,transcrib]'s ,notes3 ,und]scores 80 be=e & aft] a ^w or phrase indicate italics 9 ! orig9al text4 ,equal signs 80 be=e & aft] a ^w or phrase indicate bold 9 ! orig9al text4 ,small capitals h be5 conv]t$ to ,,solid capitals4 ,illu/rations h be5 mov$ s !y d n break up p>agraphs4 ,typographical & punctuation errors h be5 sil5tly correct$4 ,,h>p]',s ,,mod]n ,,sci5ce ,,s]ies ,,! ,a ,b ,c ,,( ,,relativity ,,by ,,b]tr& ,,russell ,,au?or ,,( 8,,! ,,pr9ciples ,,( ,,ma!matics0 8,,propos$ ,,roads ,,to ,,fre$om0 ,,& 8,,:y ,,m5 ,,fight0 ,,publi%]s ,,h>p] ,,bro!rs ,,new ,,york ,,& ,,london ,,! ,a ,b ,c ,,( ,,relativity ,copyright1 #aibe1 by ,h>p] ,bro!rs ,pr9t$ 9 ! ,unit$ ,/ates ( ,am]ica ,cont5ts ,,*apt] ,,page ,i4 ,,t\* ,,& ,,sight3 ,,! ,,e>? ,,& ,,! ,,heav5s #a ,,ii4 ,,:at ,,happ5s ,,& ,,:at ,,is ,,obs]v$ #ad ,,iii4 ,,! ,,velocity ,,( ,,light #bh ,,iv4 ,,clocks ,,& ,,foot ,,rules #dc ,v4 ,,space-,,"t #eh ,,vi4 ,,! ,,special ,,!ory ,,( ,,relativity #ga ,,vii4 ,,int]vals ,,9 ,,space-,,"t #ia ,,viii4 ,,e9/e9',s ,,law ,,( ,,gravitation #aaa ,,ix4 ,,pro(s ,,( ,,e9/e9',s ,,law ,,( ,,gravitation #aca ,x4 ,,mass1 ,,mom5tum1 ,,en]gy ,,& ,,action #add ,,xi4 ,,is ,,! ,,univ]se ,,f9ite8 #afc ,,xii4 ,,conv5tions ,,& ,,natural ,,laws #agg ,,xiii4 ,,! ,,abolition ,,( 8,,=ce0 #aib ,,xiv4 ,,:at ,,is ,,matt]8 #bjf ,,xv4 ,,philosophical ,,consequ5ces #bai ,,! ,a ,b ,c ,,( ,,relativity ,,*apt] ,,"o3 ,,t\* ,,& ,,sight3 ,,! ,,e>? ,,& ,,! ,,heav5s ,ev]ybody kn[s t ,e9/e9 has done some?+ a/oni%+1 b v few p "k exactly :at x is t he has done4 ,x is g5]ally recogniz$ t he has revolutioniz$ our conception ( ! physical _w1 b 8 new conceptions are wrapp$ up 9 ma!matical te*nicalities4 ,x is true t !re are innum]able popul> acc\nts ( ! !ory ( relativity1 b !y g5]ally cease to be intelligible j at ! po9t :]e !y beg9 to say some?+ important4 ,! au?ors are h>dly to blame = ?is4 ,_m ( ! new ideas c be express$ 9 non-ma!matical language1 b !y are none ! less difficult on t acc\nt4 ,:at is dem&$ is a *ange 9 our imag9ative picture ( ! _w--a picture :i* has be5 h&$ d[n f remote1 p]haps pre-human1 ance/ors1 & has be5 le>n$ by ea* "o ( u 9 e>ly *ildhood4 ,a *ange 9 our imag9ation is always difficult1 especially :5 we are no long] "y4 ,! same sort ( *ange 0 dem&$ by ,cop]nicus1 :5 he taught t ! e>? is n /ation>y & ! heav5s d n revolve ab\t x once a day4 ,to u n[ !re is no difficulty 9 ?is idea1 because we le>n$ x be=e our m5tal habits _h become fix$4 ,e9/e9's ideas1 simil>ly1 w seem easy to a g5]ation :i* has gr[n up ) !m2 b = our g5]ation a c]ta9 ef=t ( imag9ative recon/ruction is unavoidable4 ,9 explor+ ! surface ( ! e>?1 we make use ( all our s5ses1 m p>ticul>ly ( ! s5ses ( t\* & sight4 ,9 measur+ l5g?s1 p>ts ( ! human body are employ$ 9 pre-sci5tific ages3 a 8foot10 a 8cubit10 a 8span0 are def9$ 9 ?is way4 ,= long] di/ances1 we ?9k ( ! "t x takes to walk f "o place to ano!r4 ,we gradually le>n to judge di/ances r\ghly by ! eye1 b we rely ^u t\* = accuracy4 ,moreov] x is t\* t gives u our s5se ( 8reality40 ,"s ?+s _c be t\*$3 ra9b[s1 reflections 9 look+-glasses1 & s on4 ,^! ?+s puzzle *ildr51 ^: metaphysical speculations are arre/$ by ! in=mation t :at is 9 ! look+ glass is n 8real40 ,macbe?'s dagg] 0 unreal because x 0 n 8s5sible to feel+ z to sight40 ,n only our geometry & physics1 b our :ole conception ( :at exi/s outside u1 is bas$ ^u ! s5se ( t\*4 ,we c>ry ?is ev5 into our metaphors3 a good spee* is 8solid18 a bad spee* is 8gas10 because we feel t a gas is n q 8real40 ,9 /udy+ ! heav5s1 we are deb>r$ f all s5ses except sight4 ,we _c t\* ! sun1 or travel to x2 we _c walk r\nd ! moon1 or apply a foot rule to ! ,pleiades4 ,nev]!less1 a/ronom]s h unhesitat+ly appli$ ! geometry & physics :i* !y f\nd s]viceable on ! surface ( ! e>?1 & :i* !y _h bas$ ^u t\* & travel4 ,9 do+ s1 !y br\ght d[n tr\ble on _! heads1 :i* x has be5 left = ,e9/e9 to cle> up4 ,x has turn$ out t mu* ( :at we le>n$ f ! s5se ( t\* 0 unsci5tific prejudice1 :i* mu/ be reject$ if we are to h a true picture ( ! _w4 ,an illu/ration may help u to und]/& h[ mu* is impossible to ! a/ronom] z comp>$ to ! man :o is int]e/$ 9 ?+s on ! surface ( ! e>?4 ,let u suppose t a drug is adm9i/]$ to y :i* makes y tempor>ily unconsci\s1 & t :5 y wake y h lo/ y\r memory b n y\r reason+ p[]s4 ,let u suppose fur!r t :ile y 7 unconsci\s y 7 c>ri$ into a balloon1 :i*1 :5 y come to1 is sail+ ) ! w9d 9 a d>k night--! night ( ! fif? ( ,novemb] if y are 9 ,engl&1 or ( ! f\r? ( ,july if y are 9 ,am]ica4 ,y c see fireworks :i* are be+ s5t (f f ! gr\nd1 f tra9s1 & f a]oplanes travel+ 9 all directions1 b y _c see ! gr\nd or ! tra9s or ! a]oplanes be cause ( ! d>kness4 ,:at sort ( picture ( ! _w w y =m8 ,y w ?9k t no?+ is p]man5t3 !re are only brief fla%es ( light1 :i*1 dur+ _! %ort exi/5ce1 travel ?r\gh ! void 9 ! mo/ v>i\s & biz>re curves4 ,y _c t\* ^! fla%es ( light1 y c only see !m4 ,obvi\sly y\r geometry & y\r physics & y\r metaphysics w be q diff]5t f ^? ( ord9>y mortals4 ,if an ord9>y mortal is ) y 9 ! balloon1 y w f9d 8 spee* un9telligible4 ,b if ,e9/e9 is ) y1 y w und]/& him m easily ?an ! ord9>y mortal w\ld1 because y w be free f a ho/ ( preconceptions :i* prev5t mo/ p f und]/&+ him4 ,! !ory ( relativity dep5ds1 to a consid]able ext5t1 ^u gett+ rid ( notions :i* are useful 9 ord9>y life b n to our drugg$ ballooni/4 ,circum/ances on ! surface ( ! e>?1 = v>i\s m or less accid5tal reasons1 sugge/ conceptions :i* turn out to be inaccurate1 al?\gh !y h come to seem l necessities ( ?\ght4 ,! mo/ important ( ^! circum/ances is t mo/ objects on ! e>?'s surface are fairly p]si/5t & ne>ly /ation>y f a t]re/rial po9t ( view4 ,if ?is 7 n ! case1 ! idea ( go+ a j\rney w\ld n seem s def9ite z x does4 ,if y want to travel f ,k+'s ,cross to ,ed9burgh1 y "k t y w f9d ,k+'s ,cross :]e x always has be51 t ! railway l9e w take ! c\rse t x did :5 y la/ made ! j\rney1 & t ,wav]ley ,/ation 9 ,ed9burgh w n h walk$ up to ! ,ca/le4 ,y !re=e say & ?9k t y h travel$ to ,ed9burgh1 n t ,ed9burgh has travel$ to y1 ?\gh ! latt] /atem5t w\ld be j z accurate4 ,! success ( ?is common s5se po9t ( view dep5ds ^u a numb] ( ?+s :i* are really ( ! nature ( luck4 ,suppose all ! h\ses 9 ,london 7 p]petually mov+ ab\t1 l a sw>m ( bees2 suppose railways mov$ & *ang$ _! %apes l avalan*es2 & f9ally suppose t mat]ial objects 7 p]petually be+ =m$ & dissolv$ l cl\ds4 ,!re is no?+ impossible 9 ^! suppositions3 some?+ l !m mu/ h be5 v]ifi$ :5 ! e>? 0 hott] ?an x is n[4 ,b obvi\sly :at we call a j\rney to ,ed9burgh w\ld h no mean+ 9 su* a _w4 ,y w\ld beg91 no d\bt1 by ask+ ! taxi-driv]3 8,:]e is ,k+'s ,cross ?is morn+88 ,at ! /ation y w\ld h to ask a simil> "q ab\t ,ed9burgh1 b ! book+-(fice cl]k w\ld reply3 8,:at "p ( ,ed9burgh d y mean1 ,sir8 ,pr9ce's ,/reet has gone to ,glasg[1 ! ,ca/le has mov$ up into ! ,highl&s1 & ,wav]ley ,/ation is "u wat] 9 ! middle ( ! ,fir? ( ,=?40 ,& on ! j\rney ! /ations w\ld n be /ay+ quiet1 b "s w\ld be travell+ nor?1 "s s\?1 "s ea/ or we/1 p]haps mu* fa/] ?an ! tra94 ,"u ^! conditions y c\ld n say :]e y 7 at any mom5t4 ,inde$ ! :ole notion t "o is always 9 "s def9ite 8place0 is due to ! =tunate immovability ( mo/ ( ! l>ge objects on ! e>?'s surface4 ,! idea ( 8place0 is only a r\gh practical approximation3 !re is no?+ logically necess>y ab\t x1 & x _c be made precise4 ,if we 7 n mu* l>g] ?an an electron1 we %\ld n h ?is impression ( /ability1 :i* is only due to ! grossness ( our s5ses4 ,k+'s ,cross1 :i* to u looks solid1 w\ld be too va/ to be conceiv$ except by a few ecc5tric ma!maticians4 ,! bits ( x t we c\ld see w\ld consi/ ( little t9y po9ts ( matt]1 nev] com+ into contact ) ea* o!r1 b p]petually :izz+ r\nd ea* o!r 9 an inconceivably rapid ballet-dance4 ,! _w ( our exp]i5ce w\ld be q z mad z ! "o 9 :i* ! diff]5t p>ts ( ,ed9burgh g = walks 9 diff]5t directions4 ,if--to take ! opposite extreme--y 7 z l>ge z ! sun & liv$ z long1 ) a correspond+ sl[ness ( p]ception1 y w\ld aga9 f9d a higgl$y-piggl$y univ]se )\t p]man5ce--/>s & planets w\ld come & g l morn+ mi/s1 & no?+ w\ld rema9 9 a fix$ position relatively to any?+ else4 ,! notion ( comp>ative /ability :i* =ms "p ( our ord9>y outlook is ?us due to ! fact t we are ab\t ! size we are1 & live on a planet ( :i* ! surface is no long] v hot4 ,if ?is 7 n ! case1 we %\ld n f9d pre-relativity physics intellectually satisfy+4 ,inde$1 we %\ld nev] h inv5t$ su* !ories4 ,we %\ld h _h to arrive at relativity physics at "o b\nd1 or rema9 ignorant ( sci5tific laws4 ,x is =tunate = u t we 7 n fac$ ) ?is alt]native1 s9ce x is almo/ inconceivable t "o man c\ld h done ! "w ( ,euclid1 ,galileo1 ,newton1 & ,e9/e94 ,yet )\t su* an incr$ible g5ius physics c\ld h>dly h be5 discov]$ 9 a _w :]e ! univ]sal flux 0 obvi\s to non-sci5tific obs]vation4 ,9 a/ronomy1 al?\gh ! sun1 moon1 & />s cont9ue to exi/ ye> aft] ye>1 yet 9 o!r respects ! _w we h to deal ) is v diff]5t f t ( ev]yday life4 ,z already obs]v$1 we dep5d exclusively on sight3 ! heav5ly bodies _c be t\*$1 he>d1 smelt or ta/$4 ,ev]y?+ 9 ! heav5s is mov+ relatively to ev]y?+ else4 ,! e>? is go+ r\nd ! sun1 ! sun is mov+1 v mu* fa/] ?an an express tra91 t[>ds a po9t 9 ! con/ellation 8,h]cules10 ! 8fix$0 />s are scurry+ hi!r & ?i!r l a lot ( fright5$ h5s4 ,!re are no well-m>k$ places 9 ! sky1 l ,k+'s ,cross & ,ed9burgh4 ,:5 y travel f place to place on ! e>?1 y say ! tra9 moves & n ! /ations1 because ! /ations pres]ve _! topographical relations to ea* o!r & ! surr\nd+ c\ntry4 ,b 9 a/ronomy x is arbitr>y :i* y call ! tra9 & :i* ! /ation3 ! "q is to be decid$ purely by conv5i5ce & z a matt] ( conv5tion4 ,9 ?is respect1 x is int]e/+ to contra/ ,e9/e9 & ,cop]nicus4 ,be=e ,cop]nicus1 p ?\ght t ! e>? /ood /ill & ! heav5s revolv$ ab\t x once a day4 ,cop]nicus taught t 8really0 ! e>? rotates once a day1 & ! daily revolution ( sun & />s is only 8app>5t40 ,galileo & ,newton endors$ ?is view1 & _m ?+s 7 ?\ght to prove x--= example1 ! flatt5+ ( ! e>? at ! poles1 & ! fact t bodies are heavi] !re ?an at ! equator4 ,b 9 ! mod]n !ory ! "q betwe5 ,cop]nicus & 8 pr$ecessors is m]ely "o ( conv5i5ce2 all motion is relative1 & !re is no diff]5ce betwe5 ! two /atem5ts3 8! e>? rotates once a day0 & 8! heav5s revolve ab\t ! e>? once a day40 ,! two mean exactly ! same ?+1 j z x means ! same ?+ if ,i say t a c]ta9 l5g? is six feet or two y>ds4 ,a/ronomy is easi] if we take ! sun z fix$ ?an if we take ! e>?1 j z acc\nts are easi] 9 a decimal co9age4 ,b to say m = ,cop]nicus is to assume absolute motion1 :i* is a fiction4 ,all motion is relative1 & x is a m]e conv5tion to take "o body z at re/4 ,all su* conv5tions are equally legitimate1 ?\gh n all are equally conv5i5t4 ,!re is ano!r matt] ( great importance1 9 :i* a/ronomy diff]s f t]re/rial physics because ( its exclusive dep5d5ce ^u sight4 ,bo? popul> ?\ght & old-fa%ion$ physics us$ ! notion ( 8=ce10 :i* seem$ intelligible because x 0 associat$ ) famili> s5sations4 ,:5 we are walk+1 we h s5sations connect$ ) our muscles :i* we d n h :5 we are sitt+ /ill4 ,9 ! days be=e me*anical traction1 al?\gh p c\ld travel by sitt+ 9 _! c>riages1 !y c\ld see ! horses ex]t+ !mselves & evid5tly putt+ out 8=ce0 9 ! same way z human be+s d4 ,ev]ybody knew f exp]i5ce :at x is to pu% or pull1 or to be pu%$ or pull$4 ,^! v famili> facts made 8=ce0 seem a natural basis = dynamics4 ,b ,newton's law ( gravitation introduc$ a difficulty4 ,! =ce betwe5 two billi>d balls appe>$ intelligible1 because we "k :at x feels l to bump into ano!r p]son2 b ! =ce betwe5 ! e>? & ! sun1 :i* are n9ety-?ree million miles ap>t1 0 my/]i\s4 ,newton himself reg>d$ ?is 8action at a di/ance0 z impossible1 & believ$ t !re 0 "s hi!rto undiscov]$ me*anism by :i* ! sun's influ5ce 0 transmitt$ to ! planets4 ,h[ev]1 no su* me*anism 0 discov]$1 & gravitation rema9$ a puzzle4 ,! fact is t ! :ole conception ( 8=ce0 is a mi/ake4 ,! sun does n ex]t any =ce on ! planets2 9 ,e9/e9's law ( gravitation1 ! planet only pays att5tion to :at x f9ds 9 its own neighborhood4 ,! way 9 :i* ?is works w be expla9$ 9 a lat] *apt]2 = ! pres5t we are only conc]n$ ) ! necessity ( ab&on+ ! notion ( 8=ce10 :i* 0 due to mislead+ conceptions d]iv$ f ! s5se ( t\*4 ,z physics has advanc$1 x has appe>$ m & m t sight is less mislead+ ?an t\* z a s\rce ( fundam5tal notions ab\t matt]4 ,! app>5t simplicity 9 ! collision ( billi>d balls is q illusory4 ,z a matt] ( fact1 ! two billi>d balls nev] t\* at all2 :at really happ5s is inconceivably complicat$1 b is m analog\s to :at happ5s :5 a comet p5etrates ! sol> sy/em & goes away aga9 ?an to :at common s5se supposes to happ54 ,mo/ ( :at we h said hi!rto 0 already recogniz$ by physici/s be=e ,e9/e9 inv5t$ ! !ory ( relativity4 8,=ce0 0 kn[n to be m]ely a ma!matical fiction1 & x 0 g5]ally held t motion is a m]ely relative ph5om5on--t is to say1 :5 two bodies are *ang+ _! relative position1 we _c say t "o is mov+ :ile ! o!r is at re/1 s9ce ! occurr5ce is m]ely a *ange 9 _! relation to ea* o!r4 ,b a great labor 0 requir$ 9 ord] to br+ ! actual proc$ure ( physics into h>mony ) ^! new convictions4 ,newton believ$ 9 =ce & 9 absolute space & "t2 he embodi$ ^! beliefs 9 8 te*nical me?ods1 & 8 me?ods rema9$ ^? ( lat] physici/s4 ,e9/e9 inv5t$ a new te*nique1 free f ,newton's assumptions4 ,b 9 ord] to d s he _h to *ange fundam5tally ! old ideas ( space & "t1 :i* _h be5 un*all5g$ f "t immemorial4 ,?is is :at makes bo? ! difficulty & ! int]e/ ( 8 !ory4 ,b be=e expla9+ x !re are "s prelim9>ies :i* are indisp5sable4 ,^! w occupy ! next two *apt]s4 ,,*apt] ,,ii3 ,,:at ,,happ5s ,,& ,,:at ,,is ,,obs]v$ ,a c]ta9 type ( sup]ior p]son is fond ( ass]t+ t 8ev]y?+ is relative40 ,?is is1 ( c\rse1 nons5se1 because1 if ev]y?+ 7 relative1 !re w\ld be no?+ = x to be relative to4 ,h[ev]1 )\t fall+ into metaphysical absurdities x is possible to ma9ta9 t ev]y?+ 9 ! physical _w is relative to an obs]v]4 ,?is view1 true or n1 is n t adopt$ by ! 8!ory ( relativity40 ,p]haps ! "n is un=tunate2 c]ta9ly x has l$ philosoph]s & un$ucat$ p into confusions4 ,!y imag9e t ! new !ory proves ev]y?+ 9 ! physical _w to be relative1 :]eas1 on ! contr>y1 x is :olly conc]n$ to exclude :at is relative & arrive at a /atem5t ( physical laws t %all 9 no way dep5d ^u ! circum/ances ( ! obs]v]4 ,x is true t ^! circum/ances h be5 f\nd to h m effect ^u :at appe>s to ! obs]v] ?an !y 7 =m]ly ?\ght to h1 b at ! same "t ,e9/e9 %[$ h[ to disc\nt ?is effect completely4 ,?is 0 ! s\rce ( almo/ ev]y?+ t is surpris+ 9 8 !ory4 ,:5 two obs]v]s p]ceive :at is reg>d$ z "o occurr5ce1 !re are c]ta9 simil>ities1 & also c]ta9 diff]5ces1 betwe5 _! p]ceptions4 ,! diff]5ces are obscur$ by ! requirem5ts ( daily life1 because f a bus9ess po9t ( view !y are z a rule unimportant4 ,b bo? psy*ology & physics1 f _! diff]5t angles1 are compell$ to emphasize ! respects 9 :i* "o man's p]ception ( a giv5 occurr5ce diff]s f ano!r man's4 ,"s ( ^! diff]5ces are due to diff]5ces 9 ! bra9s or m9ds ( ! obs]v]s1 "s to diff]5ces 9 _! s5se organs1 "s to diff]5ces ( physical situation3 ^! ?ree k9ds may be call$ respectively psy*ological1 physiological1 & physical4 ,a rem>k made 9 a language we "k w be he>d1 :]eas an equally l\d rem>k 9 an unkn[n language may pass entirely unnotic$4 ,( two m5 9 ! ,alps1 "o w p]ceive ! beauty ( ! sc5]y :ile ! o!r w notice ! wat]falls ) a view to obta9+ p[] f !m4 ,su* diff]5ces are psy*ological4 ,! diff]5ce betwe5 a long-sight$ & a %ort-sight$ man1 or betwe5 a deaf man & a man :o he>s well1 are physiological4 ,nei!r ( ^! k9ds conc]ns u1 & ,i h m5tion$ !m only 9 ord] to exclude !m4 ,! k9d t conc]ns u is ! purely physical k9d4 ,physical diff]5ces betwe5 two obs]v]s w be pres]v$ :5 ! obs]v]s are replac$ by cam]as or phonographs1 & c be reproduc$ on ! movies or ! gramophone4 ,if two m5 bo? li/5 to a ?ird man speak+1 & "o ( !m is ne>] to ! speak] ?an ! o!r is1 ! ne>] "o w he> l\d] & slightly e>li] s\nds ?an are he>d by ! o!r4 ,if two m5 bo? wat* a tree fall+1 !y see x f diff]5t angles4 ,bo? ^! diff]5ces w\ld be %[n equally by record+ in/rum5ts3 !y are 9 no way due to idiosyncrasies 9 ! obs]v]s1 b are "p ( ! ord9>y c\rse ( physical nature z we exp]i5ce x4 ,! physici/1 l ! pla9 man1 believes t 8 p]ceptions give him k ab\t :at is really occurr+ 9 ! physical _w1 & n only ab\t 8 private exp]i5ces4 ,pr(essionally1 he reg>ds ! physical _w z 8real10 n m]ely z some?+ :i* human be+s dream4 ,an eclipse ( ! sun1 = in/ance1 c be obs]v$ by any p]son :o is suitably situat$1 & is also obs]v$ by ! photographic plates t are expos$ = ! purpose4 ,! physici/ is p]suad$ t some?+ has really happ5$ ov] & above ! exp]i5ces ( ^? :o h look$ at ! sun or at photographs ( x4 ,i h emphasiz$ ?is po9t1 :i* might seem a trifle obvi\s1 because "s p imag9e t ,e9/e9 has made a diff]5ce 9 ?is respect4 ,9 fact he has made none4 ,b if ! physici/ is ju/ifi$ 9 ?is belief t a numb] ( p c obs]ve ! 8same0 physical occurr5ce1 !n cle>ly ! physici/ mu/ be conc]n$ ) ^? features :i* ! occurr5ce has 9 common = all obs]v]s1 = ! o!rs _c be reg>d$ z belong+ to ! occurr5ce itself4 ,at lea/1 ! physici/ mu/ conf9e himself to ! features :i* are common to all 8equally good0 obs]v]s4 ,! obs]v] :o uses a microscope or a telescope is pref]r$ to "o :o does n1 because he sees all t ! latt] sees & m too4 ,a s5sitive photographic plate may 8see0 /ill m1 & is !n pref]r$ to any eye4 ,b su* ?+s z diff]5ces ( p]spective1 or diff]5ces ( app>5t size due to diff]5ce ( di/ance1 are obvi\sly n attributable to ! object2 !y belong solely to ! po9t ( view ( ! spectator4 ,common s5se elim9ates ^! 9 judg+ ( objects2 physics has to c>ry ! same process mu* fur!r1 b ! pr9ciple is ! same4 ,i want to make x cle> t ,i am n conc]n$ ) any?+ t c be call$ inaccuracy4 ,i am conc]n$ ) g5u9e physical diff]5ces betwe5 occurr5ces ea* ( :i* is a correct record ( a c]ta9 ev5t1 f its own po9t ( view4 ,:5 a man fires a gun1 p :o are n q close to him see ! fla% be=e !y he> ! report4 ,?is is n due to any defect 9 _! s5ses1 b to ! fact t s\nd travels m sl[ly ?an light4 ,light travels s fa/ t1 f ! po9t ( view ( ph5om5a on ! surface ( ! e>?1 x may be reg>d$ z in/antane\s4 ,any?+ t we c see on ! e>? happ5s practically at ! mom5t :5 we see x4 ,9 a second1 light travels #cjj1jjj kilomet]s 7ab\t #ahf1jjj miles74 ,x travels f ! sun to ! e>? 9 ab\t eight m9utes1 & f ! />s to u 9 any?+ f ?ree to a ?\s& ye>s4 ,b ( c\rse we _c place a clock 9 ! sun1 & s5d out a fla% ( light f x at #ab noon1 ,gre5wi* ,mean ,"t1 & h x receiv$ at ,gre5wi* at #ab4jh ,p4,m4 ,our me?ods ( e/imat+ ! spe$ ( light h to be m or less indirect4 ,! only direct me?od w\ld be t :i* we apply to s\nd :5 we use an e*o4 ,we c\ld s5d a fla% to a mirror1 & obs]ve h[ long x took = ! reflection to rea* u2 ?is w\ld give ! "t ( ! d\ble j\rney to ! mirror & back4 ,on ! e>?1 h[ev]1 ! "t w\ld be s %ort t a great deal ( !oretical physics has to be utiliz$ if ?is me?od is to be employ$--m ev5 ?an is requir$ = ! employm5t ( a/ronomical data4 ,! problem ( all[+ = ! spectator's po9t ( view1 we may be told1 is "o ( :i* physics has at all times be5 fully aw>e2 inde$ x has dom9at$ a/ronomy ev] s9ce ! "t ( ,cop]nicus4 ,?is is true4 ,b pr9ciples are (t5 ackn[l$g$ long be=e _! full consequ5ces are drawn4 ,mu* ( traditional physics is incompatible ) ! pr9ciple1 9 spite ( ! fact t x 0 ackn[l$g$ !oretically by all physici/s4 ,!re exi/$ a set ( rules :i* caus$ uneas9ess to ! philosophically m9d$1 b 7 accept$ by physici/s because !y work$ 9 practice4 ,locke _h di/+ui%$ 8second>y0 qualities--colors1 noises1 ta/es1 smells1 etc4--z subjective1 :ile all[+ 8prim>y0 qualities--%apes & positions & sizes--to be g5u9e prop]ties ( physical objects4 ,! physici/'s rules 7 su* z w\ld foll[ f ?is doctr9e4 ,colors & noises 7 all[$ to be subjective1 b due to waves proce$+ ) a def9ite velocity--t ( light or s\nd z ! case may be--f _! s\rce to ! eye or e> ( ! p]cipi5t4 ,app>5t %apes v>y accord+ to ! laws ( p]spective1 b ^! laws are simple & make x easy to inf] ! 8real0 %apes f sev]al visual app>5t %apes2 moreov]1 ! 