al !ory ( relativity4 ,x /ates t 9 our *oice ( coord9ate sy/ems we %\ld n be limit$ 9 any way s f> z _! /ate ( motion is conc]n$4#a ,?is leads to ! ?ree a/ronomical consequ5ces m5tion$ lat] 9 ?is pap]1 two ( :i* h be5 m or less confirm$1 & ! ?ird practically contradict$ z f> z quantitative measures are conc]n$4#e ,z is well kn[n ! k9etic en]gy ( a mov+ body may be express$ z e #a_/bmv#b1 b if ! body is *>g$ electrically1 ! fraction becomes #a_/b7m m'7v#b1 :]e m' is a quantity dep5d5t on ! squ>e ( ! electrical *>ge4 ,t is to say1 we h ! normal mass ( ! body1 & also :at we may call its electrical mass4 ,if :5 9 ?is condition a portion ( ! mass is electrical1 ! "q at once occurs to u1 :y may n ! :ole mass be electrical1 9 o!r words1 a =m ( en]gy8 ,al?\gh ?is has n be5 satisfactorily prov$ hi!rto1 yet su* is ! g5]al belief among physici/s4 ,z ,e9/e9 puts x in]t mass is no?+ else ?an lat5t en]gy4#a ,! same idea is sometimes express$ z ! mass ( ord9>y matt] is due to ! electromagnetic en]gy ( its ultimate p>ticles1 & electromagnetic en]gy :]ev] f\nd mu/ possess mass1 i4e41 in]tia4#f ,if t is s1 s9ce a ray ( light on ! undulatory !ory is a =m ( electromagnetic en]gy1 x too mu/ possess mass4 ,s9ce all mass ) :i* we are famili> is subject to ! attraction ( gravitation1 x seem$ likely t a ray ( light w\ld be b5t out ( its c\rse 9 pass+ ne> ! sun1 & ?is z we h se5 0 prov$ to be true at ! rec5t sol> eclipse4 ,t portion ( ! mass ( a body due to its electrical *>ge c be readily %[n exp]im5tally to v>y ) ! velocity ( ! body4 ,e9/e9 has %[n ! same to be true ( ! normal mass1 z is illu/rat$ 9 ! advance ( ! p]ihelion ( ! orbit ( ,m]cury4 ,he has also po9t$ out t gravitation1 in]tia & c5trifugal =ce are all closely relat$1 & obey simil> laws4 ,?us if we rise f ! e>? ) accel]at$ velocity1 we app>5tly increase our weight4 ,aga9 if ! velocity ( rotation ( ! e>? on its axis %\ld be increas$1 our weight w\ld be dim9i%$4 ,^! facts are sugge/ive :5 we come to consid] ! ultimate cause ( gravitation4 ,ano!r fact :i* mu/ be r />tl+ to ! old] s*ool ( sci5ti/s is t mom5tum is no long] simply mv1 mass times velocity1 b t ! velocity ( light c1 comes into ! "q1 & ! =mula = mom5tum n[ assumes ! =m ( fracm vsqrt#a - fracv#b;c#b ,= ord9>y velocities ?is correction is extremely small1 b x has be5 %[n to be necess>y1 bo? !oretically & exp]im5tally1 :5 deal+ ) ! high velocities ) :i* we are n[ famili>4 ,! !ory ( relativity is s widespread 9 its application t sev]al o!r !ories h become m or less intimately comb9$ ) x1 = :i* ,e9/e9 is 9 no way responsible4 ,"o ( ^! is kn[n z ! ,fitzg]ald-,lor5tz !ory1 t all bodies are subject to a contraction 9 ! direction ( _! motions ?r\gh space4 ,?is 0 fir/ sugge/$ 9 ord] to expla9 ! ,mi*elson-,morley exp]im5t1 b has prov$ inadequate to d s1 p>ticul>ly :5 ! obs]v] is rec$+ f ! s\rce4 ,?is contraction is express$ by ! same factor us$ 9 ! d5om9ator ( ! revis$ expression = mom5tum1 giv5 above4 ,aga9 ! quantity c is s enorm\s1 t ev5 = l>ge bodies at planet>y velocities ! contraction am\nts to v little4 ,?us ! e>? mov+ at a spe$ ( eighte5 miles p] second 9 its orbit1 is flatt5$ only #a_/bjj1jjj1jjj1 or #b4e in*es4 ,on ! o!r h& = high velocities ( _m ?\s& miles p] second1 su* z we h become famili> ) 9 ! case ( ! radioactive sub/ances1 ! flatt5+ is a v consid]able fraction ( ! diamet] ( ! mov+ body1 "o-half or m1 & 9 ! case ( ! corpuscles ( light1 if t !ory 7 adopt$1 ?is flatt5+ becomes equal to ! diamet]1 & _! ?ickness is r$uc$ to z]o4 ,:5 we view ,e9/e9's !ories f ! a/ronomical /&po9t1 ! e>lie/ fact be>+ on relativity t we ne$ consid] 0 ! discov]y ( ab]ration1 by ,bradley1 9 #agbf1 z se5 above4 ,9 #ahgb ,airy obs]v$ ! /> g ,draconis ?r\gh a telescope fill$ ) wat]4 ,s9ce ! velocity ( light is less 9 wat] ?an 9 air1 we %\ld naturally expect to f9d ! ab]ration appreciably increas$4 ,x 0 f\nd1 on ! o!r h&1 h[ev]1 to be unaffect$4 ,9 #ahhg ! results ( ! fam\s ,mi*elson-,morley exp]im5t 7 publi%$4#g ,9 ?is exp]im5t ! velocity ( light 0 measur$ 9 v>i\s directions ) reg>d to ! motion ( ! e>? 9 its orbit4 ,if ! e!r 7 /ation>y1 & ! e>? mov+ ?r\gh x1 diff]5t velocities %\ld be obta9$ 9 diff]5t directions4 ,su* 0 n ! case h[ev]1 & ! exp]im5t indicat$ t ! e!r mov$ ) ! e>?4 ,x ?us flatly contradict$ ! conclusions f\nd$ on ab]ration4 ,e9/e9's ,special ,!ory ( ,relativity1 ( #aije1 z we h se51 resolves ?is contradiction4 ,b z we %all pres5tly see1 x is ! ,g5]al ,!ory1 ( #aiae1 t leads to a/ronomical applications ( broad scope4 ,x indicates1 = in/ance1 t !re is no ess5tial diff]5ce betwe5 gravitation & in]tia4 ,?is idea may be crudely illu/rat$ by our feel+s ( increas$ weight :5 an elevator />ts rapidly upw>ds4 ,a man :ile fall+ freely 9 space ceases to feel ! pull ( gravitation4 ,b we mu/ n z yet conceive ( ! !ory ( relativity z a univ]sally accept$ & unque/ion$ tru? ( sci5ce4 ,edd+ton is its lead+ ,engli% expon5t1 & he is support$ by su* m5 z ,jeans1 ,l>mor1 & ,jeffreys4 ,on ! o!r h&1 ! !ory has be5 sev]ely criticis$ by ,lodge1 ,f[l]1 ,silb]/e91 & ,sampson4 ,few ,am]ican sci5ti/s h express$ any op9ions 9 pr9t on ! subject1 & ! rec5t eclipse obs]vations1 to :i* we %all ref] lat]1 are to be repeat$ ) m suitable in/rum5ts = v]ification 9 #aibb1 9 ! hope ( obta9+ m accurate & accordant results4#h ,an appurt5ance ( ! ,e9/e9 !ories :i* be>s mu* ! same relation to !m z does ! ,lor5tz-,fitzg]ald contraction1 m5tion$ above1 is ! idea1 fir/ cle>ly /at$ by ,m9k[ski1 t "t is a k9d ( space--a f\r? dim5sion4 ,?is ! read] w d\btless f9d to be ! mo/ difficult portion ( ! !ory to picture 9 8 own m9d4 ,x is entirely unsupport$ by exp]im5t or obs]vation1 necess>ily s1 & is bas$ :olly on ma!matical & philosophical conceptions4 ,our di/9ction betwe5 space & "t seems to be t ! direction 9 :i* we progress )\t ef=t is "t2 ! o!r directions1 9 :i* we h to make an ex]tion to move ourselves1 or 9 :i* we are c>ri$1 are space4 ,h[ _m dim5sions empty space may h1 we really h no means ( kn[+1 because we c nei!r see nor feel x4 ,matt] we "k has ?ree1 l5g?1 bread?1 & ?ickness1 also t x lies remote f u 9 ?ree correspond+ directions4 ,^! facts may h giv5 u ! errone\s impression t space too has only ?ree dim5sions4 ,n[ x is claim$ t "t is a f\r?1 & t !re are also o!rs4 ,9 ord] to illu/rate ?is1 ,edd+ton asks u to imag9e a movie film tak5 ( a man or ( any mov+ object4 ,let ! sep>ate pictures be cut ap>t & pil$ on "o ano!r4 ,?is w\ld =m a sort ( pictorial hi/ory ( ! individual = a brief int]val 9 8 life1 9 ! =m ( a cube4 ,if we attempt to pick x up1 x falls ap>t1 ?us cle>ly %[+ ! diff]5ce betwe5 "t & space4 ,b suppose x n[ all glu$ toge!r 9 "o solid cube1 s t x is no easi] to cut a section 9 "o direction ?an 9 ano!r4 ,t is ,m9k[ski's idea ( space & "t1 & fur!r1 t ! direction 9 :i* we %\ld cut x dep5ds m]ely on ! velocity ) :i* we are mov+ ?r\gh space4 ,i %\ld cut x p>allel to ! films1 b a man on a rapidly mov+ />1 9 ord] to sep>ate x into space & "t1 w\ld cut x 9 an incl9$ direction4 ,t is a ?+ :i* may be true1 b x is "o :i* we believe no mortal man c cle>ly picture to himself4 ,on ! o!r h& ,turn] has rec5tly made a v int]e/+ po9t1#i namely1 t ! f\r? dim5sion z actually treat$ by ! ma!maticians is n "t itself1 b "t multipli$ by a con/ant--! velocity ( light4#aj ,)\t affect+ ! a/ronomical pro(s ( relativity at all1 ?is simplifies our conceptions enorm\sly4 ,9 ord9>y ev]yday life "t & space _c be id5tical1 any m ?an a y>d c be id5tical ) a qu>t4 ,on :at is kn[n to physici/s z ! c5timet]-gram-second sy/em1 di/ance is repres5t$ by l1 mass by m1 & "t by t4 ,velocity is !n di/ance divid$ by "t1 l_/t1 or z we say 9 ,engli% units1 s _m feet p] second1 & ! f\r? dim5sion may be express$ z "t multipli$ by velocity1 t times l_/t l4 ,t is to say1 x is simply di/ance1 j l ! o!r ?ree dim5sions4 ,to say t "t is ! f\r? dim5sion f ?is po9t ( view1 appe>s to u j z ridicul\s z x w\ld be to attempt to measure ! velocity ( a tra9 9 qu>ts4 ,x is q correct1 h[ev]1 al?