8real0 %apes c be asc]ta9$ by t\* 9 ! case ( bodies 9 our neighborhood4 ,! objective "t ( a physical occurr5ce c be inf]r$ f ! "t :5 we p]ceive x by all[+ = ! velocity ( transmission--( light or s\nd or n]ve curr5ts accord+ to circum/ances4 ,?is 0 ! view adopt$ by physici/s 9 practice1 :atev] qualms !y may h _h 9 unpr(essional mom5ts4 ,?is view work$ well en\gh until physici/s became conc]n$ ) mu* great] velocities ?an ^? t are common on ! surface ( ! e>?4 ,an express tra9 travels ab\t a mile 9 a m9ute2 ! planets travel a few miles 9 a second4 ,comets1 :5 !y are ne> ! sun1 travel mu* fa/]1 & behave some:at oddly2 b !y 7 puzzl+ 9 v>i\s ways4 ,practically1 ! planets 7 ! mo/ swiftly mov+ bodies to :i* dynamics c\ld be adequately appli$4 ,) radio-activity a new range ( obs]vations became possible4 ,individual electrons c be obs]v$1 emanat+ f radium ) a velocity n f> %ort ( t ( light4 ,! behavior ( bodies mov+ ) ^! enorm\s spe$s is n :at ! old !ories w\ld lead u to expect4 ,= "o ?+1 mass seems to increase ) spe$ 9 a p]fectly def9ite mann]4 ,:5 an electron is mov+ v fa/1 a bigg] =ce is requir$ to h a giv5 effect ^u x ?an :5 x is mov+ sl[ly4 ,!n reasons 7 f\nd = ?9k+ t ! size ( a body is affect$ by its motion--= example1 if y take a cube & move x v fa/1 x gets %ort] 9 ! direction ( its motion1 f ! po9t ( view ( a p]son :o is n mov+ ) x1 ?\gh f its own po9t ( view 7i4e4 = an obs]v] travel+ ) x7 x rema9s j z x 04 ,:at 0 /ill m a/oni%+ 0 ! discov]y t lapse ( "t dep5ds on motion2 t is to say1 two p]fectly accurate clocks1 "o ( :i* is mov+ v fa/ relatively to ! o!r1 w n cont9ue to %[ ! same "t if !y come toge!r aga9 aft] a j\rney4 ,x foll[s t :at we discov] by means ( clocks & foot rules1 :i* us$ to be reg>d$ z ! acme ( imp]sonal sci5ce1 is really 9 "p dep5d5t ^u our private circum/ances1 i4e4 ^u ! way 9 :i* we are mov+ relatively to ! bodies measur$4 ,?is %[s t we h to draw a diff]5t l9e f t :i* is cu/om>y 9 di/+ui%+ betwe5 :at belongs to ! obs]v] & :at belongs to ! occurr5ce :i* he is obs]v+4 ,if a man is we>+ blue spectacles he kn[s t ! blue look ( ev]y?+ is due to 8 spectacles1 & does n belong to :at he is obs]v+4 ,b if he obs]ves two fla%es ( lightn+1 & notes ! int]val ( "t betwe5 8 obs]vations2 if he kn[s :]e ! fla%es took place1 & all[s1 9 ea* case1 = ! "t ! light took to rea* him--9 t case1 if 8 *ronomet] is accurate1 he naturally ?9ks t he has discov]$ ! actual int]val ( "t betwe5 ! two fla%es1 & n some?+ m]ely p]sonal to himself4 ,he is confirm$ 9 ?is view by ! fact t all o!r c>eful obs]v]s to :om he has access agree ) 8 e/imates4 ,?is1 h[ev]1 is only due to ! fact t all ^! obs]v]s are on ! e>?1 & %>e its motion4 ,ev5 two obs]v]s 9 a]oplanes mov+ 9 opposite directions w\ld h at ! mo/ a relative velocity ( #djj miles an h\r1 :i* is v little 9 comp>ison ) #ahf1jjj miles a second 7! velocity ( light74 ,if an electron %ot out f a piece ( radium ) a velocity ( #agj1jjj miles a second c\ld obs]ve ! "t betwe5 ! two fla%es1 x w\ld arrive at a q diff]5t e/imate1 aft] mak+ full all[ance = ! velocity ( light4 ,h[ d y "k ?is8 ! read] may ask4 ,y are n an electron1 y _c move at ^! t]rific spe$s1 no man ( sci5ce has ev] made ! obs]vations :i* w\ld prove ! tru? ( y\r ass]tion4 ,nev]!less1 z we %all see 9 ! sequel1 !re is good gr\nd = ! ass]tion--gr\nd1 fir/ ( all1 9 exp]im5t1 &--:at is rem>kable--gr\nd 9 reason+s :i* c\ld h be5 made at any "t1 b 7 n made until exp]im5ts _h %[n t ! old reason+s mu/ be wrong4 ,!re is a g5]al pr9ciple to :i* ! !ory ( relativity appeals1 :i* turns out to be m p[]ful ?an anybody w\ld suppose4 ,if y "k t "o man is twice z ri* z ano!r1 ?is fact mu/ appe> equally :e!r y e/imate ! weal? ( bo? 9 p\nds or doll>s or francs or any o!r curr5cy4 ,! numb]s repres5t+ _! =tunes w be *ang$1 b "o numb] w always be d\ble ! o!r4 ,! same sort ( ?+1 9 m complicat$ =ms1 reappe>s 9 physics4 ,s9ce all motion is relative1 y may take any body y l z y\r /&>d body ( ref]5ce1 & e/imate all o!r motions ) ref]5ce to t "o4 ,if y are 9 a tra9 & walk+ to ! d9+-c>1 y naturally1 = ! mom5t1 treat ! tra9 z fix$ & e/imate y\r motion by relation to x4 ,b :5 y ?9k ( ! j\rney y are mak+1 y ?9k ( ! e>? z fix$1 & say y are mov+ at ! rate ( sixty miles an h\r4 ,an a/ronom] :o is conc]n$ ) ! sol> sy/em takes ! sun z fix$1 & reg>ds y z rotat+ & revolv+2 9 comp>ison ) ?is motion1 t ( ! tra9 is s sl[ t x h>dly c\nts4 ,an a/ronom] :o is int]e/$ 9 ! /ell> univ]se may add ! motion ( ! sun relatively to ! av]age ( ! />s4 ,y _c say t "o ( ^! ways ( e/imat+ y\r motion is m correct ?an ano!r2 ea* is p]fectly correct z soon z ! ref]5ce body is assign$4 ,n[ j z y c e/imate a man's =tune 9 diff]5t curr5cies )\t alt]+ its relations to ! =tunes ( o!r m51 s y c e/imate a body's motion by means ( diff]5t ref]5ce bodies )\t alt]+ its relations to o!r motions4 ,& z physics is entirely conc]n$ ) relations1 x mu/ be possible to express all ! laws ( physics by ref]r+ all motions to any giv5 body z ! /&>d4 ,we may put ! matt] 9 ano!r way4 ,physics is int5d$ to give in=mation ab\t :at really occurs 9 ! physical _w1 & n only ab\t ! private p]ceptions ( sep>ate obs]v]s4 ,physics mu/1 !re=e1 be conc]n$ ) ^? features :i* a physical process has 9 common = all obs]v]s1 s9ce su* features alone c be reg>d$ z belong+ to ! physical occurr5ce itself4 ,?is requires t ! laws ( ph5om5a %\ld be ! same :e!r ! ph5om5a are describ$ z !y appe> to "o obs]v] or z !y appe> to ano!r4 ,?is s+le pr9ciple is ! g5]at+ motive ( ! :ole !ory ( relativity4 ,n[ :at we h hi!rto reg>d$ z ! spatial & temporal prop]ties ( physical occurr5ces are f\nd to be 9 l>ge "p dep5d5t ^u ! obs]v]2 only a residue c be attribut$ to ! occurr5ces 9 !mselves1 & only ?is residue c be involv$ 9 ! =mulation ( any physical law :i* is to h an priori *ance ( be+ true4 ,e9/e9 f\nd ready to 8 h& an in/rum5t ( pure ma!matics1 call$ ! !ory ( t5sors1 :i* enabl$ him to discov] laws express$ 9 t]ms ( ! objective residue & agree+ approximately ) ! old laws4 ,:]e ,e9/e9's laws diff]$ f ! old ones1 !y h hi!rto prov$ m 9 accord ) obs]vation4 ,if !re 7 no reality 9 ! physical _w1 b only a numb] ( dreams dream$ by diff]5t p1 we %\ld n expect to f9d any laws connect+ ! dreams ( "o man ) ! dreams ( ano!r4 ,x is ! close connection betwe5 ! p]ceptions ( "o man & ! 7r\ghly7 simultane\s p]ceptions ( ano!r t makes u believe 9 a common ext]nal orig9 ( ! diff]5t relat$ p]ceptions4 ,physics acc\nts bo? = ! lik5esses & = ! diff]5ces betwe5 diff]5t p's p]ceptions ( :at we call ! 8same0 occurr5ce4 ,b 9 ord] to d ?is x is fir/ necess>y = ! physici/ to f9d out j :at are ! lik5esses4 ,!y are n q ^? traditionally assum$1 because nei!r space nor "t sep>ately c be tak5 z /rictly objective4 ,:at is objective is a k9d ( mixture ( ! two call$ 8space-"t40 ,to expla9 ?is is n easy1 b ! attempt mu/ be made2 x w be begun 9 ! next *apt]4 ,,*apt] ,,iii3 ,,! ,,velocity ,,( ,,light ,mo/ ( ! curi\s ?+s 9 ! !ory ( relativity are connect$ ) ! velocity ( light4 ,if ! read] is to grasp ! reasons = su* a s]i\s !oretical recon/ruction1 he mu/ h "s idea ( ! facts :i* made ! old sy/em break d[n4 ,! fact t light is transmitt$ ) a def9ite velocity 0 fir/ e/abli%$ by a/ronomical obs]vations4 ,jupit]'s moons are sometimes eclips$ by ,jupit]1 & x is easy to calculate ! times :5 ?is ought to occur4 ,x 0 f\nd t :5 ,jupit] 0 unusually ne> ! e>? an eclipse ( "o ( 8 moons w\ld be obs]v$ a few m9utes e>li] ?an 0 expect$2 & :5 ,jupit] 0 unusually remote1 a few m9utes lat] ?an 0 expect$4 ,x 0 f\nd t ^! deviations c\ld all be acc\nt$ = by assum+ t light has a c]ta9 velocity1 s t :at we obs]ve to be happ5+ 9 ,jupit] really happ5$ a little :ile ago--long] ago :5 ,jupit] is di/ant ?an :5 x is ne>4 ,j ! same velocity ( light 0 f\nd to acc\nt = simil> facts 9 reg>d to o!r p>ts ( ! sol> sy/em4 ,x 0 !re=e accept$ t light 9 vacuo always travels at a c]ta9 con/ant rate1 almo/ exactly #cjj1jjj kilomet]s a second4 7,a kilomet] is ab\t five-eigh?s ( a mile47 ,:5 x became e/abli%$ t light consi/s ( waves1 ?is velocity 0 t ( propagation ( waves 9 ! e!r--at lea/ !y us$ to be 9 ! e!r1 b n[ ! e!r has gr[n some:at %ad[y1 ?\gh ! waves rema94 ,?is same velocity is t ( ! waves us$ 9 wireless telegraphy 7:i* are l light waves1 only long]7 & 9 ,x-rays 7:i* are l light waves1 only %ort]74 ,x is g5]ally held n[adays to be ! velocity ) :i* gravitation is propagat$1 ?\gh ,edd+ton consid]s ?is n yet c]ta94 7,x us$ to be ?\ght t gravitation 0 propagat$ in/antane\sly1 b ?is view is n[ ab&on$47 ,s f>1 all is pla9 sail+4 ,b z x became possible to make m accurate measurem5ts1 difficulties began to accumulate4 ,! waves 7 suppos$ to be 9 ! e!r1 & !re=e _! velocity ought to be relative to ! e!r4 ,n[ s9ce ! e!r 7if x exi/s7 cle>ly (f]s no resi/ance to ! motions ( ! heav5ly bodies1 x w\ld seem natural to suppose t x does n %>e _! motion4 ,if ! e>? _h to pu% a lot ( e!r be=e x1 9 ! sort ( way t a /eam] pu%es wat] be=e x1 "o w\ld expect a resi/ance on ! "p ( ! e!r analog\s to t (f]$ by ! wat] to ! /eam]4 ,!re=e ! g5]al view 0 t ! e!r c\ld pass ?r\gh bodies )\t difficulty1 l air ?r\gh a co>se sieve1 only m s4 ,if ?is 7 ! case1 !n ! e>? 9 its orbit mu/ h a velocity relative to ! e!r4 ,if1 at "s po9t ( its orbit1 x happ5$ to be mov+ exactly ) ! e!r1 x mu/ at o!r po9ts be mov+ ?r\gh x all ! fa/]4 ,if y g = a circul> walk on a w9dy day1 y mu/ be walk+ aga9/ ! w9d "p ( ! way1 :atev] w9d may be bl[+2 ! pr9ciple 9 ?is case is ! same4 ,x foll[s t1 if y *oose two days six mon?s ap>t1 :5 ! e>? 9 its orbit is mov+ 9 exactly opposite directions1 x mu/ be mov+ aga9/ an e!r w9d on at lea/ "o ( ^! days4 ,n[ if !re is an e!r w9d1 x is cle> t1 relatively to an obs]v] on ! e>?1 light signals w seem to travel fa/] ) ! w9d ?an across x1 & fa/] across x ?an aga9/ x4 ,?is is :at ,mi*elson & ,morley set !mselves to te/ by _! fam\s exp]im5t4 ,!y s5t out light signals 9 two directions at "r angles2 ea* 0 reflect$ f a mirror1 & came back to ! place f :i* bo? _h be5 s5t out4 ,n[ anybody c v]ify1 ei!r by trial or by a little ari?metic1 t x takes long] to r[ a giv5 di/ance on a riv] up/ream & !n back aga91 ?an x takes to r[ ! same di/ance across ! /ream & back aga94 ,!re=e1 if !re 7 an e!r w9d1 "o ( ! two light signals1 :i* consi/ ( waves 9 ! e!r1 ought to h travel$ to ! mirror & back at a sl[] av]age rate ?an ! o!r4 ,mi*elson & ,morley tri$ ! exp]im5t1 !y tri$ x 9 v>i\s positions1 !y tri$ x aga9 lat]4 ,_! app>atus 0 q accurate en\gh to h detect$ ! expect$ diff]5ce ( spe$ or ev5 a mu* small] diff]5ce1 if x _h exi/$1 b n ! smalle/ diff]5ce c\ld be obs]v$4 ,! result 0 a surprise to !m z to ev]ybody else2 b c>eful repetitions made d\bt impossible4 ,! exp]im5t 0 fir/ made z long ago z #ahha1 & 0 repeat$ ) m elaboration 9 #ahhg4 ,b x 0 _m ye>s be=e x c\ld be rightly int]pret$4 ,! supposition t ! e>? c>ries ! neighbor+ e!r ) x 9 its motion 0 f\nd to be impossible1 = a numb] ( reasons4 ,consequ5tly a logical deadlock seem$ to h aris51 f :i* at fir/ physici/s s\ght to extricate !mselves by v arbitr>y hypo!ses4 ,! mo/ important ( ^! 0 t ( ,fitzg]ald1 develop$ by ,lor5tz1 & kn[n z ! ,fitzg]ald contraction hypo!sis4 ,accord+ to ?is hypo!sis1 :5 a body is 9 motion x becomes %ort5$ 9 ! direction ( motion by a c]ta9 proportion dep5d+ ^u its velocity4 ,! am\nt ( ! contraction 0 to be j en\gh to acc\nt = ! negative result ( ! ,mi*elson-,morley exp]im5t4 ,! j\rney up /ream & d[n aga9 0 to h be5 really a %ort] j\rney ?an ! "o across ! /ream1 & 0 to h be5 j s mu* %ort] z w\ld enable ! sl[] light wave to trav]se x 9 ! same "t4 ,( c\rse ! %ort5+ c\ld nev] be detect$ by measurem5t1 because our measur+ rods w\ld %>e x4 ,a foot rule plac$ 9 ! l9e ( ! e>?'s motion w\ld be %ort] ?an ! same foot rule plac$ at "r angles to ! e>?'s motion4 ,?is po9t ( view resembles no?+ s mu* z ! ,:ite ,knight's 8plan to dye my :isk]s gre51 & always use s l>ge a fan t !y c\ld n be se540 ,! odd ?+ 0 t ! plan work$ well en\gh4 ,lat] on1 :5 ,e9/e9 prop\nd$ 8 special !ory ( relativity 7#aije71 x 0 f\nd t ! !ory 0 9 a c]ta9 s5se correct1 b only 9 a c]ta9 s5se4 ,t is to say1 ! suppos$ contraction is n a physical fact1 b a result ( c]ta9 conv5tions ( measurem5t :i*1 :5 once ! "r po9t ( view has be5 f\nd1 are se5 to be su* z we are almo/ compell$ to adopt4 ,b ,i d n wi% yet to set =? ,e9/e9's solution ( ! puzzle4 ,= ! pres5t1 x is ! nature ( ! puzzle itself t ,i want to make cle>4 ,on ! face ( x1 & ap>t f hypo!ses ad hoc1 ! ,mi*elson-,morley exp]im5t 79 conjunction ) o!rs7 %[$ t1 relatively to ! e>?1 ! velocity ( light is ! same 9 all directions1 & t ?is is equally true at all times ( ! ye>1 al?\gh ! direction ( ! e>?'s motion is always *ang+ z x goes r\nd ! sun4 ,moreov]1 x appe>$ t ?is is n a peculi>ity ( ! e>?1 b is true ( all bodies3 if a light signal is s5t out f a body1 t body w rema9 at ! c5t] ( ! waves z !y travel outw>ds1 no matt] h[ x may be mov+--at lea/1 t w be ! view ( obs]v]s mov+ ) ! body4 ,?is 0 ! pla9 & natural mean+ ( ! exp]im5ts1 & ,e9/e9 succe$$ 9 inv5t+ a !ory :i* accept$ x4 ,b at fir/ x 0 ?\ght logically impossible to accept ?is pla9 & natural mean+4 ,a few illu/rations w make x cle> h[ v odd ! facts are4 ,:5 a %ell is fir$1 x moves fa/] ?an s\nd3 ! p at :om x is fir$ fir/ see ! fla%1 !n 7if !y are lucky7 see ! %ell g by1 & la/ ( all he> ! report4 ,x is cle> t if y c\ld put a sci5tific obs]v] on ! %ell1 he w\ld nev] he> ! report1 z ! %ell w\ld bur/ & kill him be=e ! s\nd _h ov]tak5 him4 ,b if s\nd work$ on ! same pr9ciples z light1 our obs]v] w\ld he> ev]y?+ j z if he 7 at re/4 ,9 t case1 if a scre51 suitable = produc+ e*oes1 7 atta*$ to ! %ell & travel+ ) x1 say a hundr$ y>ds 9 front ( x1 our obs]v] w\ld he> ! e*o ( ! report f ! scre5 aft] j ! same int]val ( "t z if he & ! %ell 7 at re/4 ,?is1 ( c\rse1 is an exp]im5t :i* _c be p]=m$1 b o!rs :i* c be p]=m$ w %[ ! diff]5ce4 ,we might f9d "s place on a railway :]e !re is an e*o f a place fur!r along ! railway--say a place :]e ! railway goes into a tunnel--& :5 a tra9 is travel+ along ! railway1 let a man on ! bank fire a gun4 ,if ! tra9 is travel+ t[>ds ! e*o1 ! pass5g]s w he> ! e*o soon] ?an ! man on ! bank2 if x is travel+ 9 ! opposite direction1 !y w he> x lat]4 ,b ^! are n q ! circum/ances ( ! ,mi*elson-,morley exp]im5t4 ,! mirrors 9 t exp]im5t correspond to ! e*o1 & ! mirrors are mov+ ) ! e>?1 s t e*o ought to move ) ! tra94 ,let u suppose t ! %ot is fir$ f ! gu>d's van1 & ! e*o comes f a scre5 on ! eng9e4 ,we w suppose ! di/ance f ! gu>d's van to ! eng9e to be ! di/ance t s\nd c travel 9 a second 7ab\t "o-fif? ( a mile71 & ! spe$ ( ! tra9 to be "o-twelf? ( ! spe$ ( s\nd 7ab\t sixty miles an h\r74 ,we n[ h an exp]im5t :i* c be p]=m$ by ! p 9 ! tra94 ,if ! tra9 7 at re/1 ! gu>d w\ld he> ! e*o 9 two seconds2 z x is1 he w he> x 9 #b & _/ seconds4 ,f ?is diff]5ce1 if he kn[s ! velocity ( s\nd1 he c calculate ! velocity ( ! tra91 ev5 if x is a foggy night s t he _c see ! banks4 ,b if s\nd behav$ l light1 he w\ld he> ! e*o 9 two seconds h[ev] fa/ ! tra9 might be travel+4 ,v>i\s o!r illu/rations w help to %[ h[ extraord9>y--f ! po9t ( view ( tradition & common s5se--are ! facts ab\t ! velocity ( light4 ,e "o kn[s t if y are on an escalator y rea* ! top soon] if y walk up ?an if y /& /ill4 ,b if ! escalator mov$ ) ! velocity ( light 7:i* x does n d ev5 9 ,new ,york71 y w\ld rea* ! top at exactly ! same mom5t :e!r y walk$ up or /ood /ill4 ,aga93 if y are walk+ along a road at ! rate ( f\r miles an h\r1 & a motor-c> passes y go+ 9 ! same direction at ! rate ( =ty miles an h\r1 if y & ! motor-c> bo? keep go+ ! di/ance betwe5 y aft] an h\r w be ?irty-six miles4 ,b if ! motor-c> met y1 go+ 9 ! opposite direction1 ! di/ance aft] an h\r w\ld be =ty-f\r miles4 ,n[ if ! motor-c> 7 travel+ ) ! velocity ( light1 x w\ld make no diff]5ce :e!r x met or pass$ y3 9 ei!r case1 x w\ld1 aft] a second1 be #ahf1jjj miles f y4 ,x w\ld also be #ahf1jjj miles f any o!r motor-c> :i* happ5$ to be pass+ or meet+ y less rapidly at ! previ\s second4 ,?is seems impossible3 h[ c ! c> be at ! same di/ance f a numb] ( diff]5t po9ts along ! road8 ,let u take ano!r illu/ration4 ,:5 a fly t\*es ! surface ( a /agnant pool1 x causes ripples :i* move outw>ds 9 wid5+ circles4 ,! c5t] ( ! circle at any mom5t is ! po9t ( ! pool t\*$ by ! fly4 ,if ! fly moves ab\t ov] ! surface ( ! pool1 x does n rema9 at ! c5t] ( ! ripples4 ,b if ! ripples 7 waves ( light1 & ! fly 7 a skill$ physici/1 x w\ld f9d t x always rema9$ at ! c5t] ( ! ripples1 h[ev] x might move4 ,mean:ile a skill$ physici/ sitt+ beside ! pool w\ld judge1 z 9 ! case ( ord9>y ripples1 t ! c5t] 0 n ! fly1 b ! po9t ( ! pool t\*$ by ! fly4 ,& if ano!r fly _h t\*$ ! wat] at ! same spot at ! same mom5t1 x also w\ld f9d t x rema9$ at ! c5t] ( ! ripples1 ev5 if x sep>at$ itself widely f ! fir/ fly4 ,?is is exactly analog\s to ! ,mi*elson-,morley exp]im5t4 ,! pool corresponds to ! e!r2 ! fly corresponds to ! e>?2 ! contact ( ! fly & ! pool corresponds to ! light signal :i* ,messrs4 ,mi*elson & ,morley s5d out2 & ! ripples correspond to ! light waves4 ,su* a /ate ( affairs seems1 at fir/ sight1 q impossible4 ,x is no wond] t1 al?\gh ! ,mi*elson-,morley exp]im5t 0 made 9 #ahha1 x 0 n rightly int]pret$ until #aije4 ,let u see :at1 exactly1 we h be5 say+4 ,take ! man walk+ along a road & pass$ by a motor-c>4 ,suppose !re are a numb] ( p at ! same po9t ( ! road1 "s walk+1 "s 9 motor-c>s2 suppose !y are go+ at v>y+ rates1 "s 9 "o direction & "s 9 ano!r4 ,i say t if1 at ?is mom5t1 a light fla% is s5t out f ! place :]e !y all are1 ! light waves w be #ahf1jjj miles f ea* "o ( !m aft] a second by 8 wat*1 al?\gh ! travel]s w n any long] be all 9 ! same place4 ,at ! end ( a second by y\r wat* x w be #ahf1jjj miles f y1 & x w also be #ahf1jjj miles f a p]son :o met y :5 x 0 s5t out1 b 0 mov+ 9 ! opposite direction1 aft] a second by 8 wat*--assum+ bo? to be p]fect wat*es4 ,h[ c ?is be8 ,!re is only "o way ( expla9+ su* facts1 & t is1 to assume t wat*es & clocks are affect$ by motion4 ,i d n mean t !y are affect$ 9 ways t c\ld be rem$i$ by great] accuracy 9 con/ruction2 ,i mean some?+ mu* m fundam5tal4 ,i mean t1 if y say an h\r has elaps$ betwe5 two ev5ts1 & if y base ?is ass]tion ^u ideally c>eful measurem5ts ) ideally accurate *ronomet]s1 ano!r equally precise p]son1 :o has be5 mov+ rapidly relatively to y1 may judge t ! "t 0 m or less ?an an h\r4 ,y _c say t "o is "r & ! o!r wrong1 any m ?an y c\ld if "o us$ a clock %[+ ,gre5wi* "t & ano!r a clock %[+ ,new ,york "t4 ,h[ ?is comes ab\t1 ,i %all expla9 9 ! next *apt]4 ,!re are o!r curi\s ?+s ab\t ! velocity ( light4 ,"o is1 t no mat]ial body c ev] travel z fa/ z light1 h[ev] great may be ! =ce to :i* x is expos$1 & h[ev] long ! =ce may act4 ,an illu/ration may help to make ?is cle>4 ,at exhibitions "o sometimes sees a s]ies ( mov+ plat=ms1 go+ r\nd & r\nd 9 a circle4 ,! outside "o goes at f\r miles an h\r2 ! next goes f\r miles an h\r fa/] ?an ! fir/2 & s on4 ,y c /ep across f ea* to ! next2 until y f9d y\rself go+ at a trem5d\s pace4 ,n[ y might ?9k t1 if ! fir/ plat=m does f\r miles an h\r1 & ! second does f\r miles an h\r relatively to ! fir/1 !n ! second does eight miles an h\r relatively to ! gr\nd4 ,?is is an error2 x does a little less1 ?\gh s little less t n ev5 ! mo/ c>eful measurem5ts c\ld detect ! diff]5ce4 ,i want to make q cle> :at x is t ,i mean4 ,i w suppose t1 9 ! morn+1 :5 ! app>atus is j ab\t to />t1 ?ree m5 ) ideally accurate *ronomet]s /& 9 a r[1 "o on ! gr\nd1 "o on ! fir/ plat=m1 & "o on ! second4 ,! fir/ plat=m moves at ! rate ( f\r miles an h\r ) respect to ! gr\nd4 ,f\r miles an h\r is #ceb feet 9 a m9ute4 ,! man on ! gr\nd1 aft] a m9ute by 8 wat*1 notes ! place on ! gr\nd opposite ! man on ! fir/ plat=m1 :o has be5 /&+ /ill :ile ! plat=m c>ri$ him along4 ,! man on ! gr\nd measures ! di/ance on ! gr\nd f himself to ! po9t opposite ! man on ! fir/ plat=m1 & f9ds x is #ceb feet4 ,! man on ! fir/ plat=m1 aft] a m9ute by 8 wat*1 notes ! po9t on 8 plat=m opposite to ! man on ! second plat=m4 ,! man on ! fir/ plat=m measures ! di/ance f himself to ! po9t opposite ! man on ! second plat=m2 x is aga9 #ceb feet4 ,problem3 h[ f> w ! man on ! gr\nd judge t ! man on ! second plat=m has travel$ 9 a m9ute8 ,t is to say1 if ! man on ! gr\nd1 aft] a m9ute by 8 wat*1 notes ! place on ! gr\nd opposite ! man on ! second plat=m1 h[ f> w ?is be f ! man on ! gr\nd8 ,y w\ld say1 twice #ceb feet1 t is to say1 #gjd feet4 ,b 9 fact x w be a little less1 ?