\gh unusual1 to speak ( a giv5 tra9 z mov+ at a spe$ ( #aj qu>ts p] squ>e in* p] second1 l#c_/l#b t l_/t4 ,?is w\ld be equival5t to a velocity ( #cc miles p] h\r4 ,if ,i wi% to give a complete dim5sional description ( myself 9 my f\r dim5sions1 ,i mu/ give my l5g?1 my bread?1 & my ?ickness1 ev] s9ce ,i came into be+1 & also ! c\rse ,i h trav]s$ ?r\gh space s9ce t "t4 ,?is latt] di/ance w be express$ 9 t]ms ( a unit ^: l5g? is #ahf1jjj miles1 ! di/ance trav]s$ by light 9 "o second4 ,! di/ance :i* ,i travel ?r\gh space annually is enorm\s1 & v complex z to direction4 ,x involves n m]ely my own motions z ,i cross ! room1 or take a tra9 or /eam]1 b also ^? due to ! rotation ( ! e>? on its axis1 its revolution r\nd ! sun1 & ! motion ( ! latt] ?r\gh ! heav5s4 ,9 g5]al ,i travel1 or 9 o!r words increase my l5g? 9 ! f\r? dim5sion1 by ov] #d1jjj units a ye>4 ,! f\r? dim5sion accord+ly1 if ?is view is accept$1 is simply a di/ance l ! o!r ?ree1 & p]fectly easy to und]/&4 ,we n[ come to ! ?ree actual te/s by :i* ! !ory has be5 tri$4 ,! planets z is well kn[n revolve ab\t ! sun 9 ellipses1 ) ! sun 9 "o ( ! foci4 ,t is to say1 ! sun is n 9 ! c5t]1 b a little on "o side ( x4 ,! end ( ! ellipse :]e ! planet comes ne>e/ to ! sun is call$ ! p]ihelion1 & "h ! planet is mov+ mo/ rapidly4 ,! o!r end is call$ ! aphelion1 & "h ! motion is sl[e/4 ,accord+ to ,newton's !ory ( gravitation1 if a sph]ical sun possesses a s+le planet or companion1 its orbit w be p]man5tly fix$ 9 space unless p]turb$ by "s o!r body4 ,if a second planet exi/1 x w cause ! p]ihelion ( ! fir/ sl[ly to advance4 ,accord+ to ,e9/e9 ! mass ( a planet dep5ds 9 "p on its velocity4 ,x w !re=e be less at aphelion :]e x is mov+ sl[ly ?an at p]ihelion :]e x is mov+ rapidly1 consequ5tly 9 addition to ! ,newtonian attraction we h ano!r "o :i* increases z we approa* ! sun4 ,! effect ( ?is w be to cause ! p]ihelion ( ! orbit to advance1 :e!r !re is a second planet or n4 ,among ! l>g] planets ,m]cury has ! mo/ ecc5tric orbit1 & x also moves mo/ rapidly1 s t x is p>ticul>ly well adapt$ to te/ ! relativity !ory4 ,! obs]v$ advance ( its p]ihelion is #egd'' p] c5tury1 in/ead ( ! !oretical figure #ecb''1 due to ! o!r planets--a diff]5ce ( #db''4aa ,?is has long be5 a puzzl+ discrepancy betwe5 obs]vation & ! law ( gravitation4 ,prior to ,e9/e91 attempts 7 made to elim9ate x by assum+ a c]ta9 oblat5ess ( ! sol> disk4 ,if ! equatorial diamet] exce$$ ! pol> by only #j''4e ! :ole advance w\ld be acc\nt$ =1 b n only has ?is ellipticity fail$ ( detection1 b if x exi/$1 x %\ld produce a v noticeable & inadmissible *ange 9 ! incl9ation ( ,m]cury's orbit1 am\nt+ to ab\t #c'' p] c5tury1 z has be5 demon/rat$ by bo? ,h]z] & ,newcomb4#ab ,e9/e9 f computations alone1 )\t introduc+ any new con/ants or hypo!ses :atev]1 %[$1 if ! !ory ( relativity be accept$1 t ! sun %\ld produce an accel]ation ( #dc'' p] c5tury1 ?us entirely acc\nt+ = ! obs]v$ discrepancy1 f> )9 ! limits ( accuracy ( ! obs]vations4 ,! only o!r planet ^: orbit has a l>ge ecc5tricity1 & t is suitable = inve/igation1 is ! planet ,m>s4 ,"h ! discrepancy betwe5 obs]vation & !ory is v slight1 only #d''1 & a portion ( t may be due to ! attraction ( ! a/]oids4 ,?is deviation is s slight t x may well be due entirely to accid5tal errors ( obs]vation1 b h[ev] t may be1 ,e9/e9's !ory r$uces x to #b''4g4 ,?is all seems v satisfactory & complete1 b ! tr\ble ) x is t ! co9cid5ce = ,m]cury is r too good4 ,x is bas$ on ! assumption t ! sun is a p]fect sph]e1 & t ! d5sity ( its surface is uni=m f ! equator to ! poles4 ,?is w\ld d\btless be true if ! sun did n revolve on its axis4 ,9 po9t ( fact x does revolve1 9 a p]iod 9 g5]al ( ab\t #bf days4 ,consequ5tly an object on its equator mu/ exp]i5ce a c]ta9 am\nt ( c5trifugal =ce4 ,!re=e if its surface 7 ( uni=m d5sity ! %ape ( ! sun w\ld be an oblate sph]oid4 ,x c be readily %[n t ! !oretical excess ( ! equatorial ov] ! pol> diamet]1 due to ! c5trifugal =ce1 %\ld am\nt to only #j''4jd1 an am\nt :i* c\ld h>dly be detect$ by obs]vation1 & might readily be conceal$ by a slight excess ( equatorial ov] pol> d5sity4 ,any reasonable excess ( d5sity at ! c5t] w\ld dim9i% ?is result b slightly4 ,! molecul> weight ( ! c5tral mat]ial#ac is probably ab\t #b4 ,?is comput$ equatorial excess is "o-twelf? ( ! am\nt necess>y to cause ! obs]v$ advance1 & %\ld !re=e cause an advance ( ! p]ihelion ( ab\t #c''4e p] c5tury1 r$uc+ ! diff]5ce betwe5 ! obs]v$ advance & t caus$ by gravitation to #ch''4e4 ,accord+ to ,e9/e9 ! advance due to relativity %\ld be1 z we saw1 #dc''1 a discrepancy ( #d''4e p] c5tury1 or #aj p] c5t4 ,jeffreys has rem>k$ t any discrepancy su* z #aj'' w\ld be fatal to a !ory su* z ,e9/e9's1 :i* conta9s no arbitr>y con/itu5t capable ( adju/m5t to suit empirical facts4#ad ,x mu/ be po9t$ out "h h[ev]1 t s f> z kn[n1 ?is small correction to ! motion ( ,m]cury's p]ihelion has n previ\sly be5 sugge/$1 s t !re has be5 no opportunity hi!rto = its criticism by o!rs4 ,x 0 due l>gely to ! success ) ,m]cury t x 0 decid$ to put ! relativity !ory to ano!r te/4 ,accord+ to ! ,newtonian !ory1 z /at$ by ,newton himself1 corpuscles z well z planets h mass1 & mu/ !re=e be attract$ by ! sun4 ,accord+ to ,e9/e91 ow+ to _! high velocity1 ?is attraction mu/ be twice z great z x w\ld be accord+ to ! !ory ( gravitation4 ,if ! ray ( light proce$+ f a /> 7 to pass ne>ly tang5t to ! sun's limb x %\ld be deflect$ #j''4hg accord+ to ,newton4 ,accord+ to ! !ory ( relativity x %\ld be deflect$ #a''4ge4 ,/>s ( c\rse _c usually be obs]v$ ne> ! sun4 ,x is !re=e necess>y to take advantage ( a total sol> eclipse1 :5 ! sun is completely hidd5 by ! moon1 9 ord] to secure ^! obs]vations4 ,two exp$itions1 "o to ,africa1 & "o to ,s\? ,am]ica1 obs]v$ successfully ! total eclipse ( ,may #bi1 #aiai4 ,! =m] 0 locat$ on ! ,isl& ( ,pr9cipe 9 ! ,gulf ( ,gu9ea4 ,! latt] 0 locat$ at ,sobral1 ,brazil4 ,_! equipm5t & results are %[n 9 ! foll[+ table1 :]e ! successive columns give ! location1 ! ap]ture 9 in*es ( ! telescopes employ$1 _! focus 9 feet1 ! numb] ( plates secur$1 ! numb] ( />s measur$1 _! mean d$uc$ deflection f _! true positions by ! attraction ( ! sun1 & ! deviations f ! !oretical results4#ae ,9 ! fir/ & la/ l9e ( ! table %[n h]e)1 ?is ,location ,ap]ture ,focus ,plates ,/>s ,defl4 ,dev4 ,pr9cipe #ac #aa #b #e #a''4fj -#j''4ae ,sobral #ac #aa #ai #ab #j 4#ic 7#j 4#jf7 11 #d #ai #h #g #a 4#ih #j 4#bc deviation is tak5 f ,e9/e9's comput$ value ( #a''4ge4 ,9 ! second l9e ! diff]5ce %[n is f ! value requir$ by ! ,newtonian !ory1 #j''4hg4 ,! results obta9$ ) ?is telescope 7 reject$ h[ev]1 al?\gh !y 7 mu* ! mo/ num]\s1 because x 0 f\nd t = "s reason1 suppos$ to be ! heat+ ( ! mirror by ! sun be=e ! eclipse1 ! /> images 7 slightly out ( focus1 & 7 !re=e consid]$ unreliable4 ,! results ) ! two o!r telescopes 7 n v accordant1 b ! #d-;in* _h ! long] focus1 secur$ ! great] numb] ( plates1 & %[$ ! great] numb] ( />s4 ,! results obta9$ ) x !re=e appe> to h be5 ! m reliable4 ,!y diff] f ,e9/e9's pr$iction by #ac p] c5t4 ,9 future exp$itions to te/ ?is "q1 ! mirror 9 front ( ! telescope w be elim9at$4 ,we n[ come to ! f9al te/ :i* has be5 appli$ to ,e9/e9's !ory4 ,e9/e9 %[$ t 9 ! int5se gravitational field ( ! sun1 ! !ory ( relativity requir$ t all ( ! spectrum l9es %\ld be %ift$ slightly t[>d ! r$ end4 ,! %ift h[ev] is exce$+ly small1 & c only be detect$ & measur$ ) ! mo/ p[]ful mod]n in/rum5ts4 ,moreov] only c]ta9 l9es c be us$1 because ow+ to v>y+ pressure 9 ! sol> atmosph]e1 :i* affects _m l9es1 z well z to rapid motion 9 ! l9e ( sight1 :i* may affect all ( !m1 /ill l>g] displacem5ts are liable to occur4 ,accord+ to ! !ory ( relativity ! displacem5t ( ! l9es %\ld be #j4jjhj ,a4 ,/4 ,john at ,mt4 ,wilson f\nd a displacem5t = ! cyanog5 l9es ( only #j4jjah ,a4#af ,ev]%$ at ,kodaikanal f\nd #j4jjfj at ! nor? pole ( ! sun1 & #j4jjhj at ! s\? pole4 ,^! latt] values h[ev] 7 only = ! /rong] l9es4 ,! weak] l9es give mu* small] %ifts1 z d ^? ( calcium & magnesium4#ag ,accord+ to ,e9/e9 all l9es %\ld give ne>ly ! same %ift1 an am\nt proportional to ! wave l5g?4 ,x !re=e appe>s t we mu/ conclude by say+ t ,e9/e9's !ory ( relativity has be5 p>tially1 b n completely1 v]ifi$4 ,! ref]5ce numb]s 9 ! above text h no?