\gh s little less z to be inappreciable4 ,! discrepancy is ow+ to ! fact t ! two wat*es d n keep p]fect "t1 9 spite ( ! fact t ea* is accurate f its own]'s po9t ( view4 ,if y _h a long s]ies ( su* mov+ plat=ms1 ea* mov+ f\r miles an h\r relatively to ! "o be=e x1 y w\ld nev] rea* a po9t :]e ! la/ 0 mov+ ) ! velocity ( light relatively to ! gr\nd1 n ev5 if y _h millions ( !m4 ,! discrepancy1 :i* is v small = small velocities1 becomes great] z ! velocity increases1 & makes ! velocity ( light an unatta9able limit4 ,h[ all ?is happ5s1 is ! next topic ) :i* we mu/ deal4 ,note4 ,! negative result ( ! ,mi*elson-,morley exp]im5t has rec5tly be5 call$ 9 "q by ,pr(essor ,dayton ,c4 ,mill]1 z a result ( obs]vations by :at is said to be an improv$ me?od4 ,8 claim is set =? by ,pr(essor ,silb]/e9 9 ,nature1 ,may #bc1 #aibe1 & discuss$ unfavorably by ,edd+ton 9 ! issue ( ,june #f4 ,! matt] is sub judice1 b x seems highly que/ionable :e!r ! results be> out ! int]pretation :i* is put ^u !m4 ,,*apt] ,,iv3 ,,clocks ,,& ,,foot ,,rules ,until ! adv5t ( ! special !ory ( relativity1 no "o _h ?\ght t !re c\ld be any ambiguity 9 ! /atem5t t two ev5ts 9 diff]5t places happ5$ at ! same "t4 ,x might be admitt$ t1 if ! places 7 v f> ap>t1 !re might be difficulty 9 f9d+ out = c]ta9 :e!r ! ev5ts 7 simultane\s1 b e "o ?\ght ! mean+ ( ! "q p]fectly def9ite4 ,x turn$ out1 h[ev]1 t ?is 0 a mi/ake4 ,two ev5ts 9 di/ant places may appe> simultane\s to "o obs]v] :o has tak5 all due precautions to insure accuracy 7&1 9 p>ticul>1 has all[$ = ! velocity ( light71 :ile ano!r equally c>eful obs]v] may judge t ! fir/ ev5t prec$$ ! second1 & /ill ano!r may judge t ! second prec$$ ! fir/4 ,?is w\ld happ5 if ! ?ree obs]v]s 7 all mov+ rapidly relatively to ea* o!r4 ,x w\ld n be ! case t "o ( !m w\ld be "r & ! o!r two wrong3 !y w\ld all be equally "r4 ,! "t ord] ( ev5ts is 9 "p dep5d5t ^u ! obs]v]2 x is n always & altoge!r an intr9sic relation betwe5 ! ev5ts !mselves4 ,e9/e9 has %[n1 n only t ?is view acc\nts = ! ph5om5a1 b also t x is ! "o :i* ought to h result$ f c>eful reason+ bas$ ^u ! old data4 ,9 actual fact1 h[ev]1 no "o notic$ ! logical basis ( ! !ory ( relativity until ! odd results ( exp]im5t _h giv5 a jog to p's reason+ p[]s4 ,h[ %\ld we naturally decide :e!r two ev5ts 9 diff]5t places 7 simultane\s8 ,"o w\ld naturally say3 !y are simultane\s if !y are se5 simultane\sly by a p]son :o is exactly half-way betwe5 !m4 7,!re is no difficulty ab\t ! simultaneity ( two ev5ts 9 ! same place1 su*1 = example1 z see+ a light & he>+ a noise47 ,suppose two fla%es ( lightn+ fall 9 two diff]5t places1 say ,gre5wi* ,obs]vatory & ,kew ,obs]vatory4 ,suppose t ,/4 ,paul's is half-way betwe5 !m1 & t ! fla%es appe> simultane\s to an obs]v] on ! dome ( ,/4 ,paul's4 ,9 t case1 a man at ,kew w see ! ,kew fla% fir/1 & a man at ,gre5wi* w see ! ,gre5wi* fla% fir/1 because ( ! "t tak5 by light to travel ov] ! int]v5+ di/ance4 ,b all ?ree1 if !y are ideally accurate obs]v]s1 w judge t ! two fla%es 7 simultane\s1 because !y w make ! necess>y all[ance = ! "t ( transmission ( ! light4 7,i am assum+ a degree ( accuracy f> beyond human p[]s47 ,?us1 s f> z obs]v]s on ! e>? are conc]n$1 ! def9ition ( simultaneity w "w well en\gh1 s long z we are deal+ ) ev5ts on ! surface ( ! e>?4 ,x gives results :i* are consi/5t ) ea* o!r1 & c be us$ = t]re/rial physics 9 all problems 9 :i* we c ignore ! fact t ! e>? moves4 ,b our def9ition is no long] s satisfactory :5 we h two sets ( obs]v]s 9 rapid motion relatively to ea* o!r4 ,suppose we see :at w\ld happ5 if we sub/itute s\nd = light1 & def9$ two occurr5ces z simultane\s :5 !y are he>d simultane\sly by a man half-way betwe5 !m4 ,?is alt]s no?+ 9 ! pr9ciple1 b makes ! matt] easi] ow+ to ! mu* sl[] velocity ( s\nd4 ,let u suppose t on a foggy night two m5 belong+ to a gang ( brig&s %oot ! gu>d & eng9e driv] ( a tra94 ,! gu>d is at ! end ( ! tra92 ! brig&s are on ! l9e1 & %oot _! victims at close qu>t]s4 ,an old g5tleman :o is exactly 9 ! middle ( ! tra9 he>s ! two %ots simultane\sly4 ,y w\ld say1 !re=e1 t ! two %ots 7 simultane\s4 ,b a /ation ma/] :o is exactly half-way betwe5 ! two brig&s he>s ! %ot :i* kills ! gu>d fir/4 ,an ,au/ralian millionaire uncle ( ! gu>d & ! eng9e driv] 7:o are c\s9s7 has left 8 :ole =tune to ! gu>d1 or1 %\ld he die fir/1 to ! eng9e driv]4 ,va/ sums are involv$ 9 ! "q ( :i* di$ fir/4 ,! case goes to ! ,h\se ( ,lords1 & ! lawy]s on bo? sides1 hav+ be5 educat$ at ,ox=d1 are agre$ t ei!r ! old g5tleman or ! /ation ma/] mu/ h be5 mi/ak54 ,9 fact1 bo? may p]fectly well be "r4 ,! tra9 travels away f ! %ot at ! gu>d1 & t[>ds ! %ot at ! eng9e driv]2 !re=e ! noise ( ! %ot at ! gu>d has f>!r to g be=e rea*+ ! old g5tleman ?an ! %ot at ! eng9e driv] has4 ,!re=e if ! old g5tleman is "r 9 say+ t he he>d ! two reports simultane\sly1 ! /ation ma/] mu/ be "r 9 say+ t he he>d ! %ot at ! gu>d fir/4 ,we1 :o live on ! e>?1 w\ld naturally1 9 su* a case1 pref] ! view ( simultaneity obta9$ f a p]son at re/ on ! e>? to ! view ( a p]son travel+ 9 a tra94 ,b 9 !oretical physics no su* p>o*ial prejudices are p]missible4 ,a physici/ on a comet1 if !re 7 "o1 w\ld h j z good a "r to 8 view ( simultaneity z an e>?ly physici/ has to 81 b ! results w\ld diff]1 9 j ! same sort ( way z 9 our illu/ration ( ! tra9 & ! %ots4 ,! tra9 is n any m 8really0 9 motion ?an ! e>?2 !re is no 8really0 ab\t x4 ,y might imag9e a rabbit & a hippopotamus argu+ z to :e!r man is 8really0 a l>ge animal2 ea* w\ld ?9k 8 own po9t ( view ! natural "o1 & ! o!r a pure flight ( fancy4 ,!re is j z little sub/ance 9 an argum5t z to :e!r ! e>? or ! tra9 is 8really0 9 motion4 ,&1 !re=e1 :5 we are def9+ simultaneity betwe5 di/ant ev5ts1 we h no "r to pick & *oose among diff]5t bodies to be us$ 9 def9+ ! po9t half-way betwe5 ! ev5ts4 ,all bodies h an equal "r to be *os54 ,b if1 = "o body1 ! two ev5ts are simultane\s accord+ to ! def9ition1 !re w be o!r bodies = :i* ! fir/ prec$es ! second1 & /ill o!rs = :i* ! second prec$es ! fir/4 ,we _c !re=e say unambigu\sly t two ev5ts 9 di/ant places are simultane\s4 ,su* a /atem5t only acquires a def9ite mean+ 9 relation to a def9ite obs]v]4 ,x belongs to ! subjective "p ( our obs]vation ( physical ph5om5a1 n to ! objective "p :i* is to ent] into physical laws4 ,?is "q ( "t 9 diff]5t places is p]haps1 = ! imag9ation1 ! mo/ difficult aspect ( ! !ory ( relativity4 ,we are accu/om$ to ! idea t ev]y?+ c be dat$4 ,hi/orians make use ( ! fact t !re 0 an eclipse ( ! sun visible 9 ,*9a on ,augu/ #bi 9 ! ye> #ggf ,b4 ,c4#a ,no d\bt a/ronom]s c\ld tell ! exact h\r & m9ute :5 ! eclipse began to be total at any giv5 spot 9 ,nor? ,*9a4 ,& x seems obvi\s t we c speak ( ! positions ( ! planets at a giv5 in/ant4 ,! ,newtonian !ory enables u to calculate ! di/ance betwe5 ! e>? & 7say7 ,jupit] at a giv5 "t by ! ,gre5wi* clocks2 ?is enables u to "k h[ long light takes at t "t to travel f ,jupit] to ! e>?--say half an h\r2 ?is enables u to inf] t half an h\r ago ,jupit] 0 :]e we see x n[4 ,all ?is seems obvi\s4 ,b 9 fact x only works 9 practice because ! relative velocities ( ! planets are v small comp>$ ) ! velocity ( light4 ,:5 we judge t an ev5t on ! e>? & an ev5t on ,jupit] h happ5$ at ! same "t--= example1 t ,jupit] eclips$ "o ( 8 moons :5 ! ,gre5wi* clocks %[$ twelve midnight--a p]son mov+ rapidly relatively to ! e>? w\ld judge diff]5tly1 assum+ t bo? he & we _h made ! prop] all[ance = ! velocity ( light4 ,& naturally ! disagreem5t ab\t simultaneity involves a disagreem5t ab\t p]iods ( "t4 ,if we judg$ t two ev5ts on ,jupit] 7 sep>at$ by tw5ty-f\r h\rs1 ano!r p]son might judge t !y 7 sep>at$ by a long] "t1 if he 7 mov+ rapidly relatively to ,jupit] & ! e>?4 #a ,a contempor>y ,*9ese ode1 aft] giv+ ! day ( ! ye> correctly1 proce$s3 8,= ! moon to be eclips$ ,is b an ord9>y matt]4 ,n[ t ! sun has be5 eclips$1 ,h[ bad x is40 ,! univ]sal cosmic "t :i* us$ to be tak5 = grant$ is ?us no long] admissible4 ,= ea* body1 !re is a def9ite "t ord] = ! ev5ts 9 its neighborhood2 ?is may be call$ ! 8prop]0 "t = t body4 ,our own exp]i5ce is gov]n$ by ! prop] "t = our own body4 ,z we all rema9 v ne>ly /ation>y on ! e>?1 ! prop] times ( diff]5t human be+s agree1 & c be lump$ toge!r z t]re/rial "t4 ,b ?is is only ! "t appropriate to l>ge bodies on ! e>?4 ,= ,beta-p>ticles 9 laboratories1 q diff]5t times w\ld be want$2 x is because we insi/ ^u us+ our own "t t ^! p>ticles seem to increase 9 mass ) rapid motion4 ,f _! own po9t ( view1 _! mass rema9s con/ant1 & x is we :o sudd5ly gr[ ?9 or corpul5t4 ,! hi/ory ( a physici/ z obs]v$ by a ,beta-p>ticle w\ld resemble ,gulliv]'s travels4 ,! "q n[ arises3 :at really is measur$ by a clock8 ,:5 we speak ( a clock 9 ! !ory ( relativity1 we d n mean only clocks made by human h&s3 we mean any?+ :i* goes ?r\gh "s regul> p]iodic p]=mance4 ,! e>? is a clock1 because x rotates once 9 e tw5ty-?ree h\rs & fifty-six m9utes4 ,an atom is a clock1 because ! electrons g r\nd ! nucleus a c]ta9 numb] ( times 9 a second2 its prop]ties z a clock are exhibit$ to u 9 its spectrum1 :i* is due to light waves ( v>i\s frequ5cies4 ,! _w is full ( p]iodic occurr5ces1 & fundam5tal me*anisms1 su* z atoms1 %[ an extraord9>y simil>ity 9 diff]5t p>ts ( ! univ]se4 ,any "o ( ^! p]iodic occurr5ces may be us$ = measur+ "t2 ! only advantage ( humanly manufactur$ clocks is t !y are specially easy to obs]ve4 ,"o "q is3 ,if cosmic "t is ab&on$1 :at is really measur$ by a clock 9 ! wide s5se t we h j giv5 to ! t]m8 ,ea* clock gives a correct measure ( its own 8prop]0 "t1 :i*1 z we %all see pres5tly1 is an important physical quantity4 ,b x does n give an accurate measure ( any physical quantity connect$ ) ev5ts on bodies t are mov+ rapidly 9 relation to x4 ,x gives "o datum t[>ds ! discov]y ( a physical quantity connect$ ) su* ev5ts1 b ano!r datum is requir$1 & ?is has to be d]iv$ f measurem5t ( di/ances 9 space4 ,di/ances 9 space1 l p]iods ( "t1 are 9 g5]al n objective physical facts1 b p>tly dep5d5t ^u ! obs]v]4 ,h[ ?is comes ab\t mu/ n[ be expla9$4 ,fir/ ( all1 we h to ?9k ( ! di/ance betwe5 two ev5ts1 n betwe5 two bodies4 ,?is foll[s at once f :at we h f\nd z reg>ds "t4 ,if two bodies are mov+ relatively to ea* o!r--& ?is is really always ! case--! di/ance betwe5 !m w be cont9ually *ang+1 s t we c only speak ( ! di/ance betwe5 !m at a giv5 "t4 ,if y are 9 a tra9 travel+ t[>ds ,ed9burgh1 we c speak ( y\r di/ance f ,ed9burgh at a giv5 "t4 ,b1 z we said1 diff]5t obs]v]s w judge diff]5tly z to :at is ! 8same0 "t = an ev5t 9 ! tra9 & an ev5t 9 ,ed9burgh4 ,?is makes ! measurem5t ( di/ances relative1 9 j ! same way z ! measurem5t ( times has be5 f\nd to be relative4 ,we commonly ?9k t !re are two sep>ate k9ds ( int]val betwe5 two ev5ts1 an int]val 9 space & an int]val 9 "t3 betwe5 y\r dep>ture f ,london & y\r arrival 9 ,ed9burgh1 !re are #djj miles & t5 h\rs4 ,we h already se5 t ano!r obs]v] w judge ! "t diff]5tly2 x is ev5 m obvi\s t he w judge ! di/ance diff]5tly4 ,an obs]v] 9 ! sun w ?9k ! motion ( ! tra9 q trivial1 & w judge t y h travel$ ! di/ance travel$ by ! e>? 9 its orbit & its diurnal rotation4 ,on ! o!r h&1 a flea 9 ! railway c>riage w judge t y h n mov$ at all 9 space1 b h af=d$ him a p]iod ( pleasure :i* he w measure by 8 8prop]0 "t1 n by ,gre5wi* ,obs]vatory4 ,x _c be said t y or ! sun dwell] or ! flea are mi/ak53 ea* is equally ju/ifi$1 & is only wrong if he ascribes an objective validity to 8 subjective measures4 ,! di/ance 9 space betwe5 two ev5ts is1 !re=e1 n 9 itself a physical fact4 ,b1 z we %all see1 !re is a physical fact :i* c be inf]r$ f ! di/ance 9 "t toge!r ) ! di/ance 9 space4 ,?is is :at is call$ ! 8int]val0 9 space-"t4 ,tak+ any two ev5ts 9 ! univ]se1 !re are two diff]5t possibilities z to ! relation betwe5 !m4 ,x may be physically possible = a body to travel s z to be pres5t at bo? ev5ts1 or x may n4 ,?is dep5ds ^u ! fact t no body c travel z fa/ z light4 ,suppose1 = example1 t x 7 possible to s5d out a fla% ( light f ! e>? & h x reflect$ back f ! moon4 ,! "t betwe5 ! s5d+ ( ! fla% & ! return ( ! reflection w\ld be ab\t two & a half seconds4 ,no body c\ld travel s fa/ z to be pres5t on ! e>? dur+ any "p ( ^? two & a half seconds & also pres5t on ! moon at ! mom5t ( ! arrival ( ! fla%1 because 9 ord] to d s ! body w\ld h to travel fa/] ?an light4 ,b !oretically a body c\ld be pres5t on ! e>? at any "t be=e or aft] ^? two & a half seconds & also pres5t on ! moon at ! "t :5 ! fla% arriv$4 ,:5 x is physically impossible = a body to travel s z to be pres5t at bo? ev5ts1 we %all say t ! int]val#b betwe5 ! two ev5ts is 8space-l02 :5 x is physically possible = a body to be pres5t at bo? ev5ts1 we %all say t ! int]val betwe5 ! two ev5ts is 8"t-l40 ,:5 ! int]val is 8space-l10 x is possible = a body to move 9 su* a way t an obs]v] on ! body w judge ! two ev5ts to be simultane\s4 ,9 t case1 ! 8int]val0 betwe5 ! two ev5ts is :at su* an obs]v] w judge to be ! di/ance 9 space betwe5 !m4 ,:5 ! int]val is 8"t-l10 a body c be pres5t at bo? ev5ts2 9 t case1 ! 8int]val0 betwe5 ! two ev5ts is :at an obs]v] on ! body w judge to be ! "t betwe5 !m1 t is to say1 x is 8 8prop]0 "t betwe5 ! two ev5ts4 ,!re is a limit+ case betwe5 ! two1 :5 ! two ev5ts are p>ts ( "o light fla%--or1 z we might say1 :5 ! "o ev5t is ! see+ ( ! o!r4 ,9 t case1 ! int]val betwe5 ! two ev5ts is z]o4 #b ,i %all def9e 8int]val0 9 a mom5t4 ,!re are ?us ?ree cases4 7#a7 ,x may be possible = a ray ( light to be pres5t at bo? ev5ts2 ?is happ5s :5ev] "o ( !m is ! see+ ( ! o!r4 ,9 ?is case ! int]val betwe5 ! two ev5ts is z]o4 7#b7 ,x may happ5 t no body c travel f "o ev5t to ! o!r1 because 9 ord] to d s x w\ld h to travel fa/] ?an light4 ,9 t case1 x is always physically possible = a body to travel 9 su* a way t an obs]v] on ! body w\ld judge ! two ev5ts to be simultane\s4 ,! int]val is :at he w\ld judge to be ! di/ance 9 space betwe5 ! two ev5ts4 ,su* an int]val is call$ 8space-l40 7#c7 ,x may be physically possible = a body to travel s z to be pres5t at bo? ev5ts2 9 t case1 ! int]val betwe5 !m is :at an obs]v] on su* a body w judge to be ! "t betwe5 !m4 ,su* an int]val is call$ 8"t-l40 ,! int]val betwe5 two ev5ts is a physical fact ab\t !m1 n dep5d5t ^u ! p>ticul> circum/ances ( ! obs]v]4 ,!re are two =ms ( ! !ory ( relativity1 ! special & ! g5]al4 ,! =m] is 9 g5]al only approximate1 b is exact at great di/ances f gravitat+ matt]4 ,:5 ! special !ory c be appli$1 ! int]val c be calculat$ :5 we "k ! di/ance 9 space & ! di/ance 9 "t betwe5 ! two ev5ts1 e/imat$ by any obs]v]4 ,if ! di/ance 9 space is great] ?an ! di/ance t light w\ld h travel$ 9 ! "t1 ! sep>ation is space-l4 ,!n ! foll[+ con/ruction gives ! int]val betwe5 ! two ev5ts3 ,draw a l9e ,,ab z long z ! di/ance t light w\ld travel 9 ! "t2 r\nd ,a describe a circle ^: radius is ! di/ance 9 space betwe5 ! two ev5ts2 ?r\gh ,b draw ,,bc p]p5dicul> to ,,ab1 meet+ ! circle 9 ,c4 ,!n ,,bc is ! l5g? ( ! int]val betwe5 ! two ev5ts4 ,illu/ration ,:5 ! di/ance is "t-l1 use ! same figure1 b let ,,ac be n[ ! di/ance t light w\ld travel 9 ! "t1 :ile ,,ab is ! di/ance 9 space betwe5 ! two ev5ts4 ,! int]val betwe5 !m is n[ ! "t t light w\ld take to travel ! di/ance ,,bc4 ,al?\gh ,,ab & ,,ac are diff]5t = diff]5t obs]v]s1 ,,bc is ! same l5g? = all obs]v]s1 subject to corrections made by ! g5]al !ory4 ,x repres5ts ! "o int]val 9 8space-"t0 :i* replaces ! two int]vals 9 space & "t ( ! old] physics4 ,s f>1 ?is notion ( int]val may appe> some:at my/]i\s1 b z we proce$ x w gr[ less s1 & its reason 9 ! nature ( ?+s w gradually em]ge4 ,,*apt] ,v3 ,,space-,,"t ,ev]ybody :o has ev] he>d ( relativity kn[s ! phrase 8space-"t10 & kn[s t ! correct ?+ is to use ?is phrase :5 =m]ly we %\ld h said 8space & "t40 ,b v few p :o are n ma!maticians h any cle> idea ( :at is meant by ?is *ange ( phraseology4 ,be=e deal+ fur!r ) ! special !ory ( relativity1 ,i want to try to convey to ! read] :at is involv$ 9 ! new phrase 8space-"t10 because t is1 f a philosophical & imag9ative po9t ( view1 p]haps ! mo/ important ( all ! novelties t ,e9/e9 has introduc$4 ,suppose y wi% to say :]e & :5 "s ev5t has occurr$--say an explosion on an air%ip--y w h to m5tion f\r quantities1 say ! latitude & longitude1 ! height above ! gr\nd1 & ! "t4 ,accord+ to ! traditional view1 ! fir/ ?ree ( ^! give ! position 9 space1 :ile ! f\r? gives ! position 9 "t4 ,! ?ree quantities t give ! position 9 space may be assign$ 9 all sorts ( ways4 ,y might1 = in/ance1 take ! plane ( ! equator1 ! plane ( ! m]idian ( ,gre5wi*1 & ! plane ( ! n9etie? m]idian1 & say h[ f> ! air%ip 0 f ea* ( ^! planes2 ^! ?ree di/ances w\ld be :at are call$ 8,c>tesian co-ord9ates10 aft] ,desc>tes4 ,y might take any o!r ?ree planes all at "r angles to ea* o!r1 & y w\ld /ill h ,c>tesian co-ord9ates4 ,or y might take ! di/ance f ,london to a po9t v]tically bel[ ! air%ip1 ! direction ( ?is di/ance 7nor!a/1 we/-s\?we/1 or :atev] x might be71 & ! height ( ! air%ip above ! gr\nd4 ,!re are an inf9ite numb] ( su* ways ( fix+ ! position 9 space1 all equally legitimate2 ! *oice betwe5 !m is m]ely "o ( conv5i5ce4 ,:5 p said t space _h ?ree dim5sions1 !y meant j ?is3 t ?ree quantities 7 necess>y 9 ord] to specify ! position ( a po9t 9 space1 b t ! me?od ( assign+ ^! quantities 0 :olly arbitr>y4 ,) reg>d to "t1 ! matt] 0 ?\ght to be q diff]5t4 ,! only arbitr>y elem5ts 9 ! reckon+ ( "t 7 ! unit1 & ! po9t ( "t f :i* ! reckon+ />t$4 ,"o c\ld reckon 9 ,gre5wi* "t1 or 9 ,p>is "t1 or 9 ,new ,york "t2 t made a diff]5ce z to ! po9t ( dep>ture4 ,"o c\ld reckon 9 seconds1 m9utes1 h\rs1 days1 or ye>s2 t 0 a diff]5ce ( unit4 ,bo? ^! 7 obvi\s & trivial matt]s4 ,!re 0 no?+ correspond+ to ! lib]ty ( *oice z to ! me?od ( fix+ position 9 space4 ,&1 9 p>ticul>1 x 0 ?\ght t ! me?od ( fix+ position 9 space & ! me?od ( fix+ position 9 "t c\ld be made :olly indep5d5t ( ea* o!r4 ,= ^! reasons1 p reg>d$ "t & space z q di/9ct4 ,! !ory ( relativity has *ang$ ?is4 ,!re are n[ a numb] ( diff]5t ways ( fix+ position 9 "t1 :i* d n diff] m]ely z to ! unit & ! />t+ po9t4 ,inde$1 z we h se51 if "o ev5t is simultane\s ) ano!r 9 "o reckon+1 x w prec$e x 9 ano!r1 & foll[ x 9 a ?ird4 ,moreov]1 ! space & "t reckon+s are no long] indep5d5t ( ea* o!r4 ,if y alt] ! way ( reckon+ position 9 space1 y may also alt] ! "t int]val betwe5 two ev5ts4 ,if y alt] ! way ( reckon+ "t1 y may also alt] ! di/ance 9 space betwe5 two ev5ts4 ,?us space & "t are no long] indep5d5t1 any m ?an ! ?ree dim5sions ( space are4 ,we /ill ne$ f\r quantities to det]m9e ! position ( an ev5t1 b we _c1 z be=e1 divide (f "o ( ! f\r z q indep5d5t ( ! o!r ?ree4 ,x is n q true to say t !re is no long] any di/9ction betwe5 "t & space4 ,z we h se51 !re are "t-l int]vals & space-l int]vals4 ,b ! di/9ction is ( a diff]5t sort f t :i* 0 =m]ly assum$4 ,!re is no long] a univ]sal "t :i* c be appli$ )\t ambiguity to any "p ( ! univ]se2 !re are only ! v>i\s 8prop]0 times ( ! v>i\s bodies 9 ! univ]se1 :i* agree approximately = two bodies :i* are n 9 rapid relative motion1 b nev] agree exactly except = two bodies :i* are at re/ relatively to ea* o!r4 ,! picture ( ! _w :i* is requir$ = ?is new /ate ( affairs is z foll[s3 ,suppose an ev5t ,e occurs to me1 & simultane\sly a fla% ( light goes out f me 9 all directions4 ,any?+ t happ5s to any body aft] ! light f ! fla% has rea*$ x is def9itely aft] ! ev5t ,e 9 any sy/em ( reckon+ "t4 ,any ev5t any:]e :i* ,i c\ld h se5 be=e ! ev5t ,e occurr$ to me is def9itely be=e ! ev5t ,e 9 any sy/em ( reckon+ "t4 ,b any ev5t :i* happ5$ 9 ! int]v5+ "t is n def9itely ei!r be=e or aft] ! ev5t ,e4 ,to make ! matt] def9ite3 suppose ,i c\ld obs]ve a p]son 9 ,sirius1 & he c\ld obs]ve me4 ,any?+ :i* he does1 & :i* ,i see be=e ! ev5t ,e occurs to me1 is def9itely be=e ,e2 any?+ he does aft] he has se5 ! ev5t ,e is def9itely aft] ,e4 ,b any?+ t he does be=e he sees ! ev5t ,e1 b s t ,i see x aft] ! ev5t ,e has happ5$1 is n def9itely be=e or aft] ,e4 ,s9ce light takes _m ye>s to travel f ,sirius to ! e>?1 ?is gives a p]iod ( twice z _m ye>s 9 ,sirius :i* may be call$ 8contempor>y0 ) ,e1 s9ce ^! ye>s are n def9itely be=e or aft] ,e4 ,dr4 ,a4 ,a4 ,robb1 9 8 ,!ory ( ,"t & ,space1 sugge/s a po9t ( view :i* may or may n be philosophically fundam5tal1 b is at any rate a help 9 und]/&+ ! /ate ( affairs we h be5 describ+4 ,he ma9ta9s t "o ev5t c only be said to be def9itely be=e ano!r if x c influ5ce t o!r 9 "s way4 ,n[ influ5ces spread f a c5t] at v>y+ rates4 ,newspap]s ex]cise an influ5ce emanat+ f ,london at an av]age rate ( ab\t tw5ty miles an h\r--r m = long di/ances4 ,any?+ a man does because ( :at he reads 9 ! newspap] is cle>ly subsequ5t to ! pr9t+ ( ! newspap]4 ,s\nds travel mu* fa/]3 x w\ld be possible to arrange a s]ies ( l\d speak]s along ! ma9 roads1 & h newspap]s %\t$ f ea* to ! next4 ,b telegraph+ is quick]1 & wireless telegraphy travels ) ! velocity ( light1 s t no?+ quick] c ev] be hop$ =4 ,n[ :at a man does 9 consequ5ce ( receiv+ a wireless message he does aft] ! message 0 s5t2 ! mean+ "h is q indep5d5t ( conv5tions z to ! measurem5t ( "t4 ,b any?+ t he does :ile ! message is on its way _c be influ5c$ by ! s5d+ ( ! message1 & _c influ5ce ! s5d] until "s little "t aft] he s5t ! message4 ,t is to say1 if two bodies are widely sep>at$1 nei!r c influ5ce ! o!r except aft] a c]ta9 lapse ( "t2 :at happ5s be=e t "t has elaps$ _c affect ! di/ant body4 ,suppose1 = in/ance1 t "s notable ev5t happ5s on ! sun3 !re is a p]iod ( sixte5 m9utes on ! e>? dur+ :i* no ev5t on ! e>? c h influ5c$ or be5 influ5c$ by ! said notable ev5t on ! sun4 ,?is gives a sub/antial gr\nd = reg>d+ t p]iod ( sixte5 m9utes on ! e>? z nei!r be=e nor aft] ! ev5t on ! sun4 ,! p>adoxes ( ! special !ory ( relativity are only p>adoxes because we are unaccu/om$ to ! po9t ( view1 & 9 ! habit ( tak+ ?+s = grant$ :5 we h no "r to d s4 ,?is is especially true z reg>ds ! measurem5t ( l5g?s4 ,9 daily life1 our way ( measur+ l5g?s is to apply a foot rule or "s o!r measure4 ,at ! mom5t :5 ! foot rule is appli$1 x is at re/ relatively to ! body :i* is be+ measur$4 ,consequ5tly ! l5g? t we arrive at by measurem5t is ! 8prop]0 l5g?1 t is to say1 ! l5g? z e/imat$ by an obs]v] :o %>es ! motion ( ! body4 ,we nev]1 9 ord9>y life1 h to tackle ! problem ( measur+ a body :i* is 9 cont9ual motion4 ,& ev5 if we did1 ! velocities ( visible bodies on ! e>? are s small relatively to ! e>? t ! anomalies dealt ) by ! !ory ( relativity w\ld n appe>4 ,b 9 a/ronomy1 or 9 ! inve/igation ( atomic /ructure1 we are fac$ ) problems :i* _c be tackl$ 9 ?is way4 ,n be+ ,jo%ua1 we _c make ! sun /& /ill :ile we measure x2 if we are to e/imate its size1 we mu/ d s :ile x is 9 motion relatively to u4 ,& simil>ly if y want to e/imate ! size ( an electron1 y h to d s :ile x is 9 rapid motion1 because x nev] /&s /ill = a mom5t4 ,?is is ! sort ( problem ) :i* ! !ory ( relativity is conc]n$4 ,measurem5t ) a foot rule1 :5 x is possible1 gives always ! same result1 because x gives ! 8prop]0 l5g? ( a body4 ,b :5 ?is me?od is n possible1 we f9d t curi\s ?+s happ51 p>ticul>ly if ! body to be measur$ is mov+ v fa/ relatively to ! obs]v]4 ,a figure l ! "o at ! end ( ! previ\s *apt] w help u to und]/& ! /ate ( affairs4 ,illu/ration ,let u suppose t ! body on :i* we wi% to measure l5g?s is mov+ relatively to ourselves1 & t 9 "o second x moves ! di/ance ,,om4 ,let u draw a circle r\nd ,o ^: radius is ! di/ance t light travels 9 a second4 ,?r\gh ,m draw ,,mp p]p5dicul> to ,,om1 meet+ ! circle 9 ,p4 ,?us ,,op is ! di/ance t light travels 9 a second4 ,! ratio ( ,,op to ,,om is ! ratio ( ! velocity ( light to ! velocity ( ! body4 ,! ratio ( ,,op to ,,mp is ! ratio 9 :i* app>5t l5g?s are alt]$ by ! motion4 ,t is to say1 if ! obs]v] judges t two po9ts 9 ! l9e ( motion on ! mov+ body are at a di/ance f ea* o!r repres5t$ by ,,mp1 a p]son mov+ ) ! body w\ld judge t !y 7 at a di/ance repres5t$ 7on ! same scale7 by ,,op4 ,di/ances on ! mov+ body at "r angles to ! l9e ( motion are n affect$ by ! motion4 ,! :ole ?+ is reciprocal2 t is to say1 if an obs]v] mov+ ) ! body 7 to measure l5g?s on ! previ\s obs]v]'s body1 !y w\ld be alt]$ 9 j ! same proportion4 ,:5 two bodies are mov+ relatively to ea* o!r1 l5g?s on ei!r appe> %ort] to ! o!r ?an to !mselves4 ,?is is ! ,fitzg]ald contraction1 :i* 0 fir/ inv5t$ to acc\nt = ! result ( ! ,mi*elson-,morley exp]im5t4 ,b x n[ em]ges naturally f ! fact t ! two obs]v]s d n make ! same judgm5t ( simultaneity4 ,! way 9 :i* simultaneity comes 9 is ?is3 ,we say t two po9ts on a body are a foot ap>t :5 we c simultane\sly apply "o end ( a foot rule to ! "o & ! o!r end to ! o!r4 ,if1 n[1 two p disagree ab\t simultaneity1 & ! body is 9 motion1 !y w obvi\sly get diff]5t results f _! measurem5ts4 ,?us ! tr\ble ab\t "t is at ! bottom ( ! tr\ble ab\t di/ance4 ,! ratio ( ,,op to ,,mp is ! ess5tial ?+ 9 all ^! matt]s4 ,times & l5g?s & masses are all alt]$ 9 ?is proportion :5 ! body conc]n$ is 9 motion relatively to ! obs]v]4 ,x w be se5 t1 if ,,om is v mu* small] ?an ,,op1 t is to say1 if ! body is mov+ v mu* m sl[ly ?an light1 ,,mp & ,,op are v ne>ly equal1 s t ! alt]ations produc$ by ! motion are v small4 ,b if ,,om is ne>ly z l>ge z ,,op1 t is to say1 if ! body is mov+ ne>ly z fa/ z light1 ,,mp becomes v small comp>$ to ,,op1 & ! effects become v great4 ,! app>5t increase ( mass 9 swiftly mov+ p>ticles _h be5 obs]v$1 & ! "r =mula _h be5 f\nd1 be=e ,e9/e9 inv5t$ 8 special !ory ( relativity4 ,9 fact1 ,lor5tz _h arriv$ at ! =mul call$ ! 8,lor5tz trans=mation10 :i* embody ! :ole ma!matical ess5ce ( ! special !ory ( relativity4 ,b x 0 ,e9/e9 :o %[$ t ! :ole ?+ 0 :at we ought to h expect$1 & n a set ( make%ift devices to acc\nt = surpris+ exp]im5tal results4 ,nev]!less1 x mu/ n be =gott5 t exp]im5tal results 7 ! orig9al motive ( ! :ole !ory1 & h rema9$ ! gr\nd = und]tak+ ! trem5d\s logical recon/ruction involv$ 9 ,e9/e9's !ories4 ,we may n[ recapitulate ! reasons :i* h made x necess>y to sub/itute 8space-"t0 = space & "t4 ,! old sep>ation ( space & "t re/$ ^u ! belief t !re 0 no ambiguity 9 say+ t two ev5ts 9 di/ant places happ5$ at ! same "t2 consequ5tly x 0 ?\ght t we c\ld describe ! topography ( ! univ]se at a giv5 in/ant 9 purely spatial t]ms4 ,b n[ t simultaneity has become relative to a p>ticul> obs]v]1 ?is is no long] possible4 ,:at is1 = "o obs]v]1 a description ( ! /ate ( ! _w at a giv5 in/ant1 is1 = ano!r obs]v]1 a s]ies ( ev5ts at v>i\s diff]5t times1 ^: relations are n m]ely spatial b also temporal4 ,= ! same reason1 we are conc]n$ ) ev5ts1 r ?an ) bodies4 ,9 ! old !ory1 x 0 possible to consid] a numb] ( bodies all at ! same in/ant1 & s9ce ! "t 0 ! same = all ( !m x c\ld be ignor$4 ,b n[ we _c d t if we are to obta9 an objective acc\nt ( physical occurr5ces4 ,we mu/ m5tion ! date at :i* a body is to be consid]$1 & ?us we arrive at an 8ev5t10 t is to say1 some?+ :i* happ5s at a giv5 "t4 ,:5 we "k ! "t & place ( an ev5t 9 "o obs]v]'s sy/em ( reckon+1 we c calculate its "t & place accord+ to ano!r obs]v]4 ,b we mu/ "k ! "t z well z ! place1 because we c no long] ask :at is its place = ! new obs]v] at ! 8same0 "t z = ! old obs]v]4 ,!re is no su* ?+ z ! 8same0 "t = diff]5t obs]v]s1 unless !y are at re/ relatively to ea* o!r4 ,we ne$ f\r measurem5ts to fix a position1 & f\r measurem5ts fix ! position ( an ev5t 9 space-"t1 n m]ely ( a body 9 space4 ,?ree measurem5ts are n en\gh to fix any position4 ,t is ! ess5ce ( :at is meant by ! sub/itution ( space-"t = space & "t4 ,,*apt] ,,vi3 ,,! ,,special ,,!ory ,,( ,,relativity ,! special !ory ( relativity arose z a way ( acc\nt+ = ! facts ( electromagnetism4 ,we h "h a some:at curi\s hi/ory4 ,9 ! eighte5? & e>ly n9ete5? c5turies ! !ory ( electricity 0 :olly dom9at$ by ! ,newtonian analogy4 ,two electric *>ges attract ea* o!r if !y are ( diff]5t k9ds1 "o positive & "o negative1 b repel ea* o!r if !y are ( ! same k9d2 9 ea* case1 ! =ce v>ies z ! inv]se squ>e ( ! di/ance1 z 9 ! case ( gravitation4 ,?is =ce 0 conceiv$ z an action at a di/ance1 until ,f>aday1 by a numb] ( rem>kable exp]im5ts1 demon/rat$ ! effect ( ! int]v5+ m$ium4 ,f>aday 0 no ma!matician2 ,cl]k ,maxwell fir/ gave a ma!matical =m to ! results sugge/$ by ,f>aday's exp]im5ts4 ,moreov] ,cl]k ,maxwell gave gr\nds = ?9k+ t light is an electromagnetic ph5om5on1 consi/+ ( electromagnetic waves4 ,! m$ium = ! transmission ( electromagnetic effects c\ld !re=e be tak5 to be ! e!r1 :i* _h long be5 assum$ = ! transmission ( light4 ,! correctness ( ,maxwell's !ory ( light 0 prov$ by ! exp]im5ts ( ,h]tz 9 manufactur+ electromagnetic waves2 ^! exp]im5ts af=d$ ! basis = wireless telegraphy4 ,s f>1 we h a record ( triumphant progress1 9 :i* !ory & exp]im5t alt]nately assume ! lead+ role4 ,at ! "t ( ,h]tz's exp]im5ts1 ! e!r seem$ securely e/abli%$1 & 9 j z /rong a position z any o!r sci5tific hypo!sis n capable ( direct v]ification4 ,b a new set ( facts began to be discov]$1 & gradually ! :ole picture 0 *ang$4 ,! movem5t :i* culm9at$ ) ,h]tz 0 a movem5t = mak+ ev]y?+ cont9u\s4 ,! e!r 0 cont9u\s1 ! waves 9 x 7 cont9u\s1 & x 0 hop$ t matt] w\ld be f\nd to consi/ ( "s cont9u\s /ructure 9 ! e!r4 ,!n came ! discov]y ( ! electron1 a small f9ite unit ( negative electricity1 & ! proton1 a small f9ite unit ( positive electricity4 ,! mo/ mod]n view is t electricity is nev] f\nd except 9 ! =m ( electrons & protons2 all electrons h ! same am\nt ( negative electricity1 & all protons h an exactly equal & opposite am\nt ( positive electricity4 ,x appe>$ t an electric curr5t1 :i* _h be5 ?\ght ( z a cont9u\s ph5om5on1 consi/s ( electrons travel+ "o way & positive ions travel+ ! o!r way2 x is no m /rictly cont9u\s ?an ! /ream ( p go+ up & d[n an escalator4 ,!n came ! discov]y ( quanta1 :i* seems to %[ a fundam5tal discont9uity 9 all su* natural processes z c be measur$ ) suffici5t precision4 ,?us physics has _h to dige/ new facts & face new problems4 ,b ! problems rais$ by ! electron & ! quantum are n ^? t ! !ory ( relativity c solve1 at any rate at pres5t2 z yet1 x ?r[s no light ^u ! discont9uities :i* exi/ 9 nature4 ,! problems solv$ by ! special !ory ( relativity are typifi$ by ! ,mi*elson-,morley exp]im5t4 ,assum+ ! correctness ( ,maxwell's !ory ( electromagnetism1 !re %\ld h be5 c]ta9 discov]able effects ( motion ?r\gh ! e!r2 9 fact1 !re 7 none4 ,!n !re 0 ! obs]v$ fact t a body 9 v rapid motion appe>s to increase its mass2 ! increase is 9 ! ratio ( ,,op to ,,mp 9 ! figure 9 ! prec$+ *apt]4 ,facts ( ?is sort gradually accumulat$1 until x became imp]ative to f9d "s !ory :i* w\ld acc\nt = !m all4 ,maxwell's !ory r$uc$ itself to c]ta9 equations1 kn[n z 8,maxwell's equations40 ,?r\gh all ! revolutions :i* physics has und]gone 9 ! la/ fifty ye>s1 ^! equations h rema9$ /&+2 inde$ !y h cont9ually gr[n 9 importance z well z 9 c]ta9ty--= ,maxwell's argum5ts 9 _! favor 7 s %aky t ! correctness ( 8 results mu/ almo/ be ascrib$ to intuition4 ,n[ ^! equations 71 ( c\rse1 obta9$ f exp]im5ts 9 t]re/rial laboratories1 b !re 0 a tacit assumption t ! motion ( ! e>? ?r\gh ! e!r c\ld be ignor$4 ,9 c]ta9 cases1 su* z ! ,mi*elson-,morley exp]im5t1 ?is ought n to h be5 possible )\t measurable error2 b x turn$ out to be always possible4 ,physici/s 7 fac$ ) ! odd difficulty t ,maxwell's equations 7 m accurate ?an !y %\ld be4 ,a v simil> difficulty 0 expla9$ by ,galileo at ! v beg9n+ ( mod]n physics4 ,mo/ p ?9k t if y let a weight drop x w fall v]tically4 ,b if y try ! exp]im5t 9 ! cab9 ( a mov+ %ip1 ! weight falls1 9 relation to ! cab91 j z if ! %ip 7 at re/2 = in/ance1 if x />ts f ! middle ( ! ceil+ x w drop onto ! middle ( ! floor4 ,t is to say1 f ! po9t ( view ( an obs]v] on ! %ore x does n fall v]tically1 s9ce x %>es ! motion ( ! %ip4 ,s long z ! %ip's motion is /eady1 ev]y?+ goes on inside ! %ip z if ! %ip 7 n mov+4 ,galileo expla9$ h[ ?is happ5s1 to ! great indignation ( ! disciples ( ,ari/otle4 ,9 or?odox physics1 :i* is d]iv$ f ,galileo1 a uni=m motion 9 a /raight l9e has no discov]able effects4 ,?is 01 9 its day1 z a/oni%+ a =m ( relativity z t ( ,e9/e9 is to u4 ,e9/e91 9 ! special !ory ( relativity1 set to "w to %[ h[ electromagnetic ph5om5a c\ld be unaffect$ by uni=m motion ?r\gh ! e!r if !re be an e!r4 ,?is 0 a m difficult problem1 :i* c\ld n be solv$ by m]ely adh]+ to ! pr9ciples ( ,galileo4 ,! really difficult ef=t requir$ = solv+ ?is problem 0 9 reg>d to "t4 ,x 0 necess>y to introduce ! notion ( 8prop]0 "t :i* we h already consid]$1 & to ab&on ! old belief 9 "o univ]sal "t4 ,! quantitative laws ( electromagnetic ph5om5a are express$ 9 ,maxwell's equations1 & ^! equations are f\nd to be true = any obs]v]1 h[ev] he may be mov+4#c ,x is a /raight-=w>d ma!matical problem to f9d out :at diff]5ces !re mu/ be betwe5 ! measures appli$ by "o obs]v] & ! measures appli$ by ano!r1 if1 9 spite ( _! relative motion1 !y are to f9d ! same equations v]ifi$4 ,! answ] is conta9$ 9 ! 8,lor5tz trans=mation10 f\nd z a =mula by ,lor5tz1 b int]pret$ & made intelligible by ,e9/e94 ,! ,lor5tz trans=mation tells u :at e/imate ( di/ances & p]iods ( "t w be made by an obs]v] ^: relative motion is kn[n1 :5 we are giv5 ^? ( ano!r obs]v]4 ,we may suppose t y are 9 a tra9 on a railway :i* travels due ea/4 ,y h be5 travel+ = a "t :i*1 by ! clocks at ! /ation f :i* y />t$1 is t4 ,at a di/ance x f y\r />t+ po9t1 z measur$ by ! p on ! l9e1 an ev5t occurs at ?is mom5t--say ! l9e is /ruck by lightn+4 ,y h be5 travel+ all ! "t ) a uni=m velocity v4 ,! "q is3 ,h[ f> f y w y judge t ?is ev5t has tak5 place1 & h[ long aft] y />t$ w x be by y\r wat*1 assum+ t y\r wat* is correct f ! po9t ( view ( an obs]v] on ! tra98 #c ,s long z he has no consid]able accel]ation4 ,! treatm5t ( accel]ation belongs to ! g5]al !ory ( relativity4 ,our solution ( ?is problem has to satisfy c]ta9 conditions4 ,x has to br+ out ! result t ! velocity ( light is ! same = all obs]v]s1 h[ev] !y may be mov+4 ,& x has to make physical ph5om5a--9 p>ticul>1 ^? ( electromagnetism--obey ! same laws = diff]5t obs]v]s1 h[ev] !y may f9d _! measures ( di/ances & times affect$ by _! motion4 ,& x has to make all su* effects on measurem5t reciprocal4 ,t is to say1 if y are 9 a tra9 & y\r motion affects y\r e/imate ( di/ances outside ! tra91 !re mu/ be an exactly simil> *ange 9 ! e/imate :i* p outside ! tra9 make ( di/ances inside x4 ,^! conditions are suffici5t to det]m9e ! solution ( ! problem1 b ! me?od ( obta9+ ! solution _c be expla9$ )\t m ma!matics ?an is possible 9 ! pres5t "w4 ,be=e deal+ ) ! matt] 9 g5]al t]ms1 let u take an example4 ,let u suppose t y are 9 a tra9 on a long /raight railway1 & t y are travel+ at ?ree-fif?s ( ! velocity ( light4 ,suppose t y measure ! l5g? ( y\r tra91 & f9d t x is a hundr$ y>ds4 ,suppose t ! p :o cat* a glimpse ( y z y pass succe$1 by skilful sci5tific me?ods1 9 tak+ obs]vations :i* enable !m to calculate ! l5g? ( y\r tra94 ,if !y d _! "w correctly1 !y w f9d t x is eighty y>ds long4 ,ev]y?+ 9 ! tra9 w seem to !m %ort] 9 ! direction ( ! tra9 ?an x does to y4 ,d9n] plates1 :i* y see z ord9>y circul> plates1 w look to ! outsid] z if !y 7 oval3 !y w seem only f\r-fif?s z broad 9 ! direction 9 :i* ! tra9 is mov+ z 9 ! direction ( ! bread? ( ! tra94 ,& all ?is is reciprocal4 ,suppose y see out ( ! w9d[ a man c>ry+ a fi%+ rod :i*1 by 8 measurem5t1 is fifte5 feet long4 ,if he is hold+ x upright1 y w see x z he does2 s y w if he is hold+ x horizontally at "r angles to ! railway4 ,b if he is po9t+ x along ! railway1 x w seem to y to be only twelve feet long4 ,all l5g?s 9 ! direction ( motion are dim9i%$ by tw5ty p] c5t1 bo? = ^? :o look into ! tra9 f outside & = ^? :o look out ( ! tra9 f inside4 ,b ! effects 9 reg>d to "t are ev5 m /range4 ,?is matt] has be5 expla9$ ) almo/ ideal lucidity by ,edd+ton 9 ,space1 ,"t & ,gravitation4 ,he supposes an aviator travel+1 relatively to ! e>?1 at a spe$ ( #afa1jjj miles a second1 & he says3 8,if we obs]v$ ! aviator c>efully we %\ld inf] t he 0 unusually sl[ 9 8 movem5ts2 & ev5ts 9 ! conveyance mov+ ) him w\ld be simil>ly ret>d$--z ?\gh "t _h =gott5 to g on4 ,8 cig> la/s twice z long z "o ( ours4 ,i said #8inf]' delib]ately2 we %\ld see a /ill m extravagant sl[+ d[n ( "t2 b t is easily expla9$1 because ! aviator is rapidly increas+ 8 di/ance f u & ! light impressions take long] & long] to rea* u4 ,! m mod]ate ret>dation ref]r$ to rema9s aft] we h all[$ = ! "t ( transmission ( light4 ,b "h aga9 reciprocity comes 91 because 9 ! aviator's op9ion x is we :o are travel+ at #afa1jjj miles a second pa/ him2 & :5 he has made all all[ances1 he f9ds t x is we :o are sluggi%4 ,our cig> la/s twice z long z 840 ,:at a situation = envy6 ,ea* man ?9ks t ! o!r's cig> la/s twice z long z 8 own4 ,x may1 h[ev]1 be "s consolation to reflect t ! o!r man's visits to ! d5ti/ also la/ twice z long4 ,?is "q ( "t is r intricate1 ow+ to ! fact t ev5ts :i* "o man judges to be simultane\s ano!r consid]s to be sep>at$ by a lapse ( "t4 ,9 ord] to try to make cle> h[ "t is affect$1 ,i %all rev]t to our railway tra9 travel+ due ea/ at a rate ?ree-fif?s ( t ( light4 ,= ! sake ( illu/ration1 ,i assume t ! e>? is l>ge & flat1 in/ead ( small & r\nd4 ,if we take ev5ts :i* happ5 at a fix$ po9t on ! e>?1 & ask ourselves h[ long aft] ! beg9n+ ( ! j\rney !y w seem to be to ! travel]1 ! answ] is t !re w be t ret>dation t ,edd+ton speaks (1 :i* means 9 ?is case t :at seems an h\r 9 ! life ( ! /ation>y p]son is judg$ to be an h\r & a qu>t] by ! man :o obs]ves him f ! tra94 ,reciprocally1 :at seems an h\r 9 ! life ( ! p]son 9 ! tra9 is judg$ by ! man obs]v+ him f outside to be an h\r & a qu>t]4 ,ea* makes p]iods ( "t obs]v$ 9 ! life ( ! o!r a qu>t] z long aga9 z !y are to ! p]son :o lives ?r\gh !m4 ,! proportion is ! same 9 reg>d to times z 9 reg>d to l5g?s4 ,b :51 in/ead ( comp>+ ev5ts at ! same place on ! e>?1 we comp>e ev5ts at widely sep>at$ places1 ! results are /ill m odd4 ,let u n[ take all ! ev5ts along ! railway :i*1 f ! po9t ( view ( a p]son :o is /ation>y on ! e>?1 happ5 at a giv5 in/ant1 say ! in/ant :5 ! obs]v] 9 ! tra9 passes ! /ation>y p]son4 ,( ^! ev5ts1 ^? :i* occur at po9ts t[>ds :i* ! tra9 is mov+ w seem to ! travel] to h already happ5$1 :ile ^? :i* occur at po9ts beh9d ! tra9 w1 = him1 be /ill 9 ! future4 ,:5 ,i say t ev5ts 9 ! =w>d direction w seem to h already happ5$1 ,i am say+ some?+ n /rictly accurate1 because he w n yet h se5 !m2 b :5 he does see !m1 he w1 aft] all[+ = ! velocity ( light1 come to ! conclusion t !y mu/ h happ5$ be=e ! mom5t 9 "q4 ,an ev5t :i* happ5s 9 ! =w>d direction along ! railway1 & :i* ! /ation>y obs]v] judges to be n[ 7or r1 w judge to h be5 n[ :5 he comes to "k ( x71 if x occurs at a di/ance along ! l9e :i* light c\ld travel 9 a second1 w be judg$ by ! travel] to h occurr$ ?ree-qu>t]s ( a second ago4 ,if x occurs at a di/ance f ! two obs]v]s :i* ! man on ! e>? judges t light c\ld travel 9 a ye>1 ! travel] w judge 7:5 he comes to "k ( x7 t x occurr$ n9e mon?s e>li] ?an ! mom5t :5 he pass$ ! e>? dwell]4 ,& g5]ally1 he w ante-date ev5ts 9 ! =w>d direction along ! railway by ?ree-qu>t]s ( ! "t t x w\ld take light to travel f !m to ! man on ! e>? :om he is j pass+1 & :o holds t ^! ev5ts are happ5+ n[--or r1 w hold t !y happ5$ n[ :5 ! light f !m rea*es him4 ,ev5ts happ5+ on ! railway beh9d ! tra9 w be po/-dat$ by an exactly equal am\nt4 ,we h ?us a two-fold correction to make 9 ! date ( an ev5t :5 we pass f ! t]re/rial obs]v] to ! travel]4 ,we mu/ fir/ take five-f\r?s ( ! "t z e/imat$ by ! e>? dwell]1 & !n subtract ?ree-f\r?s ( ! "t t x w\ld take light to travel f ! ev5t 9 "q to ! e>? dwell]4 ,take "s ev5t 9 a di/ant "p ( ! univ]se1 :i* becomes visible to ! e>? dwell] & ! travel] j z !y pass ea* o!r4 ,! e>? dwell]1 if he kn[s h[ f> (f ! ev5t occurr$1 c judge h[ long ago x occurr$1 s9ce he kn[s ! spe$ ( light4 ,if ! ev5t occurr$ 9 ! direction t[>ds :i* ! travel] is mov+1 ! travel] w inf] t x happ5$ twice z long ago z ! e>? dwell] ?9ks4 ,b if x occurr$ 9 ! direction f :i* he has come1 he w argue t x happ5$ only half z long ago z ! e>? dwell] ?9ks4 ,if ! travel] moves at a diff]5t spe$1 ^! proportions w be diff]5t4 ,suppose n[ t 7z sometimes occurs7 two new />s h sudd5ly fl>$ up1 & h j become visible to ! travel] & to ! e>? dwell] :om he is pass+4 ,let "o ( !m be 9 ! direction t[>ds :i* ! tra9 is travel+1 ! o!r 9 ! direction f :i* x has come4 ,suppose t ! e>? dwell] is able1 9 "s way1 to e/imate ! di/ance ( ! two />s1 & to inf] t light takes fifty ye>s to rea* him f ! "o 9 ! direction t[>ds :i* ! travel] is mov+1 & "o hundr$ ye>s to rea* him f ! o!r4 ,he w !n argue t ! explosion :i* produc$ ! new /> 9 ! =w>d direction occurr$ fifty ye>s ago1 :ile ! explosion :i* produc$ ! o!r new /> occurr$ a hundr$ ye>s ago4 ,! travel] w exactly rev]se ^! figures3 he w inf] t ! =w>d explosion occurr$ a hundr$ ye>s ago1 & ! backw>d "o fifty ye>s ago4 ,i assume t bo? argue correctly on correct physical data4 ,9 fact1 bo? are "r1 unless !y imag9e t ! o!r mu/ be wrong4 ,x %\ld be not$ t bo? w h ! same e/imate ( ! velocity ( light1 because _! e/imates ( ! di/ances ( ! two new />s w v>y 9 exactly ! same proportion z _! e/imates ( ! times s9ce ! explosions4 ,inde$1 "o ( ! ma9 motives ( ?is :ole !ory is to secure t ! velocity ( light %all be ! same = all obs]v]s1 h[ev] !y may be mov+4 ,?is fact1 e/abli%$ by exp]im5t1 0 incompatible ) ! old !ories1 & made x absolutely necess>y to admit some?