+ to d ) ! numb]s us$ 9 o!r p>ts ( ?is volume to ackn[l$ge ! "w ( ! v>i\s conte/ants2 !y ref] to ,dr4 ,pick]+'s s\rces1 z foll[s3 #a ,j\rn4 ,brit4 ,a/ron4 ,assoc41 #aiai1 #cj1 #gf4 #b ,comptes ,r5dus1 #afe1 #dbd1 & #afg1 #ga4 #c ,mon?ly ,notices ,r4 ,a4 ,s41 #aiai1 #hj1 #ajd4 #d ,mon?ly ,notices ,r4 ,a4 ,s41 #aiag1 #gg1 #cgi4 #e ,a/ro-,physical ,j\rnal1 #aiag1 #df1 #bdi4 ,j\rn4 ,brit4 ,a/ron4 ,assoc41 #aibj1 #cj1 #bgf4 #f ,mon?ly ,notices1 ,r4 ,a4 ,s41 #aiag1 #gg1 #cgg4 #g ,am]4 ,j\rn4 ,sci41 #cd1 #ccc4 #h ,mon?ly ,notices1 ,r4 ,a4 ,s41 #aibj1 #hj1 #fbh4 #i ,! ,obs]vatory #aibj1 ,april4 ,f an ,ox=d ,note ,book4 #aj ,mon?ly ,notices1 ,r4 ,a4 ,s41 #aiag4 #gh1 #c ,de ,sitt]1 #aiai1 #hj1 #aba1 ,jeans1 #hj1 #adf ,jeffreys4 #aa ,gravitation & ! ,pr9ciple ( ,relativity1 ,edd+ton4 ,royal ,in/itution ( ,great ,brita91 #aiah4 #ab ,j\rn4 ,brit4 ,a/ron4 ,assoc41 #aibj1 #cj1 #abe4 #ac ,! ,int]ior ( a ,/>1 ,edd+ton4 ,sci5tia1 #aiah1 #bc1 #ae4 #ad ,mon?ly ,notices1 ,r4 ,a4 ,s41 #aiai1 #hj1 #ach4 #ae ,mon?ly ,notices4 ,r4 ,a4 ,s41 #aibj1 #hj1 #dae4 ,j\rn4 ,brit4 ,a/ron4 ,assoc41 #aiai1 #cj1 #df4 #af ,a/ro-,physical ,j\rn41 #aiag1 #df1 #bdi4 #ag ,j\rn4 ,brit4 ,a/ron4 ,assoc41 #aibj1 #cj1 #bgf4 ,,xviii ,,! ,,practical ,,significance ,,( ,,relativity ,! ,be/ ,discussion ( ! ,special ,!ory ,among ,all ! ,compet+ ,essays ,,by ,,pr(essor ,,h5ry ,,norris ,,russell1 ,,pr9ceton ,,univ]sity ,c a small *ild cat* a baseball mov+ sixty miles an h\r )\t gett+ hurt8 ,we %\ld probably answ] ,no--b suppose t ! boy & 8 fa!r 7 sitt+ side by side 9 an express tra91 & ! ball 0 toss$ lightly f "o to ! o!r4 ,!n !re w\ld be no tr\ble ab\t x1 :e!r ! tra9 0 /&+ /ill1 or go+ at full spe$4 ,only ! relative motion ( ball & boy w\ld c\nt4 ,?is e-day exp]i5ce is a good illu/ration ( ! mu* discuss$ ,pr9ciple ( ,relativity1 9 its simple/ =m4 ,if !re 7 no jolt+1 ! motion ( ! tra91 /raight ahead at a uni=m spe$1 w\ld h no effect at all ^u ! relative motions ( objects inside x1 nor on ! =ces requir$ to produce or *ange ^! motions4 ,inde$1 ! motion ( ! e>? 9 its orbit1 :i* is free f all j>1 b a ?\s& times fa/]1 does n influ5ce ev5 ! mo/ delicate app>atus4 ,we are q unconsci\s ( x1 & w\ld n "k t ! e>? 0 mov+1 if we c\ld n see o!r bodies outside x4 ,?is sort ( relativity has be5 recogniz$ = m ?an two c5turies & lies at ! bottom ( all our ord9>y dynamical reason+1 ^u :i* bo? sci5ce & eng9e]+ are bas$4 ,b !re are o!r ?+s 9 nature besides mov+ bodies1--above all1 light1 :i* is intimately relat$ to electricity & magnetism1 & c travel ?r\gh empty space1 betwe5 ! />s4 ,x moves at ! enorm\s spe$ ( #ahf1jjj miles p] second1 & behaves exactly l a s]ies ( vibrations or waves4 ,we naturally ?9k ( x z travell+ ?r\gh "s m$ium1 & call ?is ?+1 :i* c>ries ! light1 ! e!r4 ,c we tell :e!r we are mov+ ?r\gh ?is e!r1 ev5 ?\gh all p>ts ( our app>atus move toge!r1 & at ! same rate8 ,suppose t we h two mirrors1 ,m & ,n1 at equal di/ances1 d1 f a po9t ,o1 b 9 directions at "r angles to "o ano!r1 & s5d out a fla% ( light f ,o4 ,if ev]y?+ is at re/1 ! reflect$ fla%es w evid5tly come back to ,o at ! same in/ant1 & ! elaps$ "t w be #b;d_/c seconds if c is ! velocity ( light4 ,b suppose t ,o1 ,m1 & ,n are fa/5$ to a rigid frame "w1 & all mov+ 9 ! direction ,o ,m1 ) velocity ,v4 ,! light :i* goes f ,o t[>d ,m1 at ! spe$ c1 w ov]take x ) ! diff]5ce ( _! spe$s1 c-v1 tak+ d_/7c-v7 seconds to rea* ,m4 ,on ! way back1 ,o w be advanc+ to meet x1 & ! return trip w occupy d_/7cv7 seconds4 ,! elaps$ "t = ! r\nd trip comes out #b;cd_/7c#b-v#b7 seconds1 :i* is long] ?an :5 ! sy/em 0 at re/--! loss ( "t 9 ! /]n *ase exce$+ ! sav+ on ! return4 ,! light :i* is reflect$ f ,n has a diff]5t hi/ory4 ,:5 x />ts1 ,o & ,n h c]ta9 positions 9 ! e!r1 ,o#a & ,n#a4 ,by ! "t x rea*es ! mirror1 ?is is at ,n#b1 & ,o is at ,o#b1 & :5 x returns1 x f9ds ,o at ,o#c4 ,! di/ances = ! outw>d & inw>d j\rneys are n[ equal1 b 7z is obvi\s f ! figure71 ea* ( !m is great] ?an d1 or ,o#b,n#b1 & ! "t = ! r\nd trip w be correspond+ly increas$4 ,a simple calculation %[s t x is #b;d_/sqrtc#b-v#b4 ,! increase above ! "t requir$ :5 ! sy/em 0 at re/ is less 9 ?is case ?an ! prec$+4 ,h5ce1 if ! app>atus is mov+ ?r\gh ! e!r1 ! fla%es reflect$ f ,m & ,n w n return at ! same in/ant4 ,= su* velocities z are atta9able--ev5 ! #ah miles p] second ( ! e>? 9 its orbit--! diff]5ce is less ?an a hundr$-million? ( ! elaps$ "t4 ,nev]!less1 ,mi*elson & ,morley tri$ to detect x 9 _! fam\s exp]im5t4 ,a beam ( light 0 all[$ to fall obliquely ^u a cle> glass mirror 7plac$ at ,o 9 ! diagram7 :i* reflect$ "p ( x t[>d ! mirror1 ,m1 & let ! re/ pass ?r\gh to ! mirror ,n4 ,by reunit+ ! beams aft] _! r\nd trips1 x 0 possible to tell :e!r "o _h ga9$ ^u ! o!r by ev5 a small fraction ( ! "t ( vibration ( a s+le light wave4 ,! app>atus 0 s s5sitive t ! pr$ict$ diff]5ce1 ?\gh am\nt+ to less ?an a million? "p ( a billion? ( a second1 c\ld easily h be5 measur$2 b !y actually f\nd no diff]5ce at all--?\gh ! e>? is c]ta9ly 9 motion4 ,o!r optical exp]im5ts1 m intricate1 & ev5 m delicate1 7 attempt$1 ) ! same object ( detect+ ! motion ( ! e>? ?r\gh ! e!r2 & !y all fail$4 ,,! ,,special ,,!ory ,,& ,,its ,,surpris+ ,,consequ5ces ,x 0 ^u ^! facts t ,e9/e9 bas$ 8 orig9al1 or special !ory ( ,relativity4 ,he assum$ boldly t ! univ]se is s con/itut$ t uni=m /raight-ahead motion ( an obs]v] & all 8 app>atus w n produce any diff]5ce :atev] 9 ! result ( any physical process or exp]im5t ( any k9d4 ,grant+ ?is1 x foll[s t if all objects 9 ! visible univ]se 7 mov+ uni=mly toge!r 9 any direction1 no matt] h[ fa/1 we c\ld n f9d ?is out at all4 ,we _c det]m9e :e!r ! univ]se1 z a :ole1 is at re/ or 9 motion1 & may z well make "o guess z ano!r4 ,only ! relative motions ( its p>ts c be detect$ or /udi$4 ,?is seems simple & easy en\gh to und]/&4 ,b ! consequ5ces :i* foll[ f x are extraord9>y1 & at fir/ acqua9tance seem almo/ absurd4 ,9 ! fir/ place1 if an obs]v] measures ! velocity ( light1 he mu/ always get ! same result1 no matt] h[ fa/ he & 8 app>atus are mov+1 or 9 :at direction 7s long z ! motion is uni=m & rectil9e>74 ,?is s\nds h>mless2 b let u g back to ! ,mi*elson-,morley exp]im5t :]e ! light came back 9 exactly ! same "t f ! two mirrors4 ,if ! obs]v] supposes himself to be at re/1 he w say t ! di/ances ,o ,m & ,o ,n 7 equal4 ,b if he fancies t ! :ole univ]se is mov+ 9 ! direction ,o ,m1 he w conclude t ,m is ne>] to ,o ?an ,n is--= if !y 7 equidi/ant1 ! r\nd-trip w\ld take long] 9 ! fir/ case1 z we h prov$4 ,if once m he fancies t ! univ]se is mov+ 9 ! direction ,o ,n1 he w conclude t ,n is ne>] to ,o ?an ,m is4 ,8 answ] to ! "q :i* ( ! two di/ances1 ,o ,m or ,o ,n1 is ! great] w !re=e dep5d on 8 assumption ab\t ! motion ( ! univ]se z a :ole4 ,simil> complications arise 9 ! measurem5t ( "t4 ,suppose t we h two obs]v]s1 ,a & ,b1 provid$ ) clocks :i* run ) p]fect uni=mity1 & mirrors to reflect light signals to "o ano!r4 ,at noon exactly by 8 clock1 ,a s5ds a fla% ( light t[>ds ,b4 ,b sees x come 9 at #ab3ja by 8 clock4 ,! fla% reflect$ f ,b's mirror rea*es ,a at #ab3jb by ,a's clock4 ,!y communicate ^! obs]vations to "o ano!r4 ,if ,a & ,b reg>d !mselves z be+ at re/1 !y w agree t ! light took z long to g out z x did to come back1 & !re=e t x rea*$ ,b at j #ab3ja by ,a's clock1 & t ! two clocks are syn*roniz$4 ,b !y may1 if !y please1 suppose t !y 7& ! :ole univ]se7 are mov+ 9 ! direction f ,a t[>ds ,b1 ) half ! spe$ ( light4 ,!y w !n say t ! light _h a /]n *ase to rea* ,b1 & took ?ree times z long to g out z to come back4 ,?is means t x got to ,b at #a #a_/b m9utes pa/ noon by ,a's clock1 & t ,b's clock is sl[ comp>$ ) ,a's4 ,if !y %\ld assume t !y 7 mov+ ) ! same spe$ 9 ! opposite direction1 !y w\ld conclude t ,b's clock is half a m9ute fa/4 ,h5ce _! answ] to ! "q :e!r two ev5ts at diff]5t places happ5 at ! same "t1 or at diff]5t times1 w dep5d on _! assumption ab\t ! motion ( ! univ]se z a :ole4 ,once m1 let u suppose t ,a & ,b1 ) _! clocks & mirrors1 are 9 relative motion1 ) half ! spe$ ( light1 & pass "o ano!r at noon by bo? clocks4 ,at #ab3jb by ,a's clock1 he s5ds a fla% ( light1 :i* rea*es ,b at #ab3jd by 8 clock1 is reflect$1 & gets back to ,a's clock at #ab3jf4 ,!y signal ^! results to ea* o!r1 & sit d[n to "w !m out4 ,a ?9ks t he is at re/1 & ,b mov+4 ,he !re=e concludes t ! light _h ! same di/ance to g out z to return to him & took two seconds ea* way1 rea*+ ,b at #ab3jd by ,a's clock1 & t ! two clocks1 :i* agre$ !n1 z well z at noon1 are runn+ at ! same rate4 ,b1 on ! contr>y1 ?9ks t he is at re/ & ,a 9 motion4 ,he !n concludes t ,a 0 mu* ne>] :5 he s5t out ! fla% ?an :5 he got x back1 & t ! light _h ?ree times z f> to travel on ! return j\rney4 ,?is means t x 0 #ab3jc by ,a's clock at ! in/ant :5 ! light rea*$ ,b & ,b's clock read #ab3jd4 ,h5ce ,a's clock is runn+ sl[1 comp>$ ) ,b's4 ,h5ce ! answ] to ! "q :e!r two int]vals ( "t1 measur$ by obs]v]s :o are 9 motion relative to "o ano!r1 are ( ! same or ( diff]5t durations1 dep5ds ^u _! assumptions ab\t ! motion ( ! univ]se z a :ole4 ,n[ we mu/ rememb] t "o assumption ab\t ! motion ( ! univ]se z a :ole is exactly z good--or bad--z ano!r4 ,no possible exp]im5t c di/+ui% betwe5 !m4 ,h5ce on ! ,pr9ciple ( ,relativity1 we h left no absolute measurem5t ( "t or space4 ,:e!r two di/ances 9 diff]5t directions are to be call$ equal or n--:e!r two ev5ts 9 diff]5t places are to be call$ simultane\s or n--dep5ds on our arbitr>y *oice ( su* an assumption1 or frame ( ref]5ce4 ,all ! v>i\s s*emes ( measurem5t correspond+ to ^! assumptions w1 :5 appli$ to any imag9able exp]im5t1 pr$ict exactly ! same ph5om5a4 ,b1 9 c]ta9 important cases1 ^! pr$ictions diff] f ^? ( ! old famili> !ory1 &1 e "t t su* exp]im5ts h be5 tri$1 ! result has agre$ ) ! new !ory1 & n ) ! old4 ,we are !re=e driv5 to accept ! !ory ( relativity1 /range z x is1 z be+ m ne>ly true to nature ?an our old] ideas4 ,=tunately1 ! diff]5ce betwe5 ! results ( ! two become important only :5 we assume t ! :ole visible univ]se is mov+ toge!r mu* fa/] ?an any ( its p>ts are mov+ relatively to "o ano!r4 ,unless we make su* an unw>rant$ assumption1 ! diff]5ces are s small t x takes ! mo/ +5i\s & precise exp]im5ts to reveal !m4 ,,! ,,g5]alization ,n cont5t ) all ?is1 ,e9/e9 proce$$1 a few ye>s ago1 to develop a g5]al !ory ( relativity1 :i* includes ! effects ( gravitation4 ,to make ?is idea cle>1 let u imag9e two obs]v]s1 ea*1 ) 8 measur+ in/rum5ts1 9 a l>ge & p]fectly imp]vi\s box1 :i* =ms 8 clos$ sy/em4 ,! fir/ obs]v]1 ) 8 box & its cont5ts1 alone 9 space1 is entirely at re/4 ,! second obs]v]1 ) 8 box & its cont5ts1 is1 x may be imag9$1 ne> ! e>? or ! sun or "s />1 & fall+ freely "u ! influ5ce ( its gravitation4 ,?is second box & its cont5ts1 includ+ ! obs]v]1 w !n fall "u ! gravitational =ce1 t is1 get up an ev]-increas+ spe$1 b at exactly ! same rate1 s t !re w be no t5d5cy = _! relative positions to be alt]$4 ,accord+ to ,newton's pr9ciples1 ?is w make n ! slighte/ diff]5ce 9 ! motions ( ! physical objects compris+ ! sy/em or _! attractions on "o ano!r1 s t no dynamical exp]im5t c di/+ui% betwe5 ! condition ( ! freely fall+ obs]v] 9 ! second box & ! obs]v] at re/ 9 ! fir/4 ,b once m ! "q arises3 ,:at c\ld be done by an optical exp]im5t8 ,e9/e9 assum$ t ! pr9ciple ( relativity /ill appli$ 9 ?is case1 s t x w\ld be impossible to di/+ui% betwe5 ! conditions ( ! obs]v]s 9 ! two boxes by any optical exp]im5t4 ,x c easily be se5 t x foll[s f ?is new g5]aliz$ relativity t light _c travel 9 a /raight l9e 9 a gravitational field4 ,imag9e t ! fir/ obs]v] sets up ?ree slits1 all 9 a /raight l9e4 ,a ray ( light :i* passes ?r\gh ! fir/ & second w obvi\sly pass exactly ?r\gh ! ?ird4 ,suppose ! obs]v] 9 ! freely fall+ sy/em attempts ! same exp]im5t1 hav+ 8 slits ,p1 ,q1 ,r1 equally spac$1 & plac+ !m at "r angles to ! direction 9 :i* he is fall+4 ,:5 ! light passes ?r\gh ,p1 ! slits w be 9 c]ta9 position ,p#a ,q#a ,r#a 7,figure74 ,by ! "t x rea*es ,q1 !y w h fall5 to a l[] level1 ,p#b ,q#b ,r#b1 & :5 x rea*es ,r1 !y w be /ill l[]1 ,p#c ,q#c ,r#c4 ,! times :i* ! light takes to move f ,p to ,q & ,q to ,r w be ! same3 b1 s9ce ! sy/em is fall+ ev] fa/] & fa/] ! di/ance ,r#b ,r#c w be great] ?an ,q#a ,q#b4 ,h5ce1 if ! light :i* has pass$ ?r\gh ,p & ,q moves 9 a /raight l9e1 x w /rike above ,r1 z is illu/rat$ by ! /raight l9e 9 ! figure4 ,b1 on ,e9/e9's assumption1 ! light mu/ g ?r\gh ! ?ird slit1 z x w\ld d 9 ! sy/em at re/1 & mu/ !re=e move 9 a curv$ l9e1 l ! curv$ l9e 9 ! figure1 & b5d d[nw>d 9 ! direction ( ! gravitational =ce4 ,,! ,,te/s ,calculation %[s t ! deviation ( light by ! moon or planets w\ld be too small to detect4 ,b = a ray :i* _h pass$ ne> ! sun1 ! deflection comes out #a4g''1 :i* ! mod]n a/ronom] reg>ds z a l>ge quantity1 easy to measure4 ,obs]vations to te/ ?is c be made only at a total eclipse1 :5 we c photograph />s ne> ! sun1 on a ne>ly d>k sky4 ,a v f9e *ance came 9 ,may1 #aiai1 & two ,engli% exp$itions 7 s5t to ,brazil & ! ,african coa/4 ,^! photographs 7 measur$ ) extreme c>e1 & !y %[ t ! />s actually appe> to be %ift$1 9 almo/ exactly ! way pr$ict$ by ,e9/e9's !ory4 ,ano!r consequ5ce ( g5]al relativity is t ,newton's law ( gravitation ne$s a m9ute correction4 ,?is is s small t !re is b a s+le case 9 :i* x c be te/$4 ,on ,newton's !ory1 ! l9e jo9+ ! sun to ! ne>e/ po9t ^u a planet's orbit 7its p]ihelion7 %\ld rema9 fix$ 9 direction1 7b>r+ c]ta9 effects ( ! attraction ( ! o!r planets1 :i* c be all[$ =74 ,on ,e9/e9's !ory x %\ld move sl[ly =w>d4 ,x has be5 kn[n = ye>s t ! p]ihelion ( ,m]cury 0 actually mov+ =w>d1 & all explanations _h fail$4 ,b ,e9/e9's !ory n only pr$icts ! direction ( ! motion1 b exactly ! obs]v$ am\nt4 ,e9/e9 also pr$icts t ! l9es ( any elem5t 9 ! sol> spectrum %\ld be slightly %ift$ t[>ds ! r$1 z comp>$ ) ^? produc$ 9 our laboratories4 ,diff]5t obs]v]s h inve/igat$ ?is1 & s f> !y disagree4 ,! tr\ble is t !re are sev]al o!r influ5ces :i* may %ift ! l9es1 su* z pressure 9 ! sun's atmosph]e1 motion ( curr5ts on ! sun's surface1 etc41 & x is v h>d to dis5tangle ?is ,gordian knot4 ,at pres5t1 ! results ( ^! obs]vations c nei!r be c\nt$ = or aga9/ ! !ory1 :ile ^? 9 ! o!r two cases are decisively favorable4 ,! ma!matical expression ( ?is g5]al relativity is intricate & difficult4 ,ma!maticians--:o are us$ to conceptions :i* are unfamili>1 if n incompreh5sible1 to mo/ ( u--f9d t ^! expressions may be describ$ 7to ! tra9$ /ud5t7 9 t]ms ( space ( f\r dim5sions & ( ! non-,euclidean geometry4 ,we !re=e he> su* phrases z "t z a sort ( f\r? dim5sion1 curvature ( space & o!rs4 ,b ^! are simply attempts--n altoge!r successful--to put ma!matical relation%ips into ord9>y language1 in/ead ( algebraic equations4 ,m important to ! g5]al read] are ! physical be>+s ( ! new !ory1 & ^! are f> easi] to und]/&4 ,v>i\s assumptions :i* we may make ab\t ! motion ( ! univ]se z a :ole1 ?\gh !y d n influ5ce ! obs]v$ facts ( nature1 w lead u to diff]5t ways ( int]pret+ our obs]vations z measurem5ts ( space & "t4 ,!oretically1 "o ( ^! assumptions is z good z any o!r4 ,h5ce we no long] believe 9 absolute space & "t4 ,?is is ( great int]e/ philosophically4 ,practically1 x is unimportant1 =1 unless our *oice ( an assumption is v wild1 our conclusions & measurem5ts w agree sub/antially ) ^? :i* are already famili>4 ,f9ally1 ! g5]al relativity %[s t gravitation & electro-magnetic ph5om5a--7includ+ light7 d n =m two indep5d5t sides ( nature1 z we once suppos$1 b influ5ce "o ano!r 7?\gh slightly7 & are p>ts ( "o great] :ole4 ,,xix ,,e9/e9',s ,,!ory ,,( ,,relativity ,a ,simple ,explanation ( ,8 ,po/ulates & ,_! ,consequ5ces ,,by ,t4 ,,royds1 ,,kodaikanal ,,obs]vatory1 ,,india ,e9/e9's !ory ( relativity seeks to repres5t to u ! _w z x really is in/ead ( ! _w ( appe>ances :i* may be deceiv+ u4 ,:5 ,i 0 9 t[n la/ week to buy #e y>ds ( calico ,i wat*$ ! drap] v c>efully z he measur$ ! clo? to make sure ,i 0 n *eat$4 ,yet exp]im5t c demon/rate1 & ,e9/e9's !ory c expla91 t ! drap]'s y>d/ick became long] or %ort] accord+ to ! direction 9 :i* x 0 held4 ,! l5g? ( ! y>d/ick did n appe> to me to *ange simply because ev]y?+ else 9 ! same direction1 ! /ore1 ! drap]1 ! clo?1 ! ret9a ( my eye1 *ang$ l5g? 9 ! same ratio4 ,e9/e9's !ory po9ts out n only ?is1 b e case :]e appe>ances are deceptive1 & tries to %[ u ! _w ( reality4 ,e9/e9's !ory is bas$ on ! pr9ciple ( relativity & be=e we try to foll[ 8 reason+ we mu/ sp5d a little "t 9 und]/&+ :at he means by relativity & 9 grasp+ h[ ! idea arises4 ,suppose ,i wi% to def9e my motion z ,i travel along 9 an automobile4 ,i may be mov+ at ! rate ( #be miles an h\r relative to objects fix$ on ! roadside1 b relative to a fell[-pass5g] ,i am n mov+ at all2 relative to ! sun ,i am mov+ ) a spe$ ( #ah #a_/b miles p] second 9 an elliptical orbit1 & aga9 relative to ! />s ,i am mov+ 9 ! direction ( ! /> ,vega at a spe$ ( #ab miles p] second4 ,?us motion c only be def9$ relative to "s object or po9t ( ref]5ce4 ,n[ ?is is n satisfactory to ! exact sci5ti/4 ,sci5ti/s are n cont5t ) kn[+1 = example1 t ! temp]ature ( boil+ wat] is #ajj ,c4 relative to ! temp]ature ( freez+2 !y h set out to det]m9e absolute temp]atures & h f\nd t wat] boils at #cgc ,c4 above absolute z]o4 ,:y %\ld ,i n1 !re=e1 det]m9e ! absolute motion ( ! automobile1 n its motion relative to ! road1 e>?1 sun or />s1 b relative to absolute re/8 ,mi*elson & ,morley set out 9 _! fam\s exp]im5t to measure ! absolute velocity ( _! laboratory1 :i* 01 ( c\rse1 fix$ on ! e>?4 ,! exp]im5t consi/$ ( tim+ two rays ( light