+ />tl+4 ,! !ory ( relativity is j z little />tl+ z is compatible ) ! facts4 ,inde$1 aft] a "t1 x ceases to seem />tl+ at all4 ,!re is ano!r feature ( v great importance 9 ! !ory we h be5 consid]+1 & t is t1 al?\gh di/ances & times v>y = diff]5t obs]v]s1 we c d]ive f !m ! quantity call$ 8int]val10 :i* is ! same = all obs]v]s4 ,! 8int]val10 9 ! special !ory ( relativity1 is obta9$ z foll[s3 ,take ! squ>e ( ! di/ance betwe5 two ev5ts1 & ! squ>e ( ! di/ance travel$ by light 9 ! "t betwe5 ! two ev5ts2 subtract ! less] ( ^! f ! great]1 & ! result is def9$ z ! squ>e ( ! int]val betwe5 ! ev5ts4 ,! int]val is ! same = all obs]v]s1 & repres5ts a g5u9e physical relation betwe5 ! two ev5ts1 :i* ! "t & ! di/ance d n4 ,we h already giv5 a geometrical con/ruction = ! int]val at ! end ( ,*apt] ,,iv2 ?is gives ! same result z ! above rule4 ,! int]val is 8"t-l0 :5 ! "t betwe5 ! ev5ts is long] ?an light w\ld take to travel f ! place ( ! "o to ! place ( ! o!r2 9 ! contr>y case x is 8space-l40 ,:5 ! "t betwe5 ! two ev5ts is exactly equal to ! "t tak5 by light to travel f "o to ! o!r1 ! int]val is z]o2 ! two ev5ts are !n situat$ on p>ts ( "o light ray1 unless no light happ5s to be pass+ t way4 ,:5 we come to ! g5]al !ory ( relativity1 we %all h to g5]alize ! notion ( int]val4 ,! m deeply we p5etrate into ! /ructure ( ! _w1 ! m important ?is concept becomes2 we are tempt$ to say t x is ! reality ( :i* di/ances & p]iods ( "t are confus$ repres5tations4 ,! !ory ( relativity has alt]$ our view ( ! fundam5tal /ructure ( ! _w2 t is ! s\rce bo? ( its difficulty & ( its importance4 ,! rema9d] ( ?is *apt] may be omitt$ by read]s :o h n ev5 ! mo/ elem5t>y acqua9tance ) geometry or algebra4 ,b = ! b5efit ( ^? ^: education has n be5 entirely neglect$1 ,i w add a few explanations ( ! g5]al =mula ( :i* ,i h hi!rto giv5 only p>ticul> examples4 ,! g5]al =mula 9 "q is ! 8,lor5tz trans=mation10 :i* tells1 :5 "o body is mov+ 9 a giv5 mann] relatively to ano!r1 h[ to inf] ! measures ( l5g?s & times appropriate to ! "o body f ^? appropriate to ! o!r4 ,be=e giv+ ! algebraical =mul1 ,i w give a geometrical con/ruction4 ,z be=e1 we w suppose t !re are two obs]v]s1 :om we w call ,o & ,o1 "o ( :om is /ation>y on ! e>? :ile ! o!r is travel+ at a uni=m spe$ along a /raight railway4 ,at ! beg9n+ ( ! "t consid]$1 ! two obs]v]s 7 at ! same po9t ( ! railway1 b n[ !y are sep>at$ by a c]ta9 di/ance4 ,a fla% ( lightn+ /rikes a po9t ,x on ! railway1 & ,o judges t at ! mom5t :5 ! fla% takes place ! obs]v] 9 ! tra9 has rea*$ ! po9t ,o4 ,! problem is3 h[ f> w ,o judge t he is f ! fla%1 & h[ long aft] ! beg9n+ ( ! j\rney 7:5 he 0 at ,o7 w he judge t ! fla% took place8 ,we are suppos$ to "k ,os e/imates1 & we want to calculate ^? ( ,o4 ,illu/ration ,9 ! "t t1 accord+ to ,o1 has elaps$ s9ce ! beg9n+ ( ! j\rney1 let ,,oc be ! di/ance t light w\ld h travel$ along ! railway4 ,describe a circle ab\t ,o1 ) ,,oc z radius1 & ?r\gh ,o draw a p]p5dicul> to ! railway1 meet+ ! circle 9 ,d4 ,on ,,od take a po9t ,y su* t ,,oy is equal to ,,ox 7,x is ! po9t ( ! railway :]e ! lightn+ /rikes74 ,draw ,,ym p]p5dicul> to ! railway1 & ,,os p]p5dicul> to ,,od4 ,let ,,ym & ,,os meet 9 ,s4 ,also let ,,d produc$ & ,,os produc$ meet 9 ,r4 ,?r\gh ,x & ,c draw p]p5dicul>s to ! railway meet+ ,,os produc$ 9 ,q & ,z respectively4 ,!n ,,rq 7z measur$ by ,o7 is ! di/ance at :i* ,o w believe himself to be f ! fla%1 n ,o,x z x w\ld be accord+ to ! old view4 ,& :]eas ,o ?9ks t1 9 ! "t f ! beg9n+ ( ! j\rney to ! fla%1 light w\ld travel a di/ance ,,oc1 ,o ?9ks t ! "t elaps$ is t requir$ = light to travel ! di/ance ,,sz 7z measur$ by ,o74 ,! int]val z measur$ by ,o is got by subtract+ ! squ>e on ,,ox f ! squ>e on ,,oc2 ! int]val z measur$ by ,o is got by subtract+ ! squ>e on ,,rq f ! squ>e on ,,sz4 ,a little v elem5t>y geometry %[s t ^! are equal4 ,! algebraical =mul embodi$ 9 ! above con/ruction are z foll[s3 ,f ! po9t ( view ( ,o1 let an ev5t occur at a di/ance x along ! railway1 & at a "t t aft] ! beg9n+ ( ! j\rney 7:5 ,o 0 at ,o74 ,f ! po9t ( view ( ,o1 let ! same ev5t occur at a di/ance x along ! railway1 & at a "t t aft] ! beg9n+ ( ! j\rney4 ,let c be ! velocity ( light1 & v ! velocity ( ,o relative to ,o4 ,put c ------------------------ 7c - v7 ,!n x 7x - vt7 7 vx 7 t 7t - ----------7 7 c 7 ,?is is ! ,lor5tz trans=mation1 f :i* ev]y?+ 9 ?is *apt] c be d$uc$4 ,,*apt] ,,vii3 ,,int]vals ,,9 ,,space-,,"t ,! special !ory ( relativity1 :i* we h be5 consid]+ hi!rto1 solv$ completely a c]ta9 def9ite problem3 to acc\nt = ! exp]im5tal fact t1 :5 two bodies are 9 uni=m relative motion1 all ! laws ( physics1 bo? ^? ( ord9>y dynamics & ^? connect$ ) electricity & magnetism1 are exactly ! same = ! two bodies4 8,uni=m0 motion1 "h1 means motion 9 a /raight l9e ) con/ant velocity4 ,b al?\gh "o problem 0 solv$ by ! special !ory1 ano!r 0 imm$iately sugge/$3 :at if ! motion ( ! two bodies is n uni=m8 ,suppose1 = in/ance1 t "o is ! e>? :ile ! o!r is a fall+ /one4 ,! /one has an accel]at$ motion3 x is cont9ually fall+ fa/] & fa/]4 ,no?+ 9 ! special !ory enables u to say t ! laws ( physical ph5om5a w be ! same = an obs]v] on ! /one z = "o on ! e>?4 ,?is is p>ticul>ly awkw>d1 z ! e>? itself is1 9 an ext5d$ s5se1 a fall+ body3 ,x has at e mom5t an accel]ation#d t[>ds ! sun1 :i* makes x g r\nd ! sun in/ead ( mov+ 9 a /raight l9e4 ,z our k ( physics is d]iv$ f exp]im5ts on ! e>?1 we _c re/ satisfi$ ) a !ory 9 :i* ! obs]v] is suppos$ to h no accel]ation4 ,! g5]al !ory ( relativity removes ?is re/riction1 & all[s ! obs]v] to be mov+ 9 any way1 /raight or crook$1 uni=mly or ) an accel]ation4 ,9 ! c\rse ( remov+ ! re/riction1 ,e9/e9 0 l$ to 8 new law ( gravitation1 :i* we %all consid] pres5tly4 ,! "w 0 extraord9>ily difficult1 & occupi$ him = t5 ye>s4 ,! special !ory dates f #aije1 ! g5]al !ory f #aiae4 #d ,?is does n mean t its velocity is increas+1 b t x is *ang+ its direction4 ,! only sort ( motion :i* is call$ 8unaccel]at$0 is motion ) uni=m velocity 9 a /raight l9e4 ,x is obvi\s f exp]i5ces ) :i* we are all famili> t an accel]at$ motion is mu* m difficult to deal ) ?an a uni=m "o4 ,:5 y are 9 a tra9 :i* is travel+ /eadily1 ! motion is n noticeable s long z y d n look out ( ! w9d[2 b :5 ! brakes are appli$ sudd5ly y are precipitat$ =w>ds1 & y become aw>e t some?+ is happ5+ )\t hav+ to notice any?+ outside ! tra94 ,simil>ly 9 a lift ev]y?+ seems ord9>y :ile x is mov+ /eadily1 b at />t+ & /opp+1 :5 its motion is accel]at$1 y h odd s5sations 9 ! pit ( ! /oma*4 7,we call a motion 8accel]at$0 :5 x is gett+ sl[] z well z :5 x is gett+ quick]2 :5 x is gett+ sl[] ! accel]ation is negative47 ,! same ?+ applies to dropp+ a weight 9 ! cab9 ( a %ip4 ,s long z ! %ip is mov+ uni=mly1 ! weight w behave1 relatively to ! cab91 j z if ! %ip 7 at re/3 if x />ts f ! middle ( ! ceil+1 x w hit ! middle ( ! floor4 ,b if !re is an accel]ation ev]y?+ is *ang$4 ,if ! boat is increas+ its spe$ v rapidly1 ! weight w seem to an obs]v] 9 ! cab9 to fall 9 a curve direct$ t[>ds ! /]n2 if ! spe$ is be+ rapidly dim9i%$1 ! curve w be direct$ t[>ds ! b[4 ,all ^! facts are famili>1 & !y l$ ,galileo & ,newton to reg>d an accel]at$ motion z some?+ radically diff]5t1 9 its own nature1 f a uni=m motion4 ,b ?is di/9ction c\ld only be ma9ta9$ by reg>d+ motion z absolute1 n relative4 ,if all motion is relative1 ! e>? is accel]at$ relatively to ! lift j z truly z ! lift relatively to ! e>?4 ,yet ! p on ! gr\nd h no s5sations 9 ! pits ( _! /oma*s :5 ! lift />ts to g up4 ,?is illu/rates ! difficulty ( our problem4 ,9 fact1 ?\gh few physici/s 9 mod]n times h believ$ 9 absolute motion1 ! te*nique ( ma!matical physics /ill embodi$ ,newton's belief 9 x1 & a revolution 9 me?od 0 requir$ to obta9 a te*nique free f ?is assumption4 ,?is revolution 0 accompli%$ 9 ,e9/e9's g5]al !ory ( relativity4 ,x is some:at optional :]e we beg9 9 expla9+ ! new ideas :i* ,e9/e9 introduc$1 b p]haps we %all d be/ by tak+ ! conception ( 8int]val40 ,?is conception1 z x appe>s 9 ! special !ory ( relativity1 is already a g5]alization ( ! traditional notion ( di/ance 9 space & "t2 b x is necess>y to g5]alize x /ill fur!r4 ,h[ev]1 x is necess>y fir/ to expla9 a c]ta9 am\nt ( hi/ory1 & = ?is purpose we mu/ g back z f> z ,py?agoras4 ,py?agoras1 l _m ( ! greate/ *>act]s 9 hi/ory1 p]haps nev] exi/$3 he is a semi-my?ical "*1 :o comb9$ ma!matics & prie/craft 9 unc]ta9 proportions4 ,i %all1 h[ev]1 assume t he exi/$1 & t he discov]$ ! !orem attribut$ to him4 ,he 0 r\ghly a contempor>y ( ,confucius & ,buddha2 he f\nd$ a religi\s sect1 :i* ?\ght x wick$ to eat beans1 & a s*ool ( ma!maticians1 :o took a p>ticul> int]e/ 9 "r-angl$ triangles4 ,! !orem ( ,py?agoras 7! =ty-sev5? proposition ( ,euclid7 /ates t ! sum ( ! squ>es on ! two %ort] sides ( a "r-angl$ triangle is equal to ! squ>e on ! side opposite ! "r angle4 ,no proposition 9 ! :ole ( ma!matics has _h su* a di/+ui%$ hi/ory4 ,we all le>n$ to 8prove0 x 9 y\?4 ,x is true t ! 8pro(0 prov$ no?+1 & t ! only way to prove x is by exp]im5t4 ,x is also ! case t ! proposition is n q true--x is only approximately true4 ,b ev]y?+ 9 geometry1 & subsequ5tly 9 physics1 has be5 d]iv$ f x by successive g5]alizations4 ,! late/ ( ^! g5]alizations is ! g5]al !ory ( relativity4 ,! !orem ( ,py?agoras 0 itself1 9 all probability1 a g5]alization ( an ,egyptian rule ( ?umb4 ,9 ,egypt1 x _h be5 kn[n = ages t a triangle ^: sides are #c1 #d1 & #e units ( l5g? is a "r-angl$ triangle2 ! ,egyptians us$ ?is k practically 9 measur+ _! fields4 ,n[ if ! sides ( a triangle are #c1 #d1 & #e in*es1 ! squ>es on ^! sides w conta9 respectively #i1 #af1 & #be squ>e in*es2 & #i & #af add$ toge!r make #be4 ,?ree times ?ree is writt5 8#c02 f\r times f\r1 8#d02 five times five1 8#e40 ,s t we h #c #d #e4 ,x is suppos$ t ,py?agoras notic$ ?is fact1 aft] he _h le>n$ f ! ,egyptians t a triangle ^: sides are #c1 #d & #e has a "r angle4 ,he f\nd t ?is c\ld be g5]aliz$1 & s arriv$ at 8 fam\s !orem3 ,9 a "r-angl$ triangle1 ! squ>e on ! side opposite ! "r angle is equal to ! sum ( ! squ>es on ! o!r two sides4 ,illu/ration ,simil>ly 9 ?ree dim5sions3 if y take a "r-angl$ solid block1 ! squ>e on ! diagonal 7! dott$ l9e 9 ! figure7 is equal to ! sum ( ! squ>es on ! ?ree sides4 ,?is is z f> z ! anci5ts got 9 ?is matt]4 ,illu/ration ,! next /ep ( importance is due to ,desc>tes1 :o made ! !orem ( ,py?agoras ! basis ( 8 me?od ( analytical geometry4 ,suppose y wi% to map out sy/ematically all ! places on a pla9--we w suppose x small en\gh to make x possible to ignore ! fact t ! e>? is r\nd4 ,we w suppose t y live 9 ! middle ( ! pla94 ,"o ( ! simple/ ways ( describ+ ! position ( a place is to say3 />t+ f my h\se1 g fir/ su* & su* a di/ance ea/1 !n su* & su* a di/ance nor? 7or x may be we/ 9 ! fir/ case1 & s\? 9 ! second74 ,?is tells y exactly :]e ! place is4 ,9 ! rectangul> cities ( ,am]ica1 x is ! natural me?od to adopt3 9 ,new ,york y w be told to g s _m blocks ea/ 7or we/7 & !n s _m blocks nor? 7or s\?74 ,! di/ance y h to g ea/ is call$ x1 & ! di/ance y h to g nor? is call$ y4 7,if y h to g we/1 x is negative2 if y h to g s\?1 y is negative47 ,let ,o be y\r />t+ po9t 7! 8orig9072 let ,,om be ! di/ance y g ea/1 & ,,mp ! di/ance y g nor?4 ,h[ f> are y f home 9 a direct l9e :5 y rea* ,p8 ,! !orem ( ,py?agoras gives ! answ]4 ,! squ>e on ,,op is ! sum ( ! squ>es on ,,om & ,,mp4 ,if ,,om is f\r miles1 & ,,mp is ?ree miles1 ,,op is #e miles4 ,if ,,om is #ab miles & ,,mp is #e miles1 ,,op is #ac miles1 because #ab #e #ac4 ,s t if y adopt ,desc>tes' me?od ( mapp+1 ! !orem ( ,py?agoras is ess5tial 9 giv+ y ! di/ance f place to place4 ,9 ?ree dim5sions ! ?+ is exactly analog\s4 ,suppose t1 in/ead ( want+ m]ely to fix positions on ! pla91 y want to fix /ations = captive balloons above x1 y w !n h to add a ?ird quantity1 ! height at :i* ! balloon is to be4 ,if y call ! height z1 & if r is ! direct di/ance f ,o to ! balloon1 y w h r x y z1 & f ?is y c calculate r :5 y "k x1 y1 & z4 ,= example1 if y c get to ! balloon by go+ #ab miles ea/1 #d miles nor?1 & !n #c miles up1 y\r di/ance f ! balloon 9 a /raight l9e is #ac miles1 because #ab #ab #add1 #d #d #af1 #c #c #i1 #add #af #i #afi #ac #ac4 ,b n[ suppose t1 in/ead ( tak+ a small piece ( ! e>?'s surface :i* c be reg>d$ z flat1 y consid] mak+ a map ( ! _w4 ,an accurate map ( ! _w on flat pap] is impossible4 ,a globe c be accurate1 9 ! s5se t ev]y?+ is produc$ to scale1 b a flat map _c be4 ,i am n talk+ ( practical difficulties1 ,i am talk+ ( a !oretical impossibility4 ,= example3 ! nor!rn halves ( ! m]idian ( ,gre5wi* & ! n9etie? m]idian ( we/ longitude1 toge!r ) ! piece ( ! equator betwe5 !m1 make a triangle ^: sides are all equal & ^: angles are all "r angles4 ,on a flat surface1 a triangle ( t sort w\ld be impossible4 ,on ! o!r h&1 x is possible to make a squ>e on a flat surface1 b on a sph]e x is impossible4 ,suppose y try on ! e>?3 walk #ajj miles we/1 !n #ajj miles nor?1 !n #ajj miles ea/1 !n #ajj miles s\?4 ,y might ?9k ?is w\ld make a squ>e1 b x w\ldn't1 because y w\ld n at ! end h come back to y\r />t+ po9t4 ,if y h "t1 y may conv9ce y\rself ( ?is by exp]im5t4 ,if n1 y c easily see t x mu/ be s4 ,:5 y are ne>] ! pole1 #ajj miles takes y ?r\gh m longitude ?an :5 y are ne>] ! equator1 s t 9 do+ y\r #ajj miles ea/ 7if y are 9 ! nor!rn hemisph]e7 y get to a po9t fur!r ea/ ?an t f :i* y />t$4 ,z y walk due s\? aft] ?is1 y rema9 fur!r ea/ ?an y\r />t+ po9t1 & end up at a diff]5t place f t 9 :i* y began4 ,suppose1 to take ano!r illu/ration1 t y />t on ! equator #d1jjj miles ea/ ( ! ,gre5wi* m]idian2 y travel till y rea* ! m]idian1 !n y travel nor?w>ds along x = #d1jjj miles1 ?r\gh ,gre5wi* & up to ! neighborhood ( ! ,%etl& ,isl&s2 !n y travel ea/w>d = #d1jjj miles1 & !n #d1jjj miles s\?4 ,?is w take y to ! equator at a po9t #d1jjj miles fur!r ea/ ?an ! po9t f :i* y />t$4 ,9 a s5se1 :at we h j be5 say+ is n q fair1 because1 except on ! equator1 travel+ due ea/ is n ! %orte/ r\te f a place to ano!r place due ea/ ( x4 ,a %ip travel+ 7say7 f ,new ,york to ,lisbon1 :i* is ne>ly due ea/1 w />t by go+ a c]ta9 di/ance nor?w>d4 ,x w sail on a 8great circle10 t is to say1 a circle ^: c5tre is ! c5tre ( ! e>?4 ,?is is ! ne>e/ approa* to a /raight l9e t c be drawn on ! surface ( ! e>?4 ,m]idians ( longitude are great circles1 & s is ! equator1 b ! o!r p>allels ( latitude are n4 ,we ought1 !re=e1 to h suppos$ t1 :5 y rea* ! ,%etl& ,isl&s1 y travel #d1jjj miles1 n due ea/1 b along a great circle :i* l&s y at a po9t due ea/ ( ! ,%etl& ,isl&s4 ,?is1 h[ev]1 only re9=ces our conclusion3 y w end at a po9t ev5 fur!r ea/ ( y\r />t+ po9t ?an be=e4 ,:at are ! diff]5ces betwe5 ! geometry on a sph]e & ! geometry on a plane8 ,if y make a triangle on ! e>?1 ^: sides are great circles1 y w n f9d t ! angles ( ! triangle add up to two "r angles3 !y w add up to r m4 ,! am\nt by :i* !y exce$ two "r angles is proportional to ! size ( ! triangle4 ,on a small triangle su* z y c\ld make ) /r+s on y\r lawn1 or ev5 on a triangle =m$ by ?ree %ips :i* c j see ea* o!r1 ! angles w add up to s little m ?an two "r angles t y w n be able to detect ! diff]5ce4 ,b if y take ! triangle made by ! equator1 ! ,gre5wi* m]idian1 & ! n9etie? m]idian1 ! angles add up to ?ree "r angles4 ,& y c get triangles 9 :i* ! angles add up to any?+ up to six "r angles4 ,all ?is y c\ld discov] by measurem5ts on ! surface ( ! e>?1 )\t hav+ to take acc\nt ( any?+ 9 ! re/ ( space4 ,! !orem ( ,py?agoras also w fail = di/ances on a sph]e4 ,f ! po9t ( view ( a travel] b\nd to ! e>?1 ! di/ance betwe5 two places is _! great circle di/ance1 t is to say1 ! %orte/ j\rney t a man c make )\t leav+ ! surface ( ! e>?4 ,n[ suppose y take ?ree bits ( great circles :i* make a triangle1 & suppose "o ( !m is at "r angles to ano!r--to be def9ite1 let "o be ! equator & "o a bit ( ! m]idian ( ,gre5wi* go+ nor?w>d f ! equator4 ,suppose y g #c1jjj miles along ! equator1 & !n #d1jjj miles due nor?2 h[ f> w y be f y\r />t+ po9t1 e/imat+ ! di/ance along a great circle8 ,if y 7 on a plane1 y\r di/ance w\ld be #e1jjj miles1 z we saw be=e4 ,9 fact1 h[ev]1 y\r great circle di/ance w be consid]ably less ?an ?is4 ,9 a "r-angl$ triangle on a sph]e1 ! squ>e on ! side opposite ! "r angle is less ?an ! sum ( ! squ>es on ! o!r two sides4 ,^! diff]5ces betwe5 ! geometry on a sph]e & ! geometry on a plane are intr9sic diff]5ces2 t is to say1 !y enable y to f9d out :e!r ! surface on :i* y live is l a plane or l a sph]e1 )\t requir+ t y %\ld take acc\nt ( any?+ outside ! surface4 ,su* consid]ations l$ to ! next /ep ( importance 9 our subject1 :i* 0 tak5 by ,gauss1 :o fl\ri%$ a hundr$ ye>s ago4 ,he /udi$ ! !ory ( surfaces1 & %[$ h[ to develop x by means ( measurem5ts on ! surfaces !mselves1 )\t go+ outside !m4 ,9 ord] to fix ! position ( a po9t 9 space1 we ne$ ?ree measurem5ts2 b 9 ord] to fix ! position ( a po9t on a surface we ne$ only two--= example1 a po9t on ! e>?'s surface is fix$ :5 we "k its latitude & longitude4 ,n[ ,gauss f\nd t1 :atev] sy/em ( measurem5t y adopt1 & :atev] ! nature ( ! surface1 !re is always a way ( calculat+ ! di/ance betwe5 two n v di/ant po9ts ( ! surface1 :5 y "k ! quantities :i* fix _! positions4 ,! =mula = ! di/ance is a g5]alization ( ! =mula ( ,py?agoras3 x tells y ! squ>e ( ! di/ance 9 t]ms ( ! squ>es ( ! diff]5ces betwe5 ! measure quantities :i* fix ! po9ts1 & also ! product ( ^! two quantities4 ,:5 y "k ?is =mula1 y c discov] all ! intr9sic prop]ties ( ! surface1 t is to say1 all ^? :i* d n dep5d ^u its relations to po9ts outside ! surface4 ,y c discov]1 = example1 :e!r ! angles ( a triangle add up to two "r angles1 or m1 or less1 or m 9 "s cases & less 9 o!rs4 ,b :5 we speak ( a 8triangle10 we mu/ expla9 :at we mean1 because on mo/ surfaces !re are no /raight l9es4 ,on a sph]e1 we %all replace /raight l9es by great circles1 :i* are ! ne>e/ possible approa* to /raight l9es4 ,9 g5]al1 we %all take1 in/ead ( /raight l9es1 ! l9es t give ! %orte/ r\te on ! surface f place to place4 ,su* l9es are call$ 8geodesics40 ,on ! e>?1 ! geodesics are great circles4 ,9 g5]al1 !y are ! %orte/ way ( travel+ f po9t to po9t if y are unable to leave ! surface4 ,!y take ! place ( /raight l9es 9 ! intr9sic geometry ( a surface4 ,:5 we inquire :e!r ! angles ( a triangle add up to two "r angles or n1 we mean to speak ( a triangle ^: sides are geodesics4 ,& :5 we speak ( ! di/ance betwe5 two po9ts1 we mean ! di/ance along a geodesic4 ,! next /ep 9 our g5]aliz+ process is r difficult3 x is ! transition to non-,euclidean geometry4 ,we live 9 a _w 9 :i* space has ?ree dim5sions1 & our empirical k ( space is bas$ ^u measurem5t ( small di/ances & ( angles4 7,:5 ,i speak ( small di/ances1 ,i mean di/ances t are small comp>$ to ^? 9 a/ronomy2 all di/ances on ! e>? are small 9 ?is s5se47 ,x 0 =m]ly ?\ght t we c\ld be sure priori t space is ,euclidean--= in/ance1 t ! angles ( a triangle add up to two "r angles4 ,b x came to be recogniz$ t we c\ld n prove ?is by reason+2 if x 0 to be kn[n1 x mu/ be kn[n z ! result ( measurem5ts4 ,be=e ,e9/e91 x 0 ?\ght t measurem5ts confirm ,euclidean geometry )9 ! limits ( exactitude atta9able2 n[ ?is is no long] ?