ov] two equal tracks at "r angles to ea* o!r4 ,:5 "o track 0 situat$ 9 ! direction ( ! e>?'s motion !y expect$ to get ! same result z :5 two scull]s ( equal pr[ess are rac+ 9 a riv]1 "o up & d[n ! /ream & ! o!r across & back2 ! w9n] w be ! scull] r[+ across ! /ream1 z work+ out an example w conv9ce4 ,ev5 if ! e>? _h be5 /ation>y at ! "t ( "o exp]im5t1 ! e>?'s motion r\nd ! sun w\ld h be5 rev]s$ #f mon?s lat] & w\ld !n h giv5 d\ble ! effect4 ,!y f\nd1 h[ev]1 t ! two rays ( light arriv$ always an exact dead heat4 ,all exp]im5t]s :o h tri$ s9ce h arriv$ at ! same result & f\nd x impossible to detect absolute motion4 ,! pr9ciple ( relativity has its f\ndation 9 fact on ^! failures to detect absolute motion4 ,?is pr9ciple /ates t ! only motion we c ev] "k ab\t is relative motion4 ,if we devise an exp]im5t :i* ought to reveal absolute motion1 nature w ent] into a conspiracy to defeat u4 ,9 ! ,mi*elson & ,morley exp]im5t ! conspiracy 0 t ! track 9 ! direction ( ! e>?'s absolute motion %\ld contract its l5g? by j s mu* z w\ld all[ ! ray ( light along x to arrive up to "t4 ,we see1 !re=e1 t accord+ to ! pr9ciple ( relativity motion mu/ always rema9 a relative t]m1 9 mu* ! same way z v]tical & horizontal1 "r & left1 are relative t]ms hav+ only mean+ :5 ref]r$ to "s obs]v]4 ,we d n expect to f9d an absolute v]tical & are wise en\gh n to attempt x2 9 seek+ to f9d absolute motion physici/s 7 n s wise & only f\nd !mselves baffl$4 ,! pr9ciple t all motion is relative n[ requires to be work$ out to all its consequ5ces1 z has be5 done by ,e9/e91 & we h 8 !ory ( relativity4 ,e9/e9 conceives a _w ( f\r dim5sions built up ( ! ?ree dim5sions ( space1 namely up & d[n1 backw>ds & =w>ds1 "r & left1 ) "t z ! f\r? dim5sion4 ,?is is an unusual conception to mo/ ( u1 s let u simplify x into some?+ :i* we c m easily picture b :i* w /ill all[ u to grasp ,e9/e9's ideas4 ,let u conf9e ourselves = ! pres5t to ev5ts :i* happ5 on ?is %eet ( pap]1 i4e41 to space ( two dim5sions only & take "t z our ?ird dim5sion at "r angles to ! plane ( ! pap]4 ,we h ?us built up a ?ree dim5sional _w ( space-"t :i* is e bit z useful to u z a f\r dim5sional repres5tation s long z we only ne$ /udy objects mov+ ov] ! %eet ( pap]4 ,suppose a fly is crawl+ ov] ?is %eet ( pap] & let u make a movie record ( x4 ,if we cut up ! /rip ( movie film into ! individual pictures & cem5t !m toge!r "o above ano!r 9 _! prop] ord]1 we %all build up a solid block ( film :i* w be a model ( our simplifi$ _w ( space-"t & 9 :i* !re w be a s]ies ( dots repres5t+ ! motion ( ! fly ov] ! pap]4 ,j z ,i c /ate ! exact position ( an object 9 my room by def9+ its height above ! floor1 its di/ance f ! nor? wall & its di/ance f ! ea/ wall1 s we c r$uce ! positions ( ! dots to figures = use 9 calculations by measur+ _! di/ances f ! ?ree faces int]sect+ 9 ! l9es ,,ox1 ,,oy1 & ,,ot1 :]e ,,oxaytbcd repres5ts ! block ( film4 ,! ma!matician w\ld call ! ?ree l9es ,,ox1 ,,oy1 ,,ot ! coord9ate axes4 ,measur+ all ! dots 9 ?is way we %all obta9 ! motion ( ! fly relative to ! coord9ate axes ,,ox1 ,,oy1 ,,ot4 ,if we add a block ,,otdyefgh ( pla9 film we c use ,,ex1 ,,eh1 ,,ef z coord9ate axes & aga9 obta9 ! motion ( ! fly relative to ^! new axes2 or we c add block aft] block s z to keep ! axes mov+4 ,we c conceive ( o!r *anges ( axes4 ,! op]ator mak+ ! movie record might h tak5 ! fly = ! h]o ( ! piece & mov$ ! cam]a ab\t s z to keep ! fly m or less c5tral 9 ! picture2 or he might1 by turn+ ! h&le fir/ fa/ & !n sl[ & by mov+ ! cam]a1 h made ! fly appe> to be do+ /unts4 ,mov+ ! cam]a w\ld *ange ! axes ( x & y1 & turn+ ! h&le at diff]5t spe$s w\ld *ange ! axis ( "t4 ,aga91 we might *ange ! axes by pu%+ ! block out ( %ape or by di/ort+ x into a /ate ( /ra94 ,:atev] *ange ( axes we make1 any dot 9 ! block ( film w signify a co9cid5ce ( ! fly ) a c]ta9 po9t ( ! pap] at a c]ta9 "t1 & ! s]ies ( dots w1 9 e case1 be a repres5tation ( ! motion ( ! fly4 ,maybe ! repres5tation w be a di/ort$ "o1 b :o is to say :i* is ! absolutely undi/ort$ repres5tation8 ,! pr9ciple ( relativity :i* we laid d[n be=e says t no "o set ( coord9ates w give ! absolute motion ( ! fly1 s t "o set is z good z ano!r4 ,! pr9ciple t all motion is relative means1 !re=e1 t no matt] h[ we *ange our coord9ates ( space-"t1 ! laws ( motion :i* we d$uce mu/ be ! same = all *anges4 ,to use an analogy1 ! sculptur$ head ( ,%akespe>e on my table may appe> to h holl[ *eeks :5 ,i admit light f ! ea/ w9d[ only1 or to h sunk5 eyes ) light f ! skylight 9 ! ro(1 b ! true %ape ( ! head rema9s ! same 9 all lights4 ,h5ce1 if ) ref]5ce to two consecutive dots 9 our block ( film a ma!matical quantity c be f\nd :i* w n *ange no matt] h[ we *anges our axes ( coord9ates1 t quantity mu/ be an expression ( ! true law ( motion ( ! fly betwe5 ! two po9ts ( ! pap] & ! two times repres5t$ by ^! two dots4 ,e9/e9 has work$ out su* a quantity rema9+ con/ant = all *anges ( coord9ates ( ! f\r dim5sional _w ( space-"t4 ,9 pass+ we may notice a feature ( ,e9/e9's _w ( space-"t :i* we %all d\btless f9d x difficult to conceive1 namely1 t !re is no ess5tial diff]5ce betwe5 a "t & a di/ance 9 space4 ,s9ce "o set ( coord9ates is z good z ano!r1 we c trans=m "t into space & space into "t accord+ z we *oose our axes4 ,= example if we *ange ,,ox1 ,,ot1 ! axes ( x & "t 9 ,fig4 #b1 into ,,ox'1 ,,ot' by a simple rotation1 ! new "t repres5t$ by ,,ot' consi/s p>tly ( ,,oa 9 ! old "t & p>tly ( ,,ob 9 ! old x direction4 ,ref]r+ to our block ( movie film aga91 x means t al?\gh ,i might sep>ate ! block into space & "t by slic+ x into ! orig9al pictures1 ,i c j z readily slice x 9 any direction ,i *oose & /ill get individual pictures repres5t+ ! motion ( ! fly b )1 ( c\rse1 new "t & space4 ,s :il/ ,i may be believe t a l9] has travell$ #c1jjj miles 9 #d days1 an obs]v] on a /> :o kn[s no?+ ( my p>ticul> axes 9 space-"t may say1 ) equal tru?1 t x w5t #b1jjj miles 9 #g days4 ,?us1 "t & space are n two sep>ate id5tities 9 ,e9/e9's view2 !re only exi/s a _w ( f\r dim5sions :i* we c split up into "t & space z we *oose4 ,let u see n[ h[ ,e9/e9 expla9s gravitation4 ,:5 a body is n act$ on by any =ces 7except gravitation7 ! quantity :i* rema9s con/ant = all *anges ( coord9ates implies t ! body w foll[ t pa? 9 ! space ( an outside obs]v] :i* takes ! lea/ "t4 ,x is an obs]v$ fact t "o body attracts ano!r by gravitation2 t is1 ! pa? ( "o body is b5t f its c\rse by ! pres5ce ( ano!r4 ,n[ we c b5d ! pa? ( ! fly 9 our block ( film by /ra9+ ! block 9 "s way4 ,suppose1 !re=e1 t ,i /ra9 ! _w s z to b5d ! pa? ( a body exactly z ! gravitation due to "s o!r body b5ds x2 i4e41 by a *ange ( coord9ates ,i h obta9$ ! same effect z t produc$ by gravitation4 ,e9/e9's !ory1 !re=e1 expla9s gravitation z a di/ortion ( ! _w ( space-"t due to ! pres5ce ( matt]4 ,suppose fir/ t a body is mov+ ) no o!r bodies ne>2 accord+ to ,e9/e9 x w take ! pa? 9 space :i* requires ! lea/ "t1 i4e41 a /raight l9e z agrees ) our exp]i5ce4 ,if n[ ! _w be /ra9$ by ! pres5ce ( ano!r body or by a *ange ( coord9ates x w /ill pursue ! pa? ( lea/ "t1 b ?is pa? is n[ di/ort$ f ! /raight l9e1 j z 9 a simil> way ! pa? on a globe requir+ ! lea/ "t to travel foll[s a great circle4 ,s1 on ,e9/e9's view ( gravitation1 ! e>? moves 9 an elliptical pa? ar\nd ! sun n because a =ce is act+ on x1 b because ! _w ( space-"t is s di/ort$ by ! pres5ce ( ! sun t ! pa? ( lea/ "t ?r\gh space is ! elliptical pa? obs]v$4 ,!re is1 !re=e1 no ne$ to introduce any idea ( =ce ( gravitation4 ,e9/e9's !ory expla9s gravitation only 9 ! s5se t he has expla9$ x away z a =ce ( nature & makes x a prop]ty ( space-"t1 namely1 a di/ortion n diff]5t f an appropriate *ange ( coord9ates4 ,he does n1 h[ev]1 expla9 h[ or :y a body c di/ort space-"t4 ,x is notewor?y t :il/ ! law ( gravitation & ! law ( uni=m motion 9 a /raight l9e :5 no =ce is act+ 7 sep>ate & indep5d5t laws "u ,newton1 ,e9/e9 f9ds "o explanation = bo? "u ! pr9ciple ( relativity4 #ab ,,xx ,,e9/e9',s ,,!ory ,,( ,,gravitation ,! ,discussion ( ! ,g5]al ,!ory & ,its ,mo/ ,important ,application1 f ! ,essay by ,,pr(4 ,w4 ,f4 ,g4 ,,swann1 ,,univ]sity ,,( ,,m9nesota1 ,,m9neapolis ,newton's great discov]y reg>d+ ! motion ( ! planets consi/$ 9 8 %[+ t ^! c\ld all be summ$ up 9 ! foll[+ /atem5t3 consid] any planet 9 its relation to all p>ticles 9 ! univ]se4 ,write d[n1 = ! planet1 9 ! l9e jo9+ x to any p>ticle1 an accel]ation proportional to ! mass ( ! p>ticle & to ! inv]se squ>e ( its di/ance f ! planet4 ,!n calculate ! planet's resultant accel]ation by comb9+ all ! accel]ations ?us obta9$4 ,we h "h purposely avoid$ ! use ( ! ^w =ce1 = ,newton's law is complete z a practical /atem5t ( fact )\t x2 & ?is ^w adds no?+ to ! law by way ( enhanc+ its p[] 9 actual use4 ,nev]!less1 ! fact t ! accel]ation is made up z x 7 ( non-int]f]+ contributions f ea* p>ticle 9 ! l9e jo9+ x to ! planet /rongly sugge/s to ! m9d some?+ ( ! nature ( an ela/ic pull = :i* ! p>ticle is responsible1 & to :i* ! planet's dep>ture f a /raight-l9e motion is due4 ,! m9d likes to ?9k ( ! ela/ic2 ev] s9ce ! "t ( ,newton p h s\ght to devise "s me*anism by :i* ^! pulls might be visualiz$ z responsible = ! ph5om5a 9 ! same way z "o pictures an ela/ic ?read z controll+ ! motion ( a /one :i* sw+s ar\nd at its end4 ,?is se>* has be5 always )\t success2 & n[ ,e9/e9 has f\nd a r diff]5t law :i* fits ! facts bett] ?an ,newton's law4 ,x is ( su* a type t x does n l5d itself conv5i5tly to expression 9 t]ms ( =ce2 ! m9d w\ld ga9 no?+ by try+ to picture su* =ces z are necess>y4 ,x comp5sates = ?is1 h[ev]1 9 be+ capable ( visualization 9 t]ms ( :at is ultimately a mu* simpl] concept4 ,9 ord] to appreciate ! fundam5tal ideas involv$1 suppose = a mom5t t gravitation c\ld be annihilat$1 completely1 & suppose ,i f9d myself ^u ?is e>? 9 empty space4 ,y %all be seat$ at "s po9t 9 space & %all wat* my do+s4 ,if ,i am 9 ! condition ( m9d ( ! p ( ! reign ( ,k+ ,h5ry ,,viii1 ,i %all believe t ! e>? does n rotate4 ,if ,i let g a /one1 !re be+ no gravity1 ,i %all f9d t x flies away f me ) an accel]ation4 ,y w "k1 h[ev]1 t ! /one really moves 9 a /raight l9e ) con/ant velocity1 & t ! app>5t accel]ation :i* ,i p]ceive is due to ! e>?'s rotation4 ,if ,i h argu$ t accel]ation is due to =ce1 ,i %all say t ! e>? repels ! /one1 & %all try to f9d ! law gov]n+ ! v>iation ( ?is =ce ) di/ance4 ,i may g f>!r1 & try to imag9e "s reason = ! =ce1 "s pu%+ action transmitt$ f ! e>? to ! /one ?r\gh a surr\nd+ m$ium2 &1 y w pity me = all ?is wa/$ labor1 & p>ticul>ly = my attempt to f9d a me*anism to acc\nt = ! =ce1 s9ce y "k t if ,i w\ld only accept y\r measurem5ts all w\ld appe> s simple4 ,let u probe ?is matt] a little f>!r1 h[ev]1 f ! /&-po9t ( myself4 ,i mu/ believe 9 ! reality ( ! =ce1 s9ce ,i h to be ti$ to my *air to prev5t my dep>ture f ! e>?4 ,i might wond] h[ ?is field ( =ce w\ld affect ! propagation ( light1 *emical action & s =?4 ,=1 ev5 ?\gh ,i _h discov]$ t1 by us+ y\r measures1 ,i c\ld trans=m away ! app>5t effects ( my field ( =ce z f> z conc]n$ its p[] to hurl /ones ab\t1 ,i c\ld /ill reg>d ?is z a ma!matical accid5t1 & believe t ! =ce 0 really !re4 ,al?\gh ,i might suspect t ! same trans=mation ( view-po9t t w\ld annul ! field's effect z reg>ds ! /ones w\ld also annul its effect z reg>ds light1 etc41 ,i %\ld n be sure ( ?is1 z y w\ld be2 & my consci5ce w\ld h>dly all[ me to d m ?an look ^u ! assumption ( complete equival5ce betwe5 ! app>5t field & a *ange 9 ! sy/em ( measurem5t z a hypo!sis4 ,i %\ld be /rongly tempt$ to make ! hypo!sis1 h[ev]4 ,n[ ! "q rais$ by ,e9/e9 is :e!r ! =ce ( gravity1 :i* we exp]i5ce z a v real ?+1 may be put ^u a foot+ :i* is 9 "s way analog\s to t ( ! obvi\sly fictiti\s c5trifugal =ce cit$ above3 :e!r gravitation may be reg>d$ z a figm5t ( our imag9ation eng5d]$ by ! way 9 :i* we measure ?+s4 ,he f\nd t x c\ld be s reg>d$4 ,he w5t /ill f>!r1 & 9 8 ,pr9ciple ( ,equival5ce1 he po/ulat$ t ! app>5t effects ( gravitation 9 all ph5om5a c\ld be attribut$ to ! same *ange 9 ! sy/em ( our measurem5ts t w\ld acc\nt = ! ord9>y ph5om5a ( gravitation4 ,on ! basis ( ?is hypo!sis he 0 able to d$uce = subsequ5t exp]im5tal v]ification1 ! effects ( gravitation on light4 ,he did n limit himself to su* simple *anges 9 our measurem5ts z 7 suffici5t to s]ve ! purpose ( ! problem ( c5trifugal =ce cit$ above2 b1 embold5$ by ! assumptions1 9 ! old] !ory ( relativity1 ( *ange 9 /&>ds ( l5g? & "t on acc\nt ( motion1 he w5t ev5 f>!r ?an ?is1 & consid]$ ! possibility ( *ange ( our measures due to m]e proximity to matt]4 ,8 problem am\nt$ to an attempt to f9d "s way 9 :i* x 0 possible to conceive our scales & clocks z alt]$1 relatively to "s m fundam5tal set1 s z to all[ ( ! planet>y motions be+ uni=m & rectil9e> ) respect to ^! fundam5tal measures1 al?\gh !y appe> z !y d to u4 ,if we all[ our imag9ations p]fect fre$om z to h[ ! scales may be alt]$1 we %all n balk at assum+ alt]ations v>y+ 9 any way we please1 ,e9/e9 does1 h[ev]1 introduce re/rictions = reasons :i* we w n[ disc]n4 ,if we imag9e our :ole univ]se1 ) its obs]v]s1 planet>y orbits1 in/rum5ts1 & ev]y?+ else1 emb$d$ 9 a jelly1 & !n di/ort ! jelly & cont5ts 9 any way1 ! numb]s at :i* our planet>y orbits 7or r _! telescopic images7 int]sect our scales w be unalt]$4 ,moreov]1 we c\ld v>y1 9 any mann]1 ! times at :i* all objects 7includ+ ! clock h&s7 occupi$ _! di/ort$ positions1 & ! h& ( "s clock ne> ! po9t :]e ! planet>y image cross$ ! scale w\ld record = ?is occurr5ce ! same dial read+ z be=e4 ,an inhabitant ( ?is di/ort$ univ]se w\ld be absolutely unconsci\s ( ! *ange4 ,n[ ! ,g5]al ,!ory ( ,relativity :i* expresses itself 9 slightly v>i$ =ms1 am\nts to satisfy+ a c]ta9 philosophical crav+ ( ! m9d1 by ass]t+ t ! laws ( nature :i* control our univ]se ought to be su* t ano!r univ]se l ! above1 ^: inhabitants w\ld be unconsci\s ( _! *ange1 w\ld also satisfy ^! laws1 n m]ely f ! /&po9t ( its own inhabitants1 b also f ! /&po9t ( our measurem5ts4 ,9 o!r words1 ?is second univ]se ought to appe> possible to u z well z to its inhabitants4 ,e9/e9 decides to make 8 !ory con=m to ?is philosophical desire1 & ?is greatly limits ! modifications ( clocks & scales :i* he p]mits himself = ! purpose ( repres5t+ gravitation4 ,fur!r1 if we express ! alt]ations ( ! measures z functions ( proximity to matt]1 velocity & s =?1 our expressions = ^! alt]ations w include1 z a p>ticul> case1 t :]e matt] is abs5t1 al?\gh ! scales & obs]v] may /ill rema94 ,our alt]ation ( ! scales & clocks ) velocity mu/ ?us rev]t1 = ?is case1 to t correspond+ to ! old] !ory ( relativity1 9 ord] to avoid pr$ict+ t two obs]v]s1 9 uni=m motion relative to ea* o!r 9 empty space1 w measure diff]5t values = ! velocity ( light4 ,9 ?is way1 ! velocity ( light comes to play a "p 9 express+ ! alt]ations ( ! measures4 ,ev5 ) ^! re/rictions1 ,e9/e9 0 able to d ! equival5t ( f9d+ an alt]ation ( scales & clocks 9 ! pres5ce ( matt] :i* w\ld acc\nt = our f9d+ t ! planet>y motions take place v ne>ly 9 accordance ) ,newton's law4 ,! new law has acc\nt$ ) surpris+ accuracy = c]ta9 a/ronomical irregul>ities = :i* ,newton's law fail$ to acc\nt1 & has pr$ict$ at lea/ "o previ\sly unkn[n ph5om5on :i* 0 imm$iately v]ifi$4 ,9 conclusion1 x may be ( int]e/ to /ate h[ ! new law describes ! motion ( a p>ticle 9 ! vic9ity ( a body l ! e>?4 ,! law am\nts to /at+ t1 if we measure a %ort di/ance1 radially z reg>ds ! e>?'s c5t]1 we mu/ all[ = ! peculi>ity ( our units by divid+ by sqrt#a-;frac#bm,gc#br :]e r is ! di/ance f ! e>?'s c5t]1 m ! mass ( ! e>?1 c ! velocity ( light1 & ,g ! ,newtonian gravitational con/ant4 ,tang5tial measurem5ts require no correction1 b int]vals ( "t z measur$ by our clocks mu/ be multipli$1 = ea* p>ticul> place1 by ! above factor4 ,!n1 9 t]ms ( ! correct$ measures s obta9$1 ! p>ticle w be f\nd to describe a /raight l9e ) con/ant velocity al?\gh1 9 t]ms ( our actual measures1 x appe>s to fall ) an accel]ation4 ,,xxi ,,! ,,equival5ce ,,hypo!sis ,! ,discussion ( ,?is1 ,) ,its ,difficulties & ! ,mann] 9 ,:i* ,e9/e9 ,has ,resolv$ ,!m1 f ! ,essay by ,,pr(4 ,e4 ,n4 ,,da ,c4 ,,&rade1 ,,ordnance ,,college1 ,,woolwi*1 ,,engl& ,hav+ %[n t1 ( sev]al sy/ems all mov+ ) ref]5ce to "o ano!r ) uni=m motion1 no "o is entitl$ to any pref]5ce ov] ! o!rs1 & hav+ d$uc$ ! laws = su* sy/ems1 ,e9/e9 0 confront$ ) a difficulty :i* _h long be5 felt4 ,a body rotat+1 :i* is a special case ( an accel]at$ body1 c be di/+ui%$ f "o at re/1 )\t look+ outside x1 by ! exi/5ce ( ! s-call$ c5trifugal =ces4 ,?is circum/ance1 :i* gives c]ta9 bodies an absolute or pref]5tial motion1 is unpalatable to ! relativi/2 he w\ld l !re to be no diff]5ce z reg>ds =ces #ac betwe5 ! case :5 ! e>? rotates ) ref]5ce to outside bodies 7! />s7 consid]$ z fix$1 & ! case :5 ! e>? is consid]$ fix$ & all outside bodies rotate ar\nd x4 ,?is po9t _c be inve/igat$ by direct exp]im5t2 we c sp9 a top b we _c keep a top at re/ & sp9 ! _w r\nd x1 to see if ! =ces are same4 ,9 consid]+ ! problem ( h[ to devise laws :i* %\ld make all rotations relative1 ,e9/e9 conceiv$ ! brilliant yet simple idea t gravitation c\ld be br\ght into ! s*eme z an accel]ation effect1 s9ce bo? ord9>y accel]ational =ces & gravitational =ces are proportional to ! same ?