\ght4 ,x is /ill true t we c1 by :at may be call$ a natural artifice1 cause ,euclidean geometry to seem true ?r\gh\t a small region1 su* z ! e>?2 b 9 expla9+ gravitation ,e9/e9 is l$ to ! view t ov] l>ge regions :]e !re is matt] we _c reg>d space z ,euclidean4 ,! reasons = ?is w conc]n u lat]4 ,:at conc]ns u n[ is ! way 9 :i* non-,euclidean geometry results f a g5]alization ( ! "w ( ,gauss4 ,!re is no reason :y we %\ld n h ! same circum/ances 9 ?ree-dim5sional space z we h1 = example1 on ! surface ( a sph]e4 ,x might happ5 t ! angles ( a triangle w\ld always add up to m ?an two "r angles1 & t ! excess w\ld be proportional to ! size ( ! triangle4 ,x might happ5 t ! di/ance betwe5 two po9ts w\ld be giv5 by a =mula analog\s to :at we h on ! surface ( a sph]e1 b involv+ ?ree quantities in/ead ( two4 ,:e!r ?is does happ5 or n1 c only be discov]$ by actual measurem5ts4 ,!re are an inf9ite numb] ( su* possibilities4 ,?is l9e ( argum5t 0 develop$ by ,riemann1 9 8 diss]tation 8,on ! hypo!ses :i* und]lie geometry0 7#ahed71 :i* appli$ ,gauss's "w on surfaces to diff]5t k9ds ( ?ree-dim5sional spaces4 ,he %[$ t all ! ess5tial *>act]i/ics ( a k9d ( space c\ld be d$uc$ f ! =mula = small di/ances4 ,he assum$ t1 f ! small di/ances 9 ?ree giv5 directions :i* w\ld toge!r c>ry y f "o po9t to ano!r n f> f x1 ! di/ances betwe5 ! two po9ts c\ld be calculat$4 ,= in/ance1 if y "k t y c get f "o po9t to ano!r by fir/ mov+ a c]ta9 di/ance ea/1 !n a c]ta9 di/ance nor?1 & f9ally a c]ta9 di/ance /raight up 9 ! air1 y are to be able to calculate ! di/ance f ! "o po9t to ! o!r4 ,& ! rule = ! calculation is to be an ext5sion ( ! !orem ( ,py?agoras1 9 ! s5se t y arrive at ! squ>e ( ! requir$ di/ance by add+ toge!r multiples ( ! squ>es ( ! compon5t di/ances1 toge!r possibly ) multiples ( _! products4 ,f c]ta9 *>act]i/ics 9 ! =mula1 y c tell :at sort ( space y h to deal )4 ,^! *>act]i/ics d n dep5d ^u ! p>ticul> me?od y h adopt$ = det]m9+ ! positions ( po9ts4 ,9 ord] to arrive at :at we want = ! !ory ( relativity1 we n[ h "o m g5]alization to make3 we h to sub/itute ! 8int]val0 betwe5 ev5ts = ! di/ance betwe5 po9ts4 ,?is takes u to space-"t4 ,we h already se5 t1 9 ! special !ory ( relativity1 ! squ>e ( ! int]val is f\nd by subtract+ ! squ>e ( ! di/ance betwe5 ! ev5ts f ! squ>e ( ! di/ance t light w\ld travel 9 ! "t betwe5 !m4 ,9 ! g5]al !ory1 we d n assume ?is special =m ( int]val1 except at a great di/ance f matt]4 ,else:]e1 we assume to beg9 ) a g5]al =m1 l t :i* ,riemann us$ = di/ances4 ,moreov]1 l ,riemann1 ,e9/e9 only assumes 8 =mula = neighbor+ ev5ts1 t is to say1 ev5ts :i* h only a small int]val betwe5 !m4 ,:at goes beyond ^! initial assumptions dep5ds ^u obs]vation ( ! actual motion ( bodies1 9 ways :i* we %all expla9 9 lat] *apt]s4 ,we may n[ sum up & re-/ate ! process we h be5 describ+4 ,9 ?ree dim5sions1 ! position ( a po9t relatively to a fix$ po9t 7! 8orig907 c be det]m9$ by assign+ ?ree quantities 78co-ord9ates074 ,= example1 ! position ( a balloon relatively to y\r h\se is fix$ if y "k t y w rea* x by go+ fir/ a giv5 di/ance due ea/1 !n ano!r giv5 di/ance due nor?1 !n a ?ird giv5 di/ance /raight up4 ,:51 z 9 ?is case1 ! ?ree co-ord9ates are ?ree di/ances all at "r angles to ea* o!r1 :i*1 tak5 successively1 transport y f ! orig9 to ! po9t 9 "q1 ! squ>e ( ! direct di/ance to ! po9t 9 "q is got by add+ up ! squ>es ( ! ?ree co-ord9ates4 ,9 all cases1 :e!r 9 ,euclidean or 9 non-,euclidean spaces1 x is got by add+ multiples ( ! squ>es & products ( ! co-ord9ates accord+ to an assignable rule4 ,! co-ord9ates may be any quantities :i* fix ! position ( a po9t1 provid$ t neighbor+ po9ts mu/ h neighbor+ quantities = _! co-ord9ates4 ,9 ! g5]al !ory ( relativity1 we add a f\r? co-ord9ate to give ! "t1 & our =mula gives 8int]val0 in/ead ( spatial di/ance2 moreov] we assume ! accuracy ( our =mula = small di/ances only4 ,we assume fur!r t1 at great di/ances f matt]1 ! =mula approximates m & m closely to ! =mula = int]val :i* is us$ 9 ! special !ory4 ,we are n[ at la/ 9 a position to tackle ,e9/e9's !ory ( gravitation4 ,,*apt] ,,viii3 ,,e9/e9',s ,,law ,,( ,,gravitation ,be=e tackl+ ,e9/e9's new law1 x is z well to conv9ce ourselves1 on logical gr\nds1 t ,newton's law ( gravitation _c be q "r4 ,newton said t betwe5 any two p>ticles ( matt] !re is a =ce :i* is proportional to ! product ( _! masses & inv]sely proportional to ! squ>e ( _! di/ance4 ,t is to say1 ignor+ = ! pres5t ! "q ( mass1 if !re is a c]ta9 attraction :5 ! p>ticles are a mile ap>t1 !re w be a qu>t] z mu* attraction :5 !y are two miles ap>t1 a n9? z mu* :5 !y are ?ree miles ap>t1 & s on3 ! attraction dim9i%es mu* fa/] ?an ! di/ance increases4 ,n[1 ( c\rse1 ,newton1 :5 he spoke ( ! di/ance1 meant ! di/ance at a giv5 "t3 ,he ?\ght !re c\ld be no ambiguity ab\t "t4 ,b we h se5 t ?is 0 a mi/ake4 ,:at "o obs]v] judges to be ! same mom5t on ! e>? & ! sun1 ano!r w judge to be two diff]5t mom5ts4 8,di/ance at a giv5 mom5t0 is !re=e a subjective conception1 :i* c h>dly ent] into a cosmic law4 ,( c\rse1 we c\ld make our law unambigu\s by say+ t we are go+ to e/imate times z !y are e/imat$ by ,gre5wi* ,obs]vatory4 ,b we c h>dly believe t ! accid5tal circum/ances ( ! e>? des]ve to be tak5 s s]i\sly4 ,& ! e/imate ( di/ance1 also1 w v>y = diff]5t obs]v]s4 ,we _c1 !re=e1 all[ t ,newton's =m ( ! law ( gravitation c be q correct1 s9ce x w give diff]5t results accord+ to :i* ( _m equally legitimate conv5tions we adopt4 ,?is is z absurd z x w\ld be if ! "q :e!r "o man _h murd]$ ano!r 7 to dep5d ^u :e!r !y 7 describ$ by _! ,*ri/ian names or _! surnames4 ,x is obvi\s t physical laws mu/ be ! same :e!r di/ances are measur$ 9 miles or 9 kilomet]s1 & we are conc]n$ ) :at is ess5tially only an ext5sion ( ! same pr9ciple4 ,our measurem5ts are conv5tional to an ev5 great] ext5t ?an is admitt$ by ! special !ory ( relativity4 ,moreov]1 e measurem5t is a physical process c>ri$ out ) physical mat]ial2 ! result is c]ta9ly an exp]im5tal datum1 b may n be susceptible ( ! simple int]pretation :i* we ord9>ily assign to x4 ,we are1 !re=e1 n go+ to assume to beg9 ) t we "k h[ to measure any?+4 ,we assume t !re is a c]ta9 physical quantity1 call$ 8int]val10 :i* is a relation betwe5 two ev5ts t are n widely sep>at$2 b we d n assume 9 advance t we "k h[ to measure x1 beyond tak+ x = grant$ t x is giv5 by "s g5]alization ( ! !orem ( ,py?agoras su* z we spoke ( 9 ! prec$+ *apt]4 ,we d assume1 h[ev]1 t ev5ts h an ord]1 & t ?is ord] is f\r-dim5sional4 ,we assume1 t is to say1 t we "k :at we mean by say+ t a c]ta9 ev5t is ne>] to ano!r ?an to a ?ird1 s t be=e mak+ accurate measurem5ts we c speak ( ! 8neighborhood0 ( an ev5t2 & we assume t1 9 ord] to assign ! position ( an ev5t 9 space-"t1 f\r quantities 7co-ord9ates7 are necess>y--e4g4 9 our =m] case ( an explosion on an air%ip1 latitude1 longitude1 altitude & "t4 ,b we assume no?+ ab\t ! way 9 :i* ^! co-ord9ates are assign$1 except t neighbor+ co-ord9ates are assign$ to neighbor+ ev5ts4 ,! way 9 :i* ^! numb]s1 call$ co-ord9ates1 are to be assign$ is nei!r :olly arbitr>y nor a result ( c>eful measurem5t--x lies 9 an int]m$iate region4 ,:ile y are mak+ any cont9u\s j\rney1 y\r co-ord9ates mu/ nev] alt] by sudd5 jumps4 ,9 ,am]ica "o f9ds t ! h\ses betwe5 7say7 ,f\rte5? ,/reet & ,fifte5? ,/reet are likely to h numb]s betwe5 #adjj & #aejj1 :ile ^? betwe5 ,fifte5? ,/reet & ,sixte5? ,/reet h numb]s betwe5 #aejj & #afjj1 ev5 if ! #adjj's 7 n us$ up4 ,?is w\ld n d = our purposes1 because !re is a sudd5 jump :5 we pass f "o block to ! next4 ,or aga9 we might assign ! "t co-ord9ate 9 ! foll[+ way3 take ! "t t elapses betwe5 two successive bir?s ( p call$ ,smi?2 an ev5t occurr+ betwe5 ! bir?s ( ! #cjjj? & ! #cjja/ ,smi? kn[n to hi/ory %all h a co-ord9ate ly+ betwe5 #cjjj & #cjja2 ! fractional "p ( its co-ord9ate %all be ! fraction ( a ye> t has elaps$ s9ce ! bir? ( ! #cjjj? ,smi?4 7,obvi\sly !re c\ld nev] be z mu* z a ye> betwe5 two successive additions to ! ,smi? family47 ,?is way ( assign+ ! "t co-ord9ate is p]fectly def9ite1 b x is n admissible = our purposes1 because !re w be sudd5 jumps betwe5 ev5ts j be=e ! bir? ( a ,smi? & ev5ts j aft]1 s t 9 a cont9u\s j\rney y\r "t co-ord9ate w n *ange cont9u\sly4 ,x is assum$ t1 indep5d5tly ( measurem5t1 we "k :at a cont9u\s j\rney is4 ,& :5 y\r position 9 space-"t *anges cont9u\sly1 ea* ( y\r f\r co-ord9ates mu/ *ange cont9u\sly4 ,"o1 two1 or ?ree ( !m may n *ange at all2 b :atev] *ange does occur mu/ be smoo?1 )\t sudd5 jumps4 ,?is expla9s :at is n all[able 9 assign+ co-ord9ates4 ,to expla9 all ! *anges t are legitimate 9 y\r co-ord9ates1 suppose y take a l>ge piece ( s(t india-rubb]4 ,:ile x is 9 an un/ret*$ condition1 measure little squ>es on x1 ea* "o-t5? ( an in* ea* way4 ,put 9 little t9y p9s at ! corn]s ( ! squ>es4 ,we c take z two ( ! co-ord9ates ( "o ( ^! p9s ! numb] ( p9s pass$ 9 go+ to ! "r f a giv5 p9 until we come j bel[ ! p9 9 "q1 & !n ! numb] ( p9s we pass on ! way up to ?is p94 ,9 ! figure1 let ,o be ! p9 we />t f & ,p ! p9 to :i* we are go+ to assign co-ord9ates4 ,p is 9 ! fif? column & ! ?ird r[1 s its co-ord9ates 9 ! plane ( ! india-rubb] are to be #e & #c4 ,illu/ration3 ,fig4 #a4 ,illu/ration3 ,fig4 #b4 ,n[ take ! india-rubb] & /ret* x & twi/ x z mu* z y l4 ,let ! p9s n[ be 9 ! %ape !y h 9 ,fig4 #b4 ,! divisions n[ no long] repres5t di/ances accord+ to our usual notions1 b !y w /ill d j z well z co-ord9ates4 ,we may /ill take ,p z hav+ ! co-ord9ates #e & #c 9 ! plane ( ! india-rubb]2 & we may /ill reg>d ! india-rubb] z be+ 9 a plane1 ev5 if we h twi/$ x out ( :at we %\ld ord9>ily call a plane4 ,su* cont9u\s di/ortions d n matt]4 ,to take ano!r illu/ration3 in/ead ( us+ a /eel measur+ rod to fix our co-ord9ates1 let u use a live eel1 :i* is wriggl+ all ! "t4 ,! di/ance f ! tail to ! head ( ! eel is to c\nt z "o f ! po9t ( view ( co-ord9ates1 :atev] %ape ! creature may be assum+ at ! mom5t4 ,! eel is cont9u\s1 & its wriggles are cont9u\s1 s x may be tak5 z our unit ( di/ance 9 assign+ co-ord9ates4 ,beyond ! requirem5t ( cont9uity1 ! me?od ( assign+ co-ord9ates is purely conv5tional1 & !re=e a live eel is j z good z a /eel rod4 ,we are apt to ?9k t1 = really c>eful measurem5ts1 x is bett] to use a /eel rod ?an a live eel4 ,?is is a mi/ake3 n because ! eel tells u :at ! /eel rod 0 ?\ght to tell1 b because ! /eel rod really tells no m ?an ! eel obvi\sly does4 ,! po9t is1 n t eels are really rigid1 b t /eel rods really wriggle4 ,to an obs]v] 9 j "o possible /ate ( motion1 ! eel w\ld appe> rigid1 :ile ! /eel rod w\ld seem to wriggle j z ! eel does to u4 ,= ev]ybody mov+ diff]5tly bo? f ?is obs]v] & ourselves1 bo? ! eel & ! rod w\ld seem to wriggle4 ,& !re is no say+ t "o obs]v] is "r & ano!r wrong4 ,9 su* matt]s1 :at is se5 does n belong solely to ! physical process obs]v$1 b also to ! /&po9t ( ! obs]v]4 ,measurem5ts ( di/ances & times d n directly reveal prop]ties ( ! ?+s measur$1 b relations ( ! ?+s to ! measur]4 ,:at obs]vation c tell u ab\t ! physical _w is !re=e m ab/ract ?an we h hi!rto believ$4 ,x is important to realize t geometry1 z taught 9 s*ools s9ce ,greek times1 ceases to exi/ z a sep>ate sci5ce1 & becomes m]g$ 9 physics4 ,! two fundam5tal notions 9 elem5t>y geometry 7 ! /raight l9e & ! circle4 ,:at appe>s to y z a /raight road1 ^: p>ts all exi/ n[1 may appe> to ano!r obs]v] to be l ! flight ( a rocket1 "s k9d ( curve ^: p>ts come into exi/5ce successively4 ,! circle dep5ds ^u measurem5t ( di/ances1 s9ce x consi/s ( all ! po9ts at a giv5 di/ance f its c5t]4 ,& measurem5t ( di/ances1 z we h se51 is a subjective affair1 dep5d+ ^u ! way 9 :i* ! obs]v] is mov+4 ,! failure ( ! circle to h objective validity 0 demon/rat$ by ! ,mi*elson-,morley exp]im5t1 & is ?us1 9 a s5se1 ! />t+ po9t ( ! :ole !ory ( relativity4 ,rigid bodies1 :i* we ne$ = measurem5t1 are only rigid = c]ta9 obs]v]s2 = o!rs1 !y w be con/antly *ang+ all _! dim5sions4 ,x is only our ob/9ately e>?-b\nd imag9ation t makes u suppose a geometry sep>ate f physics to be possible4 ,t is :y we d n tr\ble to give physical significance to our co-ord9ates f ! />t4 ,=m]ly1 ! co-ord9ates us$ 9 physics 7 suppos$ to be c>efully measur$ di/ances2 n[ we realize t ?is c>e at ! />t is ?r[n away4 ,x is at a lat] /age t c>e is requir$4 ,our co-ord9ates n[ are h>dly m ?an a sy/ematic way ( catalogu+ ev5ts4 ,b ma!matics provides1 9 ! me?od ( t5sors1 su* an imm5sely p[]ful te*nique t we c use co-ord9ates assign$ 9 ?is app>5tly c>eless way j z effectively z if we _h appli$ ! :ole app>atus ( m9utely accurate measurem5t 9 arriv+ at !m4 ,! advantage ( be+ haphaz>d at ! />t is t we avoid mak+ surreptiti\s physical assumptions1 :i* we c h>dly help mak+1 if we suppose t our co-ord9ates h initially "s p>ticul> physical significance4 ,we assume t1 if two ev5ts are close toge!r 7b n necess>ily o!rwise71 !re is an int]val betwe5 !m :i* c be calculat$ f ! diff]5ces betwe5 _! co-ord9ates by "s su* =mula z we consid]$ 9 ! prec$+ *apt]4 ,t is to say1 we take ! squ>es & products ( ! diff]5ces ( co-ord9ates1 we multiply !m by suitable am\nts 7:i* 9 g5]al w v>y f place to place71 & we add ! results toge!r4 ,! sum obta9$ is ! squ>e ( ! int]val4 ,we d n assume 9 advance t we "k ! am\nts by :i* ! squ>es & products mu/ be multipli$2 ?is is go+ to be discov]$ by obs]v+ physical ph5om5a4 ,we "k1 h[ev]1 c]ta9 ?+s4 ,we "k t ! old ,newtonian physics is v ne>ly accurate :5 our co-ord9ates h be5 *os5 9 a c]ta9 way4 ,we "k t ! special !ory ( relativity is /ill m ne>ly accurate = suitable co-ord9ates4 ,f su* facts we c inf] c]ta9 ?+s ab\t our new co-ord9ates1 :i*1 9 a logical d$uction1 appe> z po/ulates ( ! new !ory4 ,z su* po/ulates we take3 #a4 ,t e body travels 9 a geodesic 9 space-"t1 except 9 s f> z electromagnetic =ces act ^u x4 #b4 ,t a light ray travels s t ! int]val betwe5 two p>ts ( x is z]o4 #c4 ,t at a great di/ance f gravitat+ matt]1 we c trans=m our co-ord9ates by ma!matical manipulation s t ! int]val %all be :at x is 9 ! special !ory ( relativity2 & t ?is is approximately true :]ev] gravitation is n v p[]ful4 ,ea* ( ^! po/ulates requires "s explanation4 ,we saw t a geodesic on a surface is ! %orte/ l9e t c be drawn on ! surface f "o po9t to ano!r2 = example1 on ! e>? ! geodesics are great circles4 ,:5 we come to space-"t1 ! ma!matics is ! same1 b ! v]bal explanations h to be r diff]5t4 ,9 ! g5]al !ory ( relativity1 x is only neighbor+ ev5ts t h a def9ite int]val1 indep5d5tly ( ! r\te by :i* we travel f "o to ! o!r4 ,! int]val betwe5 di/ant ev5ts dep5ds ^u ! r\te pursu$1 & has to be calculat$ by divid+ ! r\te into a numb] ( little bits & add+ up ! int]vals = ! v>i\s little bits4 ,if ! int]val is space-l1 a body _c travel f "o ev5t to ! o!r2 !re=e :5 we are consid]+ ! way bodies move1 we are conf9$ to "t-l int]vals4 ,! int]val betwe5 neighbor+ ev5ts1 :5 x is "t-l1 w appe> z ! "t betwe5 !m = an obs]v] :o travels f ! "o ev5t to ! o!r4 ,& s ! :ole int]val betwe5 two ev5ts w be judg$ by a p]son :o travels f "o to ! o!r to be :at 8 clocks %[ to be ! "t t he has tak5 on ! j\rney4 ,= "s r\tes ?is "t w be long]1 = o!rs %ort]2 ! m sl[ly ! man travels1 ! long] he w ?9k he has be5 on ! j\rney4 ,?is mu/ n be tak5 z a platitude4 ,i am n say+ t if y travel f ,london to ,ed9burgh y w take long] if y travel m sl[ly4 ,i am say+ some?+ mu* m odd4 ,i am say+ t if y leave ,london at #aj ,a4,m4 & arrive 9 ,ed9burgh at #f4cj ,p4,m4 ,gre5wi* "t1 ! m sl[ly y travel ! long] y w take--if ! "t is judg$ by y\r wat*4 ,?is is a v diff]5t /atem5t4 ,f ! po9t ( view ( a p]son on ! e>?1 y\r j\rney takes eight & a half h\rs4 ,b if y _h be5 a ray ( light travel+ r\nd ! sol> sy/em1 />t+ f ,london at #aj ,a4,m41 reflect$ f ,jupit] to ,saturn1 & s on1 until at la/ y 7 reflect$ back to ,ed9burgh & arriv$ !re at #f4cj ,p4,m41 y w\ld judge t ! j\rney _h tak5 y exactly no "t4 ,& if y _h gone by any circuit\s r\te1 :i* enabl$ y to arrive 9 "t by travel+ fa/1 ! long] y\r r\te ! less "t y w\ld judge t y _h tak52 ! dim9ution ( "t w\ld be cont9ual z y\r spe$ approa*$ t ( light4 ,n[ ,i say t :5 a body travels1 if x is left to itself1 x *ooses ! r\te :i* makes ! "t betwe5 two /ages ( ! j\rney z long z possible2 if x _h travel$ f "o ev5t to ano!r by any o!r r\te1 ! "t1 z measur$ by its own clocks1 w\ld h be5 %ort]4 ,?is is a way ( say+ t bodies left to !mselves d _! j\rneys z sl[ly z !y c2 x is a sort ( law ( cosmic laz9ess4 ,its ma!matical expression is t !y travel 9 geodesics1 9 :i* ! total int]val betwe5 any two ev5ts on ! j\rney is great] ?an by any alt]native r\te4 7,! fact t x is great]1 n less1 is due to ! fact t ! sort ( int]val we are consid]+ is m analog\s to "t ?an to di/ance47 ,= example1 if a p]son c\ld leave ! e>? & travel ab\t = a "t & !n return1 ! "t betwe5 8 dep>ture & return w\ld be less by 8 clocks ?an by ^? on ! e>?3 ! e>?1 9 its j\rney r\nd ! sun1 *ooses ! r\te :i* makes ! "t ( any bit ( its c\rse by its clocks long] ?an ! "t z judg$ by clocks :i* move by a diff]5t r\te4 ,?is is :at is meant by say+ t bodies left to !mselves move 9 geodesics 9 space-"t4 ,we assume t ! body consid]$ is n act$ ^u by electromagnetic =ces4 ,we are conc]n$ at pres5t ) ! law ( gravitation1 n ) ! effects ( electromagnetism4 ,^! effects h be5 br\ght into ! framework ( ! g5]al !ory ( relativity by ,weyl1#e b = ! pres5t we w ignore 8 "w4 ,! planets1 9 any case1 are n subject1 z :oles1 to appreciable electromagnetic =ces2 x is only gravitation t has to be consid]$ 9 acc\nt+ = _! motions1 ) :i* we are conc]n$ 9 ?is *apt]4 #e ,see 8 ,space1 ,"t1 ,matt]1 ,me?u51 #aibb4 ,our second po/ulate1 t a light ray travels s t ! int]val betwe5 two p>ts ( x is z]o1 has ! advantage t x does n h to be /at$ only = small di/ances4 ,if ea* little bit ( int]val is z]o1 ! sum ( !m all is z]o1 & s ev5 di/ant p>ts ( ! same light ray h a z]o int]val4 ,! c\rse ( a light ray is also a geodesic accord+ to ! def9ition4 ,?us we n[ h two empirical ways ( discov]+ :at are ! geodesics 9 space-"t1 namely light rays & bodies mov+ freely4 ,among freely-mov+ bodies are includ$ all :i* are n subject to con/ra9ts or to electromagnetic =ces1 t is to say1 ! sun1 />s1 planets & satellites1 & also fall+ bodies on ! e>?1 at lea/ :5 !y are fall+ 9 a vacuum4 ,:5 y are /&+ on ! e>?1 y are subject to electromagnetic =ces3 ! electrons & protons 9 ! neighborhood ( y\r feet ex]t a repulsion on y\r feet :i* is j en\gh to ov]come ! e>?'s gravitation4 ,?is is :at prev5ts y f fall+ ?r\gh ! e>?1 :i*1 solid z x looks1 is mo/ly empty space4 ,! ?ird po/ulate1 :i* relates ! g5]al to ! special !ory1 is v useful4 ,x is n necess>y = ! application ( ! special !ory to a limit$ region t !re %\ld be no gravitation 9 ! region2 x is en\gh if ! int5sity ( gravitation is practically ! same ?r\gh\t ! region4 ,?is enables u to apply ! special !ory )9 any small region4 ,h[ small x w h to be1 dep5ds ^u ! neighborhood4 ,on ! surface ( ! e>?1 x w\ld h to be small en\gh = ! curvature ( ! e>? to be negligible4 ,9 ! spaces betwe5 ! planets1 x ne$ only be small en\gh = ! attraction ( ! sun & ! planets to be s5sibly con/ant ?r\gh\t ! region4 ,9 ! spaces betwe5 ! />s x might be enorm\s--say half ! di/ance f "o /> to ! next--)\t introduc+ measurable inaccuracies4 ,at a great di/ance f gravitat+ matt]1 we c s *oose our co-ord9ates z to obta9 a ,euclidean space2 ?is is really only ano!r way ( say+ t ! special !ory ( relativity applies4 ,9 ! neighborhood ( matt]1 al?