+1 ! mass ( a body4 ,! impossibility ( sep>at+ ! two k9ds ( effect c be easily se5 by consid]+ ! />t+ ( an elevator4 ,:5 ! elevator is quickly accel]at$ upw>ds we feel a d[nw>d pull1 j z if ! gravitational pull _h be5 increas$1 & if ! accel]ation cont9u$ to be uni=m1 bodies te/$ ) a spr+ balance w\ld all weigh m 9 ! elevator ?an !y did on firm gr\nd4 ,9 a simil> way ! :ole ( ! gravitational pull may be consid]$ to be an accel]ational effect1 ! difficulty be+ to devise laws ( motion :i* w give ! effects t we f9d by actual obs]vation4 ,b x is obvi\s t we _c1 by ord9>y me*anics1 consid] ! e>? z be+ accel]at$ 9 all directions1 :i* we %\ld h to d1 app>5tly1 to acc\nt = ! fact t ! gravitational pull is always t[>d ! c5t]4 ,x is obvi\s t we _c expla9 gravitation by assum+ t ! e>?'s surface is cont9ually mov+ outw>d ) an accel]at$ velocity4#bbg ,s ,e9/e9 f\nd t1 z long z we treat ! problem by ,euclid's geometry1 we _c rea* a satisfactory solution4 ,b he f\nd t to ! f\r-dim5sional space made up ( ! ?ree ord9>y dim5sions ( space1 toge!r ) ! "t-dim5sion :i* we h already m5tion$ 9 discuss+ ! special !ory1 may be attribut$ a peculi> geometry1 ! nature ( :i* dep>ts m & m f ,euclidean geometry z we approa* a gravitational body1 & ! net result ( :i* is to make possible ! univ]sal correspond5ce ( gravitation & accel]ation4 ,?is modification ( ! geometry ( space is (t5 spok5 ( z ! curvature ( space1 an expression :i* is puzzl+1 especially z ! space :i* is curv$ is f\r-dim5sional "t-space4 ,b we c get an idea ( :at is meant by consid]+ figures1 triangles say1 drawn on ! surface1 ( a sph]e4 ,^! triangles1 al?\gh drawn on a surface1 w n h ! same prop]ties z triangles drawn on flat pap]--_! ?ree angles w n toge!r equal "r angles4 ,!y w be non-,euclidean4 ,?is is only a r\gh analogy1 b we c see t ! curvature ( ! surface causes a dep>ture f ,euclidean geometry = plane figures1 & consequ5tly ! dep>ture f ,euclidean laws ext5d$ to f\r dim5sions may be ref]r$ to z caus$ by curvature ( space4 ,x is difficult to imag9e a lump ( matt] affect+ ! geometry ( ! space r\nd x4 ,once m we mu/ use a r\gh illu/ration4 ,imag9e a v hot body1 & t1 kn[+ no?+ ( its prop]ties1 we h to measure up ! space r\nd x ) metal measur+-rods4 ,! ne>] we are to ! body1 ! long] ! rods w become1 ow+ to ! expansion ( ! metal4 ,:5 we measure out a squ>e1 "o side ( :i* is ne>] ! body ?an ! opposite side1 its angles w n be "r angles4 ,if we knew no?+ ( ! laws ( heat we %\ld say t ! body _h made ! space r\nd x non-,euclidean4 ,e9/e9 f\nd1 !n1 t by tak+ ! prop]ties ( space1 z giv5 by measurem5t1 to be modifi$ 9 ! neighborhood ( masses ( matt]1 he c\ld devise g5]al laws accord+ to :i* gravitational effects w\ld be produc$1 & !re w\ld be no absolute rotation4 ,all =ces w be ! same :e!r a body rotates ) ev]y?+ outside x fix$1 or ! body is fix$1 & ev]y?+ rotates r\nd x4 ,all motion is !n relative1 & ! !ory is "o ( g5]al relativity4 ,! velocity ( light is1 h[ev]1 no long] con/ant1 & its pa? is n a /raight l9e1 if x is pass+ ne> gravitat+ matt]4 ,?is does n contradict ! special !ory1 :i* did n all[ = gravitation4 ,r1 ! special !ory is a p>ticul> case to :i* ! g5]alis$ !ory r$uces :5 !re is no matt] ab\t1 j z ! ,newtonian dynamics is a special case ( ! special !ory1 :i* we obta9 :5 all velocities are small comp>$ to t ( light4 ,,xxii ,,! ,,g5]al ,,!ory ,fragm5ts ( ,p>ticul> ,m]it on ,?is ,phase ( ! ,subject ,,by ,,v>i\s ,,contributors ,:5 ,doro?y 0 c>ri$ by ! cyclone f h] home 9 ,kansas to ! l& ( ,oz1 toge!r ) h] uncle's h\se & h] little dog ,toto1 %e neglect$ to l[] ! trap door ov] ! hole 9 ! floor :i* =m]ly l$ to ! cyclone cell> & ,toto /epp$ ?r\gh4 ,doro?y ru%$ to ! op5+ expect+ to see him da%$ onto ! rocks bel[ b f\nd him float+ j bel[ ! floor4 ,%e drew him back into ! room & clos$ ! trap4 ,! au?or ( ! *ronicle ( ,doro?y's adv5tures expla9s t ! same =ce :i* held up ! h\se held up ,toto b ?is explanation is n necess>y4 ,doro?y 0 n[ float+ ?r\gh space & h\se & dog 7 subject to ! same =ces ( gravitation :i* gave !m id5tical motions4 ,doro?y mu/ h pu%$ ! dog d[n onto ! floor & 9 do+ s mu/ h]self h float$ to ! ceil+ :5ce %e might h pu%$ h]self back to ! floor4 ,9 fact gravitation 0 app>5tly susp5d$ & ,doro?y 0 9 a position to h tri$ c]ta9 exp]im5ts :i* ,e9/e9 has nev] tri$ because he 0 nev] 9 ,doro?y's unique position4#ahh ,! ,pr9ciple ( ,equival5ce1 ( :i* ,e9/e9's susp5d$ cage exp]im5t is ! usual illu/ration1 & ^u :i* ! g5]aliz$ !ory ( relativity is built1 is ?us /at$ by ,pr(4 ,edd+ton3 ,a gravitational field ( =ce is precisely equival5t to an artificial field ( =ce1 s t 9 any small region x is impossible1 by any conceivable exp]im5t1 to di/+ui% betwe5 !m4 ,9 o!r words1 =ce is purely relative4 ,?is may be o!rwise /at$ by go+ back to our idea ( a f\r-dim5sional _w1 ! po9ts ( :i* repres5t ! positions & times ( ev5ts4 ,if we m>k 9 su* a space-"t ! successive positions ( an object we get a l9e1 or curve1 :i* repres5ts ! :ole hi/ory ( ! object1 inasmu* z x %[s u ! position ( ! object at e "t4 ,! read] may imag9e t all ev5ts happ5 9 "o plane1 s t only two p]p5dicul> dim5sions are ne$$ to fix positions 9 space1 ) a ?ird p]p5dicul> dim5sion = "t4 ,he may !n conceive1 if he may n picture1 an analog\s process = f\r-dim5sional space-"t4 ,^! l9es1 tracks ( objects ?r\gh space-"t1 7 call$ by ,m9k[ski _w-l9es4 ,we may n[ say t all ! ev5ts we obs]ve are ! int]sections ( _w-l9es4 ,! temp]ature at noon 0 #gj4 ,?is means t if ,i plot ! _w-l9e ( ! top ( ! m]cury column & ! _w-l9e ( a c]ta9 m>k on ! glass !y int]sect 9 a c]ta9 po9t ( space-"t4 ,all t we "k are int]sections ( ^! _w-l9es4 ,suppose n[ we h a l>ge numb] ( !m drawn 9 our f\r-dim5sional _w1 satisfy+ all kn[n int]sections1 & let u suppose ! :ole emb$d$ 9 a jelly4 ,we may di/ort ?is jelly 9 any way1 *ang+ our coord9ates z we please1 b we %all nei!r de/roy nor create int]sections ( _w-l9es4 ,x may be prov$ t a *ange f "o sy/em ( ref]5ce1 to :i* obs]vations are ref]r$1 to any o!r sy/em1 mov+ 9 any way ) respect to ! fir/ sy/em1 may be pictur$ z a di/ortion ( ! f\r-dim5sional jelly4 ,! laws ( nature1 !re=e1 be+ laws t describe int]sections1 mu/ be expressible 9 a =m indep5d5t ( ! ref]5ce sy/em *os54 ,f ^! po/ulates1 ,e9/e9 0 able to %[ su* a =mulation possible4 ,8 law may be /at$ v simply3--,all bodies move ?r\gh space-"t 9 ! /raighte/ possible tracks4 ,! fact t an easy non-ma!matical explanation c n be giv51 ( h[ ?is law is rea*$1 or ( j :y ! /raighte/ track ( ,m]cury ?r\gh space-"t w give u an ellipse 9 space aft] we h split space-"t up into space & "t1 is no valid objection to ! !ory4 ,newton's law t bodies attract ) a =ce proportional to _! masses & inv]sely proportional to ! squ>e ( ! di/ance is simple1 b no "o has ev] giv5 an easy non-ma!matical pro( ( h[ t law requires ! pa? ( ,m]cury to be an ellipse1 ) ! sun at a focus1 in/ead ( "s o!r curve4#ahb ,"o ( ! grave difficulties we h 9 ga9+ a satisfactory compreh5sion ( ,e9/e9's conceptions1 is t !y d n readily relate !mselves to our modes ( geometrical ?\ght4 ,)9 limits we may *oose our own geometry1 b x may be at ! co/ ( unwieldy complication4 ,if we ?9k ) ,newton 9 t]ms ( ,euclidean geometry & consid] ! e>? z revolv+ ar\nd ! sun1 ! motions ( our sol> sy/em c be /at$ 9 comp>atively simple t]ms4 ,if1 on ! o!r h&1 we %\ld p]si/ 9 /at+ !m1 z ,ptolemy w\ld h done1 f ! e>? z a relatively /ation>y c5t]1 our =mulas w become complicat$ beyond ready compreh5sion4 ,= ?is reason x is mu* simpl] 9 apply+ ! !ory ( relativity1 & 9 consid]+ & describ+ :at actually happ5s 9 ! physical univ]se1 to use geometrical conceptions to :i* ! actual conditions c be easily relat$4 ,we f9d su* an in/rum5t 9 non-,euclidean geometry1 :]e9 space w appe> z ?\gh x 7 project$ f a slightly concave mirror4 ,x is 9 ?is s5se t "s speak ( space z curv$4 ,! analogy is s sugge/ive x tempts "o to l+] ov] x4 ,unless !re 7 mat]ial objects )9 ! range ( ! mirror1 its con=mation w\ld be immat]ial2 ! ?\ght ( ! space :i* ! mirror1 z x 71 circumscribes1 is dep5d5t ^u ! pres5ce ( su* mat]ial objects4 ,! l9es ( light & ( all o!r movem5t w n be q /raight f ! view-po9t ( ,euclidean geometry4 ,a l9e drawn 9 a univ]se ( su* a nature mu/ inevitably return ^u itself4 ,no?