\gh we c make our space ,euclidean 9 any small region1 we _c d s ?r\gh\t any region )9 :i* gravitation v>ies s5sibly--at lea/1 if we d1 we %all h to ab&on ! view t bodies move 9 geodesics4 ,9 ! neighborhood ( a piece ( matt]1 !re is1 z x 71 a hill 9 space-"t2 ?is hill gr[s /eep] & /eep] z x gets ne>] ! top1 l ! neck ( a *ampagne bottle4 ,x ends 9 a %e] precipice4 ,n[ by ! law ( cosmic laz9ess :i* we m5tion$ e>li]1 a body com+ into ! neighborhood ( ! hill w n attempt to g /raight ov] ! top1 b w g r\nd4 ,?is is ! ess5ce ( ,e9/e9's view ( gravitation4 ,:at a body does1 x does because ( ! nature ( space-"t 9 its own neighborhood1 n because ( "s my/]i\s =ce emanat+ f a di/ant body4 ,an analogy w s]ve to make ! po9t cle>4 ,suppose t on a d>k night a numb] ( m5 ) lant]ns 7 walk+ 9 v>i\s directions across a huge pla91 & suppose t 9 "o "p ( ! pla9 !re 0 a hill ) a fl>+ beacon on ! top4 ,our hill is to be su* z we h describ$1 gr[+ /eep] z x goes up1 & end+ 9 a precipice4 ,i %all suppose t !re are villages dott$ ab\t ! pla91 & ! m5 ) lant]ns are walk+ to & f ^! v>i\s villages4 ,pa?s h be5 made %[+ ! easie/ way f any "o village to any o!r4 ,^! pa?s w all be m or less curv$1 to avoid go+ too f> up ! hill2 !y w be m %>ply curv$ :5 !y pass ne> ! top ( ! hill ?an :5 !y keep "s way (f f x4 ,n[ suppose t y are obs]v+ all ?is1 z be/ y c1 f a place high up 9 a balloon1 s t y _c see ! gr\nd1 b only ! lant]ns & ! beacon4 ,y w n "k t !re is a hill1 or t ! beacon is at ! top ( x4 ,y w see t p turn out ( ! /raight c\rse :5 !y approa* ! beacon1 & t ! ne>] !y come ! m !y turn aside4 ,y w naturally attribute ?is to an effect ( ! beacon2 y may ?9k t x is v hot & p are afraid ( gett+ burnt4 ,b if y wait = daylight y w see ! hill1 & y w f9d t ! beacon m]ely m>ks ! top ( ! hill & does n influ5ce ! p ) lant]ns 9 any way4 ,n[ 9 ?is analogy ! beacon corresponds to ! sun1 ! p ) lant]ns correspond to ! planets & comets1 ! pa?s correspond to _! orbits1 & ! com+ ( daylight corresponds to ! com+ ( ,e9/e94 ,e9/e9 says t ! sun is at ! top ( a hill1 only ! hill is 9 space-"t1 n 9 space4 7,i advise ! read] n to try to picture ?is1 because x is impossible47 ,ea* body1 at ea* mom5t1 adopts ! easie/ c\rse op5 to x1 b ow+ to ! hill ! easie/ c\rse is n a /raight l9e4 ,ea* little bit ( matt] is at ! top ( its own little hill1 l ! cock on 8 own dung-heap4 ,:at we call a big bit ( matt] is a bit :i* is at ! top ( a big hill4 ,! hill is :at we "k ab\t2 ! bit ( matt] at ! top is assum$ = conv5i5ce4 ,p]haps !re is really no ne$ to assume x1 & we c\ld d ) ! hill alone1 = we c nev] get to ! top ( any "o else's hill1 any m ?an ! pugnaci\s cock c fight ! peculi>ly irritat+ bird t he sees 9 ! look+ glass4 ,i h giv5 only a qualitative description ( ,e9/e9's law ( gravitation2 to give its exact quantitative =mulation is impossible )\t m ma!matics ?an ,i am p]mitt+ myself4 ,! mo/ int]e/+ po9t ab\t x is t x makes ! law no long] ! result ( action at a di/ance3 ! sun ex]ts no =ce on ! planets :atev]4 ,j z geometry has become physics1 s1 9 a s5se1 physics has become geometry4 ,! law ( gravitation has become ! geometrical law t e body pursues ! easie/ c\rse f place to place1 b ?is c\rse is affect$ by ! hills & valleys t are enc\nt]$ on ! road4 ,,*apt] ,,ix3 ,,pro(s ,,( ,,e9/e9',s ,,law ,,( ,,gravitation ,! reasons = accept+ ,e9/e9's law ( gravitation r ?an ,newton's are p>tly empirical1 p>tly logical4 ,we w beg9 ) ! =m]4 ,e9/e9's law ( gravitation gives v ne>ly ! same results z ,newton's1 :5 appli$ to ! calculation ( ! orbits ( ! planets & _! satellites4 ,if x did n1 x c\ld n be true1 s9ce ! consequ5ces d$uc$ f ,newton's law h be5 f\nd to be almo/ exactly v]ifi$ by obs]vation4 ,:51 9 #aiae1 ,e9/e9 fir/ publi%$ 8 new law1 !re 0 only "o empirical fact to :i* he c\ld po9t to %[ t 8 !ory 0 bett] ?an ,newton's4 ,?is 0 :at is call$ ! 8motion ( ! p]ihelion ( ,m]cury40 ,! planet ,m]cury1 l ! o!r planets1 moves r\nd ! sun 9 an ellipse1 ) ! sun 9 "o ( ! foci4 ,at "s po9ts ( its orbit x is ne>] to ! sun ?an at o!r po9ts4 ,! po9t :]e x is ne>e/ to ! sun is call$ its 8p]ihelion40 ,n[ x 0 f\nd by obs]vation t1 f "o occasion :5 ,m]cury is ne>e/ to ! sun until ! next1 ,m]cury does n g exactly once r\nd ! sun1 b a little bit m4 ,! discrepancy is v small2 x am\nts to an angle ( =ty-two seconds 9 a c5tury4 ,t is to say1 9 ea* ye> ! planet has to move r less ?an half a second ( angle aft] x has f9i%$ a complete revolution f ! la/ p]ihelion be=e x rea*es ! next p]ihelion4 ,?is v m9ute discrepancy f ,newtonian !ory _h puzzl$ a/ronom]s4 ,!re 0 a calculat$ effect due to p]turbations caus$ by ! o!r planets1 b ?is small discrepancy 0 ! residue aft] all[+ = ^! p]turbations4 ,e9/e9's !ory acc\nt$ = ?is residue1 z well z = its abs5ce 9 ! case ( ! o!r planets4 7,9 !m x exi/s1 b is too small to be obs]v$47 ,?is 01 at fir/1 8 only empirical advantage ov] ,newton4 ,8 second success 0 m s5sational4 ,accord+ to or?odox op9ion1 light 9 a vacuum ought always to travel 9 /raight l9es4 ,n be+ compos$ ( mat]ial p>ticles1 x ought to be unaffect$ by gravitation4 ,h[ev]1 x 0 possible1 )\t any s]i\s brea* ) old ideas1 to admit t1 9 pass+ ne> ! sun1 light might be deflect$ out ( ! /raight pa? z mu* z if x 7 compos$ ( mat]ial p>ticles4 ,e9/e91 h[ev]1 ma9ta9$1 z a d$uction f 8 law ( gravitation1 t light w\ld be deflect$ twice z mu* z ?is4 ,t is to say1 if ! light ( a /> pass$ v ne> ! sun1 ,e9/e9 ma9ta9$ t ! ray f ! /> w\ld be turn$ ?r\gh an angle ( j "u "o & ?ree-qu>t]s seconds4 ,8 oppon5ts 7 will+ to conc$e half ( ?is am\nt4 ,n[ x is n e day t a /> almo/ 9 l9e ) ! sun c be se54 ,?is is only possible dur+ a total eclipse1 & n always !n1 because !re may be no bright />s 9 ! "r position4 ,edd+ton po9ts out t1 f ?is po9t ( view1 ! be/ day ( ! ye> is ,may #bi1 because !n !re are a numb] ( bright />s close to ! sun4 ,x happ5$ by incr$ible good =tune t !re 0 a total eclipse ( ! sun on ,may #bi1 #aiai--! fir/ ye> aft] ! armi/ice4 ,two ,briti% exp$itions photograph$ ! />s ne> ! sun dur+ ! eclipse1 & ! results confirm$ ,e9/e9's pr$iction4 ,"s a/ronom]s :o rema9$ d\btful :e!r suffici5t precautions _h be5 tak5 to insure accuracy 7 conv9c$ :5 _! own obs]vations 9 a subsequ5t eclipse gave exactly ! same result4 ,e9/e9's e/imate ( ! am\nt ( ! deflection ( light by gravitation is !re=e n[ univ]sally accept$4 ,! ?ird exp]im5tal te/ is on ! :ole favorable to ,e9/e91 ?\gh ! quantities conc]n$ are s small t x is only j possible to measure !m1 & ! result is !re=e n decisive4 ,b successive inve/igations h made x m & m probable t ! small effect pr$ict$ by ,e9/e9 really occurs4 ,be=e expla9+ ! effect 9 "q1 a few prelim9>y explanations are necess>y4 ,! spectrum ( an elem5t consi/s ( c]ta9 l9es ( v>i\s %ades ( light1 sep>at$ by a prism1 & emitt$ by ! elem5t :5 x gl[s4 ,!y are ! same 7to a v close approximation7 :e!r ! elem5t is 9 ! e>? or ! sun or a />4 ,ea* l9e is ( "s def9ite %ade ( color1 ) "s def9ite wave l5g?4 ,long] wave l5g?s are t[>ds ! r$ end ( ! spectrum1 %ort] ones t[>ds ! violet end4 ,:5 ! s\rce ( light is mov+ t[>ds y1 ! app>5t wave l5g?s gr[ %ort]1 j z waves at sea come quick] :5 y are travel+ aga9/ ! w9d4 ,:5 ! s\rce ( light is mov+ away f y1 ! app>5t wave l5g?s gr[ long]1 = ! same reason4 ,?is enables u to "k :e!r ! />s are mov+ t[>ds u or away f u4 ,if !y are mov+ t[>ds u1 all ! l9es 9 ! spectrum ( an elem5t are mov$ a little t[>d violet2 if away f u1 t[>d r$4 ,y may notice ! analog\s effect 9 s\nd any day4 ,if y are 9 a /ation & an express comes ?r\gh :i/l+1 ! note ( ! :i/le seems mu* m %rill :ile ! tra9 is approa*+ y ?an :5 x has pass$4 ,probably _m p ?9k ! note has 8really0 *ang$1 b 9 fact ! *ange 9 :at y he> is only due to ! fact t ! tra9 0 fir/ approa*+ & !n rec$+4 ,to p 9 ! tra91 !re 0 no *ange ( note4 ,?is is n ! effect ) :i* ,e9/e9 is conc]n$4 ,! di/ance ( ! sun f ! e>? does n *ange mu*2 = our pres5t purposes1 we may reg>d x z con/ant4 ,e9/e9 d$uces f 8 law ( gravitation t any p]iodic process :i* takes place 9 an atom 9 ! sun 7^: gravitation is v int5se7 mu/1 z measur$ by our clocks1 take place at a slightly sl[] rate ?an x w\ld 9 a simil> atom on ! e>?4 ,! 8int]val0 involv$ w be ! same 9 ! sun & on ! e>?1 b ! same int]val 9 diff]5t regions does n correspond to exactly ! same "t2 ?is is due to ! 8hilly0 "* ( space-"t :i* con/itutes gravitation4 ,consequ5tly any giv5 l9e 9 ! spectrum ought1 :5 ! light comes f ! sun1 to seem to u a little ne>] ! r$ end ( ! spectrum ?an if ! light came f a s\rce on ! e>?4 ,! effect to be expect$ is v small--s small t !re is /ill "s slight unc]ta9ty z to :e!r x exi/s or n4 ,b x n[ seems highly probable t x exi/s4 ,no o!r measurable diff]5ces betwe5 ! consequ5ces ( ,e9/e9's law & ^? ( ,newton's h hi!rto be5 discov]$4 ,b ! above exp]im5tal te/s are q suffici5t to conv9ce a/ronom]s t1 :]e ,newton & ,e9/e9 diff] z to ! motions ( ! heav5ly bodies1 x is ,e9/e9's law t gives ! "r results4 ,ev5 if ! empirical gr\nds 9 favor ( ,e9/e9 /ood alone1 !y w\ld be conclusive4 ,:e!r 8 law repres5ts ! exact tru? or n1 x is c]ta9ly m ne>ly exact ?an ,newton's1 ?\gh ! inaccuracies 9 ,newton's 7 all exce$+ly m9ute4 ,b ! consid]ations :i* orig9ally l$ ,e9/e9 to 8 law 7 n ( ?is detail$ k9d4 ,ev5 ! consequ5ce ab\t ! p]ihelion ( ,m]cury1 :i* c\ld be v]ifi$ at once f previ\s obs]vations1 c\ld only be d$uc$ aft] ! !ory 0 complete1 & c\ld n =m any "p ( ! orig9al gr\nds = inv5t+ su* a !ory4 ,^! gr\nds 7 ( a m ab/ract logical "*4 ,i d n mean t !y 7 n bas$ ^u obs]v$ facts1 & ,i d n mean t !y 7 priori fantasies su* z philosoph]s indulg$ 9 =m]ly4 ,:at ,i mean is t !y 7 d]iv$ f c]ta9 g5]al *>act]i/ics ( physical exp]i5ce1 :i* %[$ t ,newton mu/ be wrong & t some?+ l ,e9/e9's law mu/ be sub/itut$4 ,! argum5ts 9 favor ( ! relativity ( motion are1 z we saw 9 e>li] *apt]s1 q conclusive4 ,9 daily life1 :5 we say t some?+ moves1 we mean t x moves relatively to ! e>?4 ,9 deal+ ) ! motions ( ! planets1 we consid] !m z mov+ relatively to ! sun1 or to ! c5t] ( mass ( ! sol> sy/em4 ,:5 we say t ! sol> sy/em itself is mov+1 we mean t x is mov+ relatively to ! />s4 ,!re is no physical occurr5ce :i* c be call$ 8absolute motion40 ,consequ5tly ! laws ( physics mu/ be conc]n$ ) relative motions1 s9ce ^! are ! only k9d t occur4 ,we n[ take ! relativity ( motion 9 conjunction ) ! exp]im5tal fact t ! velocity ( light is ! same relatively to "o body z relatively to ano!r1 h[ev] ! two may be mov+4 ,?is leads u to ! relativity ( di/ances & times4 ,?is 9 turn %[s t !re is no objective physical fact :i* c be call$ 8! di/ance betwe5 two bodies at a giv5 "t10 s9ce ! "t & ! di/ance w bo? dep5d on ! obs]v]4 ,!re=e ,newton's law ( gravitation is logically unt5able1 s9ce x makes use ( 8di/ance at a giv5 "t40 ,?is %[s t we _c re/ cont5t ) ,newton1 b x does n %[ :at we are to put 9 8 place4 ,"h sev]al consid]ations ent] 94 ,we h 9 ! fir/ place :at is call$ 8! equality ( gravitational & in]tial mass40 ,:at ?is means is z foll[s3 ,:5 y apply a giv5 =ce#f to a heavy body1 y d n give x z mu* accel]ation z y w\ld to a light body4 ,:at is call$ ! 8in]tial0 mass ( a body is measur$ by ! am\nt ( =ce requir$ to produce a giv5 accel]ation4 ,at a giv5 po9t ( ! e>?'s surface1 ! 8mass0 is proportional to ! 8weight40 ,:at is measur$ by scales is r ! mass ?an ! weight3 ! weight is def9$ z ! =ce ) :i* ! e>? attracts ! body4 ,n[ ?is =ce is great] at ! poles ?an at ! equator1 because at ! equator ! rotation ( ! e>? produces a 8c5trifugal =ce0 :i* p>tially c\nt]acts gravitation4 ,! =ce ( ! e>?'s attraction is also great] on ! surface ( ! e>? ?an x is at a great height or at ! bottom ( a v deep m9e4 ,none ( ^! v>iations are %[n by scales1 because !y affect ! weights us$ j z mu* z ! body weigh$2 b !y are %[n if we use a spr+ balance4 ,! mass does n v>y 9 ! c\rse ( ^! *anges ( weight4 #f ,al?\gh 8=ce0 is no long] to be reg>d$ z "o ( ! fundam5tal concepts ( dynamics1 b only z a conv5i5t way ( speak+1 x c /ill be employ$1 l 8sunrise0 & 8sunset10 provid$ we realize :at we mean4 ,(t5 x w\ld require v r\ndab\t expressions to avoid ! t]m 8=ce40 ,! 8gravitational0 mass is diff]5tly def9$4 ,x is capable ( two mean+s4 ,we may mean 7#a71 ! way a body responds 9 a situation :]e gravitation has a kn[n int5sity1 = example1 on ! surface ( ! e>?1 or on ! surface ( ! sun2 or 7#b71 ! int5sity ( ! gravitational =ce produc$ by ! body1 z1 = example1 ! sun produces /rong] gravitational =ces ?an ! e>? does4 ,newton says t ! =ce ( gravitation betwe5 two bodies is proportional to ! product ( _! masses4 ,n[ let u consid] ! attraction ( diff]5t bodies to "o & ! same body1 say ! sun4 ,!n diff]5t bodies are attract$ by =ces :i* are proportional to _! masses1 & :i*1 !re=e1 produce exactly ! same accel]ation 9 all ( !m4 ,?us if we mean 8gravitational mass0 9 s5se 7#a71 t is to say1 ! way a body responds to gravitation1 we f9d t 8! equality ( in]tial & gravitational mass10 :i* s\nds =midable1 r$uces to ?is3 t 9 a giv5 gravitational situation1 all bodies behave exactly alike4 ,z reg>ds ! surface ( ! e>?1 ?is 0 "o ( ! fir/ discov]ies ( ,galileo4 ,ari/otle ?\ght t heavy bodies fall fa/] ?an light ones2 ,galileo %[$ t ?is is n ! case1 :5 ! resi/ance ( ! air is elim9at$4 ,9 a vacuum1 a fea!r falls z fa/ z a lump ( lead4 ,z reg>ds ! planets1 x 0 ,newton :o e/abli%$ ! correspond+ facts4 ,at a giv5 di/ance f ! sun1 a comet1 :i* has a v small mass1 exp]i5ces exactly ! same accel]ation t[>ds ! sun z a planet exp]i5ces at ! same di/ance4 ,?us ! way 9 :i* gravitation affects a body dep5ds only ^u :]e ! body is1 & 9 no degree ^u ! nature ( ! body4 ,?is sugge/s t ! gravitational effect is a *>act]i/ic ( ! locality1 :i* is :at ,e9/e9 makes x4 ,z = ! gravitational mass 9 s5se 7#b71 i4e41 ! int5sity ( ! =ce produc$ by a body1 ?is is no long] exactly proportional to its in]tial mass4 ,! "q involves "s r complicat$ ma!matics1 & ,i %all n g into x4#g #g ,see ,edd+ton1 ,! ,ma!matical ,!ory ( ,relativity1 ,cambridge ,univ]sity ,press1 #b;d edition1 p4 #abh4 ,we h ano!r indication z to :at sort ( ?+ ! law ( gravitation mu/ be1 if x is to be a *>act]i/ic ( a neighborhood1 z we h se5 reason to suppose t x is4 ,x mu/ be express$ 9 "s law :i* is un*ang$ :5 we adopt a diff]5t k9d ( co-ord9ates4 ,we saw t we mu/ n1 to beg9 )1 reg>d our co-ord9ates z hav+ any physical significance3 !y are m]ely sy/ematic ways ( nam+ diff]5t p>ts ( space-"t4 ,be+ conv5tional1 !y _c ent] into physical laws4 ,t means to say t1 if we h express$ a law correctly 9 t]ms ( "o set ( co-ord9ates1 x mu/ be express$ by ! same =mula 9 t]ms ( ano!r set ( co-ord9ates4 ,or1 m exactly1 x mu/ be possible to f9d a =mula :i* expresses ! law1 & :i* is un*ang$ h[ev] we *ange ! co-ord9ates4 ,x is ! bus9ess ( ! !ory ( t5sors to deal ) su* =mul4 ,& ! !ory ( t5sors %[s t !re is "o =mula :i* obvi\sly sugge/s itself z be+ possibly ! law ( gravitation4 ,:5 ?is possibility is exam9$1 x is f\nd to give ! "r results2 x is "h t ! empirical confirmations come 94 ,b if ,e9/e9's law _h n be5 f\nd to agree ) exp]i5ce1 we c\ld n h gone back to ,newton's law4 ,we %\ld h be5 compell$ by logic to seek "s law express$ 9 t]ms ( 8t5sors10 & !re=e indep5d5t ( our *oice ( co-ord9ates4 ,x is impossible )\t ma!matics to expla9 ! !ory ( t5sors2 ! non-ma!matician mu/ be cont5t to "k t x is ! te*nical me?od by :i* we elim9ate ! conv5tional elem5t f our measurem5ts & laws1 & ?us arrive at physical laws :i* are indep5d5t ( ! obs]v]'s po9t ( view4 ,( ?is me?od1 ,e9/e9's law ( gravitation is ! mo/ spl5did example4 ,,*apt] ,x3 ,,mass1 ,,mom5tum1 ,,en]gy ,,& ,,action ,! pursuit ( quantitative precision is z ardu\s z x is important4 ,physical measurem5ts are made ) extraord9>y exactitude2 if !y 7 made less c>efully1 su* m9ute discrepancies z =m ! exp]im5tal data = ! !ory ( relativity c\ld nev] be reveal$4 ,ma!matical physics1 be=e ! com+ ( relativity1 us$ a set ( conceptions :i* 7 suppos$ to be z precise z physical measurem5ts1 b x has turn$ out t !y 7 logically defective1 & t ?is defectiv5ess %[$ itself 9 v small deviations f expectations bas$ ^u calculation4 ,9 ?is *apt] ,i want to %[ h[ ! fundam5tal ideas ( pre-relativity physics are affect$1 & :at modifications !y h _h to und]go4 ,we h already _h occasion to speak ( mass4 ,= purposes ( daily life1 mass is mu* ! same z weight2 ! usual measures ( weight--ounces1 grams1 etc4--are really measures ( mass4 ,b z soon z we beg9 to make accurate measurem5ts1 we are compell$ to di/+ui% betwe5 mass & weight4 ,two diff]5t me?ods ( weigh+ are 9 common use1 "o1 t ( scales1 ! o!r t ( ! spr+ balance4 ,:5 y g a j\rney & y\r luggage is weigh$1 x is n put on scales1 b on a spr+2 ! weight depresses ! spr+ a c]ta9 am\nt1 & ! result is indicat$ by a ne$le on a dial4 ,! same pr9ciple is us$ 9 automatic ma*9es = f9d+ y\r weight4 ,! spr+ balance %[s weight1 b scales %[ mass4 ,s long z y /ay 9 "o "p ( ! _w1 ! diff]5ce does n matt]2 b if y te/ two weigh+ ma*9es ( diff]5t k9ds 9 a numb] ( diff]5t places1 y w f9d1 if !y are accurate1 t _! results d n always agree4 ,scales w give ! same result any:]e1 b a spr+ balance w n4 ,t is to say1 if y h a lump ( lead weigh+ t5 p\nds by ! scales1 x w also weigh t5 p\nds by scales 9 any o!r "p ( ! _w4 ,b if x weighs t5 p\nds by a spr+ balance 9 ,london1 x w weigh m at ! ,nor? ,pole1 less at ! equator1 less high up 9 an a]oplane1 & less at ! bottom ( a coal m9e1 if x is weigh$ 9 all ^? places on ! same spr+ balance4 ,! fact is t ! two in/rum5ts measure q diff]5t quantities4 ,! scales measure :at may be call$ 7ap>t f ref9em5ts :i* w conc]n u pres5tly7 8quantity ( matt]40 ,!re is ! same 8quantity ( matt]0 9 a p\nd ( fea!rs z 9 a p\nd ( lead4 ,/&>d 8weights10 :i* are really /&>d 8masses10 w measure ! am\nt ( mass 9 any sub/ance put into ! opposite scales4 ,b 8weight0 is a prop]ly due to ! e>?'s gravitation3 ,x is ! am\nt ( ! =ce by :i* ! e>? attracts a body4 ,?is =ce v>ies f place to place4 ,9 ! fir/ place1 any:]e outside ! e>? ! attraction v>ies inv]sely z ! squ>e ( ! di/ance f ! c5t] ( ! e>?2 x is !re=e less at great heights4 ,9 ! second place1 :5 y g d[n a coal m9e1 "p ( ! e>? is above y1 & attracts matt] upw>ds in/ead ( d[nw>ds1 s t ! net attraction d[nw>ds is less ?an on ! surface ( ! e>?4 ,9 ! ?ird place1 ow+ to ! rotation ( ! e>?1 !re is :at is call$ a 8c5trifugal =ce10 :i* acts aga9/ gravitation4 ,?is is greate/ at ! equator1 because !re ! rotation ( ! e>? involves ! fa/e/ motion2 at ! poles x does n exi/1 because !y are on ! axis ( rotation4 ,= all ^! reasons1 ! =ce ) :i* a giv5 body is attract$ to ! e>? is measureably diff]5t at diff]5t places4 ,x is ?is =ce t is measur$ by a spr+ balance2 t is :y a spr+ balance gives diff]5t results 9 diff]5t places4 ,9 ! case ( scales1 ! /&>d 8weights0 are alt]$ j z mu* z ! body to be weigh$1 s t ! result is ! same ev]y:]e2 b ! result is ! 8mass10 n ! 8weight40 ,a /&>d 8weight0 has ! same mass ev]y:]e1 b n ! same 8weight02 x is 9 fact a unit ( mass1 n ( weight4 ,= !oretical purposes1 mass1 :i* is almo/ inv>iable = a giv5 body1 is mu* m important ?an weight1 :i* v>ies accord+ to circum/ances4 ,mass may be reg>d$1 to beg9 )1 z 8quantity ( matt]02 we %all see t ?is view is n /rictly correct1 b x w s]ve z a />t+ po9t = subsequ5t ref9em5ts4 ,= !oretical purposes1 a mass is def9$ z be+ det]m9$ by ! am\nt ( =ce requir$ to produce a giv5 accel]ation3 ,! m massive a body is1 ! great] w be ! =ce requir$ to alt] its velocity by a giv5 am\nt 9 a giv5 "t4 ,x takes a m p[]ful eng9e to make a long tra9 atta9 a spe$ ( t5 miles an h\r at ! end ( ! fir/ half-m9ute1 ?an x does to make a %ort tra9 d s4 ,or we may h circum/ances :]e ! =ce is ! same = a numb] ( diff]5t bodies2 9 t case1 if we c measure ! accel]ations produc$ 9 !m1 we c tell ! ratios ( _! masses3 ! great] ! mass1 ! small] ! accel]ation4 ,we may take1 9 illu/ration ( ?is me?od1 an example :i* is important 9 connection ) relativity4 ,radio-active bodies emit beta-p>ticles 7electrons7 ) enorm\s velocities4 ,we c obs]ve _! pa? by mak+ !m travel ?r\gh wat] vapor & =m a cl\d z !y g4 ,we c at ! same "t subject !m to kn[n electric & magnetic =ces1 & obs]ve h[ mu* !y are b5t out ( a /raight l9e by ^! =ces4 ,?is makes x possible to comp>e _! masses4 ,x is f\nd t ! fa/] !y travel1 ! great] is _! mass1 z measur$ by ! /ation>y obs]v]2 ! increase is greate/ z appli$ to _! mass z measur$ by ! effect ( a =ce 9 ! l9e ( motion4 ,9 reg>d to =ces at "r angles to ! l9e ( motion1 !re is a *ange ( mass ) velocity 9 ! same proportion z ! *anges ( l5g? & "t4 ,x is kn[n o!rwise t1 ap>t f ! effect ( motion1 all electrons h ! same mass4 ,all ?is 0 kn[n be=e ! !ory ( relativity 0 inv5t$1 b x %[$ t ! traditional conception ( mass _h n q ! def9it5ess t _h be5 ascrib$ to x4 ,mass us$ to be reg>d$ z 8quantity ( matt]10 & suppos$ to be q inv>iable4 ,n[ mass 0 f\nd to be relative to ! obs]v]1 l l5g? & "t1 & to be alt]$ by motion 9 exactly ! same proportion4 ,h[ev]1 ?is c\ld be rem$i$4 ,we c\ld take ! 8prop] mass10 ! mass z measur$ by an obs]v] :o %>es ! motion ( ! body4 ,?is 0 easily inf]r$ f ! measur$ mass1 by tak+ ! same proportion z 9 ! case ( l5g?s & times4 ,b !re is a m curi\s fact1 & t is1 t aft] we h made ?is correction we /ill h n obta9$ a quantity :i* is at all times exactly ! same = ! same body4 ,:5 a body absorbs en]gy--= example1 by gr[+ hott]--its 8prop] mass0 increases slightly4 ,! increase is v slight1 s9ce x is measur$ by divid+ ! increase ( en]gy by ! squ>e ( ! velocity ( light4 ,on ! o!r h&1 :5 a body p>ts ) en]gy x loses mass4 ,! mo/ notable case ( ?is is t f\r hydrog5 atoms c come toge!r to make "o helium atom1 b a helium atom has r less ?an f\r times ! mass ( "o hydrog5 atom4 ,we h ?us two k9ds ( mass1 nei!r ( :i* q fulfils ! old ideal4 ,! mass z measur$ by an obs]v] :o is 9 motion relative to ! body 9 "q is a relative quantity1 & has no physical significance z a prop]ty ( ! body4 ,! 