+ !re=e1 c ev] pass out ( ?is unlimit$ly great b yet f9ite cosmos4 ,b ev5 n[1 s9ce our imag9>y mirror is only v slightly concave1 x foll[s t = limit$ regions l ! e>? or ev5 ! sol> sy/em1 our conception ( geometry may well be rectil9e> & ,euclidean4 ,newton's law ( gravitation w be q accurate ) only a !oretical modification drawn f ! !ory ( relativity4#hb ,! way 9 :i* a curvature ( space might appe> to u z a =ce is made pla9] by an example4 ,suppose t 9 a c]ta9 room a m>ble dropp$ any:]e on ! floor always roll$ to ! c5t] ( ! room2 suppose ! same ?+ happ5$ to a baseball1 a billi>d ball1 & a t5nis ball4 ,^! results c\ld be expla9$ 9 two ways2 we might assume t a my/]i\s =ce ( attraction exi/$ at ! c5t] ( ! floor1 :i* affect$ all k9ds ( balls alike2 or we might assume t ! floor 0 curv$4 ,we naturally pref] ! latt] explanation4 ,b :5 we f9d t 9 ! neighborhood ( a l>ge mat]ial body all o!r bodies move t[>d x 9 exactly ! same mann]1 reg>dless ( _! nature or _! condition1 we are accu/om$ to po/ulate a my/]i\s attractive =ce 7gravitation72 ,e9/e91 on ! contr>y1 adopts ! o!r alt]native1 t ! space ar\nd ! body is curv$4#bbc ,9 ! ord9>y analytical geometry1 ! position & motion ( all ! po9ts consid]$ is ref]r$ to a rigid body or frame ( ref]5ce4 ,?is usually consi/s ( an imag9>y room ( suitable size4 ,! position ( any po9t is !n giv5 by ?ree numb]s1 i4e41 its di/ances f "o side wall & f ! back wall & its height above ! floor4 ,^! ?ree numb]s c only give "o po9t1 e o!r po9t hav+ at lea/ "o numb] diff]5t4 ,9 f\r-dim5sional geometry a f\r? wall may be vaguely imag9$ z p]p5dicul> to all ?ree walls1 & a f\r? numb] add$1 giv+ ! di/ance ( ! po9t f ?is wall also4 ,s9ce rigid bodies d n exi/ 9 gravitational fields ! frame ( ref]5ce mu/ be non-rigid4 ,! frame ( ref]5ce 9 ! ,gaussian sy/em ne$ n be rigid1 x c be ( any %ape & mov+ 9 any mann]1 9 fact a k9d ( jelly4 ,a po9t or ev5t 9 ! f\r dim5sion$ _w is /ill giv5 by f\r numb]s b ^! numb]s d n repres5t di/ances f any:]e2 all t is necess>y is t no two ev5ts %all h exactly ! same f\r numb]s to repres5t !m1 & t two ev5ts :i* are v close toge!r %all be repres5t$ by numb]s :i* diff] only slightly f "o ano!r4 ,?is sy/em assumes s little t x w be se5 to be v wide 9 its scope2 al?\gh to ! ord9>y m9d1 :at is ga9$ 9 scope seems m ?an t lo/ 9 concret5ess4 ,?is does n conc]n ! ma!matician1 h[ev]1 & by us+ ?is sy/em he ga9s 8 object1 prov+ t ! g5]al laws ( nature rema9 ! same :5 express$ 9 any ,gaussian coord9ate sy/em :atev]4#bbj ,e9/e9 enunciates a g5]al pr9ciple t x is possible to f9d a trans=mation ( coord9ate axes :i* is exactly equival5t to any =ce1 & 9 p>ticul> "o :i* is equival5t to ! =ce ( gravitation4 ,t is by conc5trat+ our att5tion on ! trans=mation :i* is a purely ma!matical op]ation we c af=d to neglect ! =ce completely4 ,to get a bett] idea ( ?is pr9ciple ( equival5ce z x is call$1 let u consid] a relatively simple example 7:i* actually has no?+ to d ) gravitation1 b :i* w s]ve to make our notions cle>]47 ,a p]son on ! e>? unconsci\sly ref]s all 8 exp]i5ces1 i4e41 ! motions ( ! objects ar\nd him to a set ( axes fix$ 9 ! e>? on :i* he /&s4 ,h[ev]1 we "k t ! e>? is rotat+ ab\t its axis1 & 8 axes ( ref]5ce are also rotat+ ) respect to ! space ab\t him4 ,f ! po9t ( view ( g5]al relativity x is exactly because we d ref] motions on ! surface ( ! e>? to axes rotat+ ) ! e>? t we exp]i5ce ! s-call$ c5trifugal =ce ( ! e>?'s rotation1 ) :i* ev]yone is famili>4 ,if we c\ld f9d x conv5i5t to trans=m f mov+ axes to fix$ axes1 ! =ce w\ld vani%1 s9ce x is exactly equival5t to ! trans=mation f "o set ( axes to ! o!r4 ,h[ev]1 we f9d x unnatural to ref] daily exp]i5ces to axes t are n plac$ :]e we happ5 to be1 & s we pref] to take ! =ce & rotat+ axes in/ead ( no =ce & fix$ axes4#bgb ,we seem to h a direct exp]i5ce ( =ce 9 our muscul> s5sations4 ,by pu%+ or pull+ we c set bodies 9 motion4 ,x is natural to assume1 t some?+ simil> occurs1 :5 ,nature set bodies 9 motion4 ,b is ?is n a relic ( animism8 ,! savage & ! anci5ts peopl$ all ! woods & skies ) ,gods & demons1 :o c>ries on ! activities ( nature by _! own bodily ef=ts4 ,today we h dispossess$ ! demons1 b ! gho/ ( a muscul> pull /ill holds ! planets 9 place4#ada ,! g5]al !ory is an ext5sion ( ! special !ory :i* enables ! law ( gravitation to be d$uc$4 ,n 9 ,newton's =m1 x is true1 b 9 a bett] =m1 t is1 "o t acc\nts = two important facts o!rwise n expla9$4 ,b x is a f> m g5]al !ory t indicat$ above4 ,x is a complete /udy ( ! relations betwe5 laws express$ by means ( any f\r coord9ates 7( :i* ?ree space & "o "t is a special case71 & ! same laws express$ 9 ! f\r coord9ates ( a sy/em hav+ any motion :atev] ) respect to ! fir/ sy/em4 ,by re/rict+ ?is g5]al /udy 9 accordance ) c]ta9 po/ulates ab\t ! nature ( ! univ]se we live 91 we arrive at a numb] ( conclusions :i* fit m closely ) obs]v$ facts t ! conclusions drawn f ,newton's !ory4#bba ,,notes #a ,x w be not$ t ,mr4 ,bolton pron\nces ! geometry ( space to be ,euclidean 9 ! abs5ce ( gravitational fields1 n t ( space-"t4 ,?is is 9 accord ) :at 0 po9t$ out on page #afa4--;,editor4 #b ,! au?or "h comes p]il\sly close to ascrib+ to ?is contraction ! sort ( physical reality :i* x does n possess4 ,see page #if4--;,editor4 #c ,dr4 ,davis w5t r fully into ! algebra ( ! ,mi*elson-,morley exp]im5t4 ,b ,dr4 ,russell has cov]$ ! same gr\nd 9 a =m some:at m advantage\s f ! typographical viewpo9t1 & ! po9t is n "o :i* x is pr(itable to discuss twice2 s we elim9ate ?is "p ( ,dr4 ,davis' text4--,editor4 #d ,?is /atem5t is objectionable1 z expla9$ 9 ,*apt] ,,iv4--,editor4 #e ,a4 ,e9/e93 ,die ,grundlage d] allgeme95 ,relativitt/heorie4 ,ann4 d4 ,physik4 #d1 vol4 #di1 page #ggf4 #f ,at ?is po9t we h aga9 us$ ! blue p5cil on ,dr4 ,davis' text1 8 discussion ( ! ?ree obs]vational te/s ( ! ,g5]al ,!ory add+ no?+ to ,dr4 ,pick]+'s4--,! ,editor4 #g ,comm&] ,mc,hardy uses ! t]m ev5t 9 a s5se some:at diff]5t f t se5 9 a majority ( ! essays4 ,he res]ves = ! f\r-dim5sional elem5t--! in/ant ( "t at a po9t 9 space--! "n po9t-ev5t2 & ! t]m ev5t he applies to a collection ( ^! =m+1 toge!r1 an obs]vable :ole4 ,an actual physical happ5+1 l a railroad wreck or a laboratory exp]im5t1 x w be realiz$ is ( ! latt] sort1 occupy+ an appreciable region ( space r ?an a s+le po9t1 & an appreciable int]val ( "t r ?an a s+le second4 ,to ! elem5t1 ! po9t-ev5t ( ,comm&] ,mc,hardy's essay1 ?is be>s ! same relation t ! geomet]'s solid be>s to 8 po9t4 ,?is comm5t is 9 no s5se to be tak5 z criticism ( ,comm&] ,mc,hardy's t]m9ology1 :i* r appeals to u2 we make x m]ely to gu>d aga9/ confusion 9 ! read]'s m9d4--,editor4 #h ,?is p>agraph is ! result ( an editorial revision ( ! au?or's text1 design$ to reta9 ! sub/ance ( 8 pres5tation1 :ile ty+ up :at he has to say m def9itely ) ! prec$+ essays1 & elim9at+ ! di/9ction betwe5 f9ite & inf9itesimal int]vals1 :i* we believe to be out ( place 9 an essay ( ?is "*4 ,we w n apologize to our ma!matical read]s = hav+ us$ f9ite & diff]5tial notation 9 ! same equation1 9 violation ( ma!matical conv5tion4--,editor4 #i ,al?\gh gravitational =ce 9 a small region c be imitat$ or annull$ by accel]at+ motion1 !re rema9s ! di/urb+ influ5ce ( gravitational matt] already ref]r$ to & express$ 9 ! fabric curvature4 ,x is ?is t def9es h[ unique tracks run1 or r1 h[ bodies progress4--,au?or4 #aj ,n all gravitational fields may be trans=m$ away by a prop] *oice ( coord9ates4 ,if ?is 7 s1 ! space1 ^: nature is indep5d5t ( any *oice ( coord9ates1 w\ld always be ,euclidean4--,au?or4 #aa ,?us :5 x x said t a body contracts or t a clock runs sl[ :5 x is put 9 motion no actual physical *ange is impli$4 ,! judgm5t ( diff]5t obs]v]s--"o at re/ ) respect to ! body & "o n--are diff]5t4--,au?or4 #ab ,! balance ( ,dr4 ,royds' essay is giv5 to a discussion ( ! ph5om5a ( ,m]cury's p]ihelial advance1 ! deflection ( light "u ! gravitational field ( ! sun1 & ! %ift 9 spectral l9es1 9 connection ) :i* alone ,e9/e9's !ory makes pr$ictions :i* are suffici5tly at v>iance ) ^? ( ,newtonian sci5ce to be ( value 9 *eck+ up ! !ory obs]vationally4 ,9 ! int]e/ ( space cons]vation & 9 ! pres5ce ( ,dr4 ,pick]+'s v complete discussion ( ^! matt]s we omit ,dr4 ,royds' /atem5t4--,editor4 #ac ,!re is1 on any view1 no diff]5ce z reg>ds obs]vation ( position only4--,au?or4