8prop] mass0 is a g5u9e prop]ty ( ! body1 n dep5d5t ^u ! obs]v]2 b x1 also1 is n /rictly con/ant4 ,z we %all see %ortly1 ! notion ( mass becomes absorb$ into ! notion ( en]gy2 x repres5ts1 s to speak1 ! en]gy :i* ! body exp5ds int]nally1 z oppos$ to t :i* x displays to ! out] _w4 ,cons]vation ( mass1 cons]vation ( mom5tum1 & cons]vation ( en]gy 7 ! great pr9ciples ( classical me*anics4 ,let u next consid] cons]vation ( mom5tum4 ,! mom5tum ( a body 9 a giv5 direction is its velocity 9 t direction multipli$ by its mass4 ,?us a heavy body mov+ sl[ly may h ! same mom5tum z a light body mov+ fa/4 ,:5 a numb] ( bodies int]act 9 any way1 = in/ance by collisions1 or by mutual gravitation1 s long z no outside influ5ces come 91 ! total mom5tum ( all ! bodies 9 any direction rema9s un*ang$4 ,?is law rema9s true 9 ! !ory ( relativity4 ,= diff]5t obs]v]s1 ! mass w be diff]5t1 b s w ! velocity2 ^! two diff]5ces neutralize ea* o!r1 & x turns out t ! pr9ciple /ill rema9s true4 ,! mom5tum ( a body is diff]5t 9 diff]5t directions4 ,! ord9>y way ( measur+ x is to take ! velocity 9 a giv5 direction 7z measur$ by ! obs]v]7 & multiply x by ! mass 7z measur$ by ! obs]v]74 ,n[ ! velocity 9 a giv5 direction is ! di/ance travel$ 9 t direction 9 unit "t4 ,suppose we take in/ead ! di/ance travel$ 9 t direction :ile ! body moves ?r\gh unit 8int]val40 7,9 ord9>y cases1 ?is is only a v slight *ange1 because1 = velocities consid]ably less ?an t ( light1 int]val is v ne>ly equal to lapse ( "t47 ,& suppose t in/ead ( ! mass z measur$ by ! obs]v] we take ! prop] mass4 ,^! two *anges increase ! velocity & dim9i% ! mass1 bo? 91 ! same proportion4 ,?us ! mom5tum rema9s ! same1 b ! quantities t v>y accord+ to ! obs]v] h be5 replac$ by quantities :i* are fix$ indep5d5tly ( ! obs]v]--) ! exception ( ! di/ance travel$ by ! body 9 ! giv5 direction4 ,:5 we sub/itute space-"t = "t1 we f9d t ! measur$ mass 7z oppos$ to ! prop] mass7 is a quantity ( ! same k9d z ! mom5tum 9 a giv5 direction2 x might be call$ ! mom5tum 9 ! "t direction4 ,! measur$ mass is obta9$ by multiply+ ! inv>iant mass by ! "t trav]s$ 9 travel+ ?r\gh unit int]val2 ! mom5tum is obta9$ by multiply+ ! same inv>iant mass by ! di/ance trav]s$ 79 ! giv5 direction7 9 travel+ ?r\gh unit int]val4 ,f a space-"t po9t ( view1 ^! naturally belong toge!r4 ,al?\gh ! measur$ mass ( a body dep5ds ^u ! way ! obs]v] is mov+ relatively to ! body1 x is none ! less a v important quantity4 ,= any giv5 obs]v]1 ! measur$ mass ( ! :ole physical univ]se is con/ant4#h ,! prop] mass ( all ! bodies 9 ! _w is n necess>ily ! same at "o "t z at ano!r1 s t 9 ?is respect ! measur$ mass has an advantage4 ,! cons]vation ( measur$ mass is ! same ?+ z ! cons]vation ( en]gy4 ,?is may seem surpris+1 s9ce at fir/ sight mass & en]gy are v diff]5t ?+s4 ,b x has turn$ out t en]gy is ! same ?+ z measur$ mass4 ,to expla9 h[ ?is comes ab\t is n easy2 nev]!less we w make ! attempt4 #h ,?is is subject to ! explanations giv5 bel[ z reg>ds cons]vation ( en]gy4 ,9 popul> talk1 8mass0 & 8en]gy0 d n mean at all ! same ?+4 ,we associate 8mass0 ) ! idea ( a fat man 9 a *air1 v sl[ to move1 :ile 8en]gy0 sugge/s a ?9 p]son full ( hu/le & 8pep40 ,popul> talk associates 8mass0 & 8in]tia10 b its view ( in]tia is "o-sid$3 x includes sl[ness 9 beg9n+ to move1 b n sl[ness 9 /opp+1 :i* is equally involv$4 ,all ^! t]ms h te*nical mean+s 9 physics1 :i* are only m or less analog\s to ! mean+s ( ! t]ms 9 popul> talk4 ,= ! pres5t1 we are conc]n$ ) ! te*nical mean+ ( 8en]gy40 ,?r\gh\t ! latt] half ( ! n9ete5? c5tury1 a great deal 0 made ( ! 8cons]vation ( en]gy10 or ! 8p]si/5ce ( =ce10 z ,h]b]t ,sp5c] pref]r$ to call x4 ,?is pr9ciple 0 n easy to /ate 9 a simple way1 because ( ! diff]5t =ms ( en]gy2 b ! ess5tial po9t 0 t en]gy is nev] creat$ or de/roy$1 ?\gh x c be trans=m$ f "o k9d into ano!r4 ,! pr9ciple acquir$ its position ?r\gh ,j\le's discov]y ( 8! me*anical equival5t ( heat10 :i* %[$ t !re 0 a con/ant proportion betwe5 ! "w requir$ to produce a giv5 am\nt ( heat & ! "w requir$ to raise a giv5 weight ?r\gh a giv5 height3 9 fact1 ! same sort ( "w c\ld be utiliz$ = ei!r purpose accord+ to ! me*anism4 ,:5 heat 0 f\nd to consi/ 9 motion ( molecules1 x 0 se5 to be natural t x %\ld be analog\s to o!r =ms ( en]gy4 ,broadly speak+1 by ! help ( a c]ta9 am\nt ( !ory1 all =ms ( en]gy 7 r$uc$ to two1 :i* 7 call$ respectively 8k9etic0 & 8pot5tial40 ,^! 7 def9$ z foll[s3 ,! k9etic en]gy ( a p>ticle is half ! mass multipli$ by ! squ>e ( ! velocity4 ,! k9etic en]gy ( a numb] ( p>ticles is ! sum ( ! k9etic en]gies ( ! sep>ate p>ticles4 ,! pot5tial en]gy is m difficult to def9e4 ,x repres5ts any /ate ( /ra91 :i* c only be pres]v$ by ! application ( =ce4 ,to take ! easie/ case3 ,if a weight is lift$ to a height & kept susp5d$1 x has pot5tial en]gy1 because1 if left to itself1 x w fall4 ,its pot5tial en]gy is equal to ! k9etic en]gy :i* x w\ld acquire 9 fall+ ?r\gh ! same di/ance ?r\gh :i* x 0 lift$4 ,simil>ly :5 a comet goes r\nd ! sun 9 a v ecc5tric orbit1 x moves mu* fa/] :5 x is ne> ! sun ?an :5 x is f> f x1 s t its k9etic en]gy is mu* great] :5 x is ne> ! sun4 ,on ! o!r h&1 its pot5tial en]gy is greate/ :5 x is f>!/ f ! sun1 because x is !n l ! /one :i* has be5 lift$ to a height4 ,! sum ( ! k9etic & pot5tial en]gies ( ! comet is con/ant1 unless x suff]s collisions or loses matt] by =m+ a tail4 ,we c det]m9e accurately ! *ange ( pot5tial en]gy 9 pass+ f "o position to ano!r1 b ! total am\nt ( x is to a c]ta9 ext5t arbitr>y1 s9ce we c fix ! z]o level :]e we l4 ,= example1 ! pot5tial en]gy ( our /one may be tak5 to be ! k9etic en]gy x w\ld acquire 9 fall+ to ! surface ( ! e>?1 or :at x w\ld acquire 9 fall+ d[n a well to ! c5t] ( ! e>?1 or any assign$ less] di/ance4 ,x does n matt] :i* we take1 s long z we /ick to our decision4 ,we are conc]n$ ) a pr(it-&-loss acc\nt1 :i* is unaffect$ by ! am\nt ( ! assets ) :i* we />t4 ,bo? ! k9etic & ! pot5tial en]gies ( a giv5 set ( bodies w be diff]5t = diff]5t obs]v]s4 ,9 classical dynamics1 ! k9etic en]gy diff]$ accord+ to ! /ate ( motion ( ! obs]v]1 b only by a con/ant am\nt2 ! pot5tial en]gy did n diff] at all4 ,consequ5tly1 = ea* obs]v]1 ! total en]gy 0 con/ant--assum+ always t ! obs]v]s conc]n$ 7 mov+ 9 /raight l9es ) uni=m velocities1 or1 if n1 7 able to ref] _! motions to bodies :i* 7 s mov+4 ,b 9 relativity dynamics ! matt] becomes m complicat$4 ,we _c pr(itably adapt ! idea ( pot5tial en]gy to ! !ory ( relativity1 & !re=e ! cons]vation ( en]gy1 9 a /rict s5se1 _c be ma9ta9$4 ,b we obta9 a prop]ty1 closely analog\s to cons]vation1 :i* applies to k9etic en]gy alone4 ,z ,edd+ton puts x3 ! k9etic en]gy is n always /rictly cons]v$1 & ! classical !ory !re=e introduces a supplem5t>y quantity1 ! pot5tial en]gy1 s t ! sum ( ! two is /rictly cons]v$4 ,! relativity treatm5t1 on ! o!r h&1 discov]s ano!r =mula1 analog\s to ! "o express+ cons]vation1 :i* holds always = ! k9etic en]gy4 8,! relativity treatm5t adh]es to ! physical quantity & modifies ! law2 ! classical treatm5t adh]es to ! law & modifies ! physical quantity40 ,! new =mula1 he cont9ues1 may be spok5 ( 8z ! law ( cons]vation ( en]gy & mom5tum1 because1 ?\gh x is n =mally a law ( cons]vation1 x expresses exactly ! ph5om5a :i* classical me*anics attributes to cons]vation40#i ,x is only 9 ?is modifi$ & less rigor\s s5se t ! cons]vation ( en]gy rema9s true4 #i ,ma!matical ,!ory ( ,relativity1 p4 #ace4 ,:at is meant by 8cons]vation0 9 practice is n exactly :at x means 9 !ory4 ,9 !ory we say t a quantity is cons]v$ :5 ! am\nt ( x 9 ! _w is ! same at any "o "t z at any o!r4 ,b 9 practice we _c survey ! :ole _w1 s we h to mean some?+ m manageable4 ,we mean t1 tak+ any giv5 region1 if ! am\nt ( ! quantity 9 ! region has *ang$1 x is because "s ( ! quantity has pass$ across ! b\nd>y ( ! region4 ,if !re 7 no bir?s & dea?s1 population w\ld be cons]v$2 9 t case ! population ( a c\ntry c\ld only *ange by emigration or immigration1 t is to say1 by pass+ across ! b\nd>ies4 ,we might be unable to take an accurate c5sus ( ,*9a or ,c5tral ,africa1 &1 !re=e1 we might n be able to asc]ta9 ! total population ( ! _w4 ,b we %\ld be ju/ifi$ 9 assum+ x to be con/ant if1 :]ev] /ati/ics 7 possible1 ! population nev] *ang$ except ?r\gh p cross+ ! fronti]s4 ,9 fact1 ( c\rse1 population is n cons]v$4 ,a physiologi/ ( my acqua9tance once put f\r mice into a !rmos4 ,"s h\rs lat]1 :5 he w5t to take !m out1 !re 7 elev5 ( !m4 ,b mass is n subject to ^! fluctuations3 ! mass ( ! elev5 mice at ! end ( ! "t 0 no great] ?an ! mass ( ! f\r at ! beg9n+4 ,?is br+s u back to ! problem = ! sake ( :i* we h be5 discuss+ en]gy4 ,we /at$ t1 9 relativity !ory1 measur$ mass & en]gy are reg>d$ z ! same ?+1 & we und]took to expla9 :y4 ,x is n[ "t to emb>k ^u ?is explanation4 ,b "h1 z at ! end ( ,*apt] ,,vi1 ! totally unma!matical read] w d well to skip1 & beg9 aga9 at ! foll[+ p>agraph4 ,let u take ! velocity ( light z ! unit ( velocity2 ?is is always conv5i5t 9 relativity !ory4 ,let m be ! prop] mass ( a p>ticle1 v its velocity relative to ! obs]v]4 ,!n its measur$ mass w be m -------------------- 7#a - v7 :ile its k9etic en]gy1 accord+ to ! usual =mula1 w be mv ,z we saw be=e1 en]gy only occurs 9 a pr(it-&-loss acc\nt1 s t we c add any con/ant quantity to x t we l4 ,we may !re=e take ! en]gy to be m 7mv74 ,n[ if v is a small fraction ( ! velocity ( light1 m mv is almo/ exactly equal to m ------------------ 7#a - v74 ,consequ5tly1 = velocities su* z l>ge bodies h1 ! en]gy & ! measur$ mass turn out to be indi/+ui%able )9 ! limits ( accuracy atta9able4 ,9 fact1 x is bett] to alt] our def9ition ( en]gy1 & take x to be m -------------------- 7#a - v71 because ?is is ! quantity = :i* ! law analog\s to cons]vation holds4 ,& :5 ! velocity is v great1 x gives a bett] measure ( en]gy ?an ! traditional =mula4 ,! traditional =mula mu/ !re=e be reg>d$ z an approximation1 ( :i* ! new =mula gives ! exact v]sion4 ,9 ?is way1 en]gy & measur$ mass become id5tifi$4 ,i come n[ to ! notion ( 8action10 :i* is less famili> to ! g5]al public ?an en]gy1 b has become m important 9 relativity physics1 z well z 9 ! !ory ( quanta4#aj 7,! quantum is a small am\nt ( action47 ,! ^w 8action0 is us$ to d5ote en]gy multipli$ by "t4 ,t is to say1 if !re is "o unit ( en]gy 9 a sy/em1 x w ex]t "o unit ( action 9 a second1 #ajj units ( action 9 #ajj seconds1 & s on2 a sy/em :i* has #ajj units ( en]gy w ex]t #ajj units ( action 9 a second1 & #aj1jjj 9 #ajj seconds1 & s on4 8,action0 is ?us1 9 a loose s5se1 a measure ( h[ mu* has be5 accompli%$3 x is increas$ bo? by display+ m en]gy & by work+ = a long] "t4 ,s9ce en]gy is ! same ?+ z measur$ mass1 we may also take action to be measur$ mass multipli$ by "t4 ,9 classical me*anics1 ! 8d5sity0 ( matt] 9 any region is ! mass divid$ by ! volume2 t is to say1 if y "k ! d5sity 9 a small region1 y discov] ! total am\nt ( matt] by multiply+ ! d5sity by ! volume ( ! small region4 ,9 relativity me*anics1 we always want to sub/itute space-"t = space2 !re=e a 8region0 mu/ no long] be tak5 to be m]ely a volume1 b a volume la/+ = a "t2 a small region w be a small volume la/+ = a small "t4 ,x foll[s t1 giv5 ! d5sity1 a small region 9 ! new s5se conta9s1 n a small mass m]ely1 b a small mass multipli$ by a small "t1 t is to say1 a small am\nt ( 8action40 ,?is expla9s :y x is to be expect$ t 8action0 w prove ( fundam5tal importance 9 relativity me*anics4 ,& s 9 fact x is4 #aj ,on ?is subject1 see ! pres5t au?or's ,a4,b4,c4 ( ,atoms1 *aps4 ,,vi & ,,xiii4 ,all ! laws ( dynamics h be5 put toge!r into "o pr9ciple1 call$ 8,! ,pr9ciple ( ,lea/ ,action40 ,?is /ates t1 9 pass+ f "o /ate to ano!r1 a body *ooses a r\te involv+ less action ?an any slightly diff]5t r\te--aga9 a law ( cosmic laz9ess4 ,! pr9ciple is subject to c]ta9 limitations1 :i* h be5 po9t$ out by ,edd+ton1#aa b x rema9s "o ( ! mo/ compreh5sive ways ( /at+ ! purely =mal "p ( me*anics4 ,! fact t ! quantum is a unit ( action seems to %[ t action is also fundam5tal 9 ! empirical /ructure ( ! _w4 ,b at pres5t !re is no bridge connect+ ! quantum ) ! !ory ( relativity4 #aa ,op4 cit4 #fj4 ,,*apt] ,,xi3 ,,is ,,! ,,univ]se ,,f9ite8 ,we h be5 deal+ hi!rto ) matt]s t mu/ be reg>d$ z acquir$ sci5tific results--n t !y w nev] be f\nd to ne$ improvem5t1 b t fur!r progress mu/ be built ^u !m1 z ,e9/e9 is built ^u ,newton4 ,sci5ce does n aim at e/abli%+ immutable tru?s & et]nal dogmas3 its aim is to approa* tru? by successive approximations1 )\t claim+ t at any /age f9al & complete accuracy has be5 a*iev$4 ,!re is a diff]5ce1 h[ev]1 betwe5 results :i* are pretty c]ta9ly 9 ! l9e ( advance1 & speculations :i* may or may n prove to be well f\nd$4 ,"s v int]e/+ speculations are connect$ ) ! !ory ( relativity1 & we %all consid] c]ta9 ( !m4 ,b x mu/ n be suppos$ t we are deal+ ) !ories hav+ ! same solidity z ^? ) :i* we h be5 conc]n$ hi!rto4 ,"o ( ! mo/ fasc9at+ ( ! speculations to :i* ,i h be5 allud+ is ! sugge/ion t ! univ]se may be ( f9ite ext5t4 ,two some:at diff]5t f9ite univ]ses h be5 con/ruct$1 "o by ,e9/e91 ! o!r by ,de ,sitt]4 ,be=e consid]+ _! diff]5ces1 we w discuss :at !y h 9 common4 ,!re are1 to beg9 )1 c]ta9 reasons = ?9k+ t ! total am\nt ( matt] 9 ! univ]se is limit$4 ,if ?is 7 n ! case1 ! gravitational effects ( enorm\sly di/ant matt] w\ld make ! k9d ( _w 9 :i* we live impossible4 ,we mu/ !re=e suppose t !re is "s def9ite numb] ( electrons & protons 9 ! _w3 !oretically1 a complete c5sus w\ld be possible4 ,^! are all conta9$ )9 a c]ta9 f9ite region2 :atev] space lies outside t region is1 s to speak1 wa/e1 l unfurni%$ rooms 9 a h\se too l>ge = its inhabitants4 ,?is seems futile1 b 9 =m] days no "o knew ( any alt]native possibility4 ,x 0 obvi\sly impossible to conceive ( an edge to space1 & !re=e1 x 0 ?\ght1 space mu/ be inf9ite4 ,non-,euclidean geometry1 h[ev]1 %[$ o!r possibilities4 ,! surface ( a sph]e has no b\nd>y1 yet x is n inf9ite4 ,9 travel+ r\nd ! e>?1 we nev] rea* 8! edge ( ! _w10 & yet ! e>? is n inf9ite4 ,! surface ( ! e>? is conta9$ 9 ?ree-dim5sional space1 b !re is no reason 9 logic :y ?ree-dim5sional space %\ld n be con/ruct$ on an analog\s plan4 ,:at we imag9e to be /raight l9es go+ on = ev] w !n be l great circles on a sph]e3 !y w ultimately return to _! />t+ po9t4 ,!re w n be 9 ! univ]se any?+ /raight] ?an ^! great circles2 ! ,euclidean /raight l9e may rema9 z a beautiful dream1 b n z a possibility 9 ! actual _w4 ,9 p>ticul>1 light rays 9 empty space w travel 9 :at are really great circles4 ,if we c\ld make measurem5ts ) suffici5t accuracy1 we %\ld be able to inf] ?is /ate ( affairs ev5 f a small "p ( space1 because ! sum ( ! angles ( a triangle w\ld always be great] ?an two "r angles1 & ! excess w\ld be proportional to ! size ( ! triangle4 ,! sugge/ion we h to consid] is ! sugge/ion t our univ]se may be sph]ical 9 ?is s5se4 ,! read] mu/ n confuse ?is sugge/ion ) ! non-,euclidean "* ( space ^u :i* ! new law ( gravitation dep5ds4 ,! latt] is conc]n$ ) small regions su* z ! sol> sy/em4 ,! dep>tures f flatness :i* x notices are l hills & valleys on ! surface ( ! e>?1 local irregul>ities1 n *>act]i/ics ( ! :ole4 ,we are n[ conc]n$ ) ! possible curvature ( ! univ]se z a :ole1 n ) ! occasional ups & d[ns due to ! sun & ! />s4 ,x is sugge/$ t on ! av]age1 & 9 regions remote f matt]1 ! univ]se is n q flat1 b has a slight curvature1 analog\s1 9 ?ree dim5sions1 to ! curvature ( a sph]e 9 two dim5sions4 ,x is important to realize1 9 ! fir/ place1 t !re is n ! slighte/ reason priori :y ?is %\ld n be ! case4 ,p unaccu/om$ to non-,euclidean geometry may feel t1 ev5 if su* a ?+ be logically possible1 ! _w simply _c be s odd z all t4 ,we all h a t5d5cy to ?9k t ! _w mu/ con=m to our prejudices4 ,! opposite view involves "s ef=t ( ?\ght1 & mo/ p w\ld die soon] ?an ?9k--9 fact1 !y d s4 ,b ! fact t a sph]ical univ]se seems odd to p :o h be5 br\ght up on ,euclidean prejudices is no evid5ce t x is impossible4 ,!re is no law ( nature to ! effect t :at is taught at s*ool mu/ be true4 ,we _c !re=e dismiss ! hypo!sis ( a sph]ical univ]se z 9 any degree less wor?y ( exam9ation ?an any o!r4 ,we h to ask ourselves ! same two que/ions z we %\ld 9 any o!r case1 namely3 7#a7 ,are ! facts consi/5t ) ?is hypo!sis8 7#b7 ,is ?is hypo!sis ! only "o ) :i* ! facts are consi/5t8 ,) reg>d to ! fir/ "q1 ! answ] is und\bt$ly 9 ! affirmative4 ,all ! kn[n facts are p]fectly consi/5t ) ! hypo!sis ( a sph]ical univ]se4 ,a v slight modification ( ! law ( gravitation--a modification sugge/$ by ,e9/e9 himself--leads to a sph]ical space1 )\t produc+ any measurable diff]5ces 9 a small region su* z ! sol> sy/em4 ,! kn[n />s are all )9 a c]ta9 di/ance f u4 ,!re is no?+ :atev] 9 ! /ell> univ]se z we "k x to %[ t space mu/ be inf9ite4 ,!re c !re=e be no d\bt :atev] t1 s f> z our pres5t k goes1 ! hypo!sis ( a f9ite univ]se may be true4 ,b :5 we ask :e!r ! hypo!sis ( a f9ite univ]se mu/ be true1 ! answ] is diff]5t4 ,x is obvi\s1 on g5]al gr\nds1 t we _c1 f :at we "k1 draw conclusive inf]5ces z to ! totality ( ?+s4 ,a v slight *ange 9 ! ,newtonian =mula = gravitation w\ld prev5t masses beyond ! limits ( ! visible univ]se f hav+ appreciable effects if !y exi/$1 & w\ld !re=e de/roy our reason = suppos+ t !y d n exi/4 ,all argum5ts z to regions :i* are too di/ant to be obs]v$ dep5d ^u ext5d+ to !m ! laws :i* hold 9 our "p ( ! _w1 & ^u assum+ t !re is n1 9 ^! laws1 "s inaccuracy :i* is inappreciable = obs]vable di/ances1 b fatal to inf]5ces 9 :i* v mu* great] di/ances are involv$4 ,we _c1 !re=e1 say t ! univ]se mu/ be f9ite4 ,we c say t x may be1 & we c ev5 say a little m ?an ?is4 ,we c say t a f9ite univ]se fits 9 bett] ) ! laws t hold 9 ! "p we "k1 & t awkw>d adju/m5ts ( ! laws h to be made 9 ord] to all[ ! univ]se to be inf9ite4 ,f ! po9t ( view ( *oos+ ! be/ framework into :i* to fit :at we "k--be/1 ,i mean1 f a logico-/hetic po9t ( view--!re is no d\bt t ! hypo!sis ( a f9ite univ]se is pref]able4 ,?is1 ,i ?9k1 is ! ext5t ( :at c be said 9 its favor4 ,let u n[ see :at ! two f9ite univ]ses are l4 ,! diff]5ce betwe5 !m is t 9 ,e9/e9's _w x is only space t is que]1 :]eas 9 ,de ,sitt]'s "t is que] too4 ,consequ5tly ,e9/e9's _w is less puzzl+1 & we w describe x fir/4 ,9 ,e9/e9's _w1 light travels r\nd ! :ole univ]se 9 a "t :i* is suppos$ to be some?+ l a ?\s& million ye>s4 ,! odd ?+ is t all ! rays ( light :i* />t 7say7 f ! sun w meet aga91 aft] _! enorm\s j\rney1 9 ! place :]e ! sun 0 :5 !y />t$4 ,! case is exactly analog\s to t ( a numb] ( travel]s :o set out f ,london to g r\nd ! _w 9 great circles1 all travel+ at ! same rate 9 diff]5t a]oplanes4 ,"o />ts due nor?1 passes ! ,nor? ,pole1 !n ! ,s\? ,pole1 & f9ally comes home4 ,ano!r />ts due s\?1 rea*es ! ,s\? ,pole fir/ & !n ! ,nor? ,pole4 ,ano!r />ts we/w>d1 b he mu/ n cont9ue to travel due we/1 because !n he w\ld n be travel+ on a great circle4 ,ano!r />ts ea/w>d1 & s on4 ,!y all meet 9 ! antipodes ( ,london1 & !n !y all meet aga9 9 ,london4 ,n[ if in/ead ( a]onauts go+ r\nd ! e>? y take rays ( light go+ r\nd ! univ]se1 ! same sort ( ?+ happ5s3 !y all meet fir/ at ! antipodes ( _! />t+ po9t1 & !n meet aga9 at _! />t+ po9t4 ,t means to say t a p]son :o is ne> ! antipodes ( ! place :]e ! sun 0 ab\t five hundr$ million ye>s ago w see :at is app>5tly a body z bright z ! sun !n 0 7except = ! small am\nt ( light t has be5 /opp$ on ! way by opaque bodies71 & hav+ ! same %ape & size4 ,& a p]son :o is ne> :]e ! sun 0 a ?\s& million ye>s ago w see :at is app>5tly a body j l :at ! sun 0 a ?\s& million ye>s ago4 ,& ! same applies to ! antipodes ( ! sun fifte5 hundr$ million ye>s ago1 & to ! place ( ! sun two ?\s& million ye>s ago1 & s on4 ,?is s]ies only ends :5 x c>ries u back to a "t be=e ! sun exi/$4 ,b all ^! suns are only gho/s2 t is to say1 y c\ld pass ?r\gh !m )\t exp]i5c+ resi/ance1 & !y d n ex]t gravitation4 ,!y are1 9 fact1 l images 9 a mirror3 !y exi/ only = ! s5se ( sight1 n = any o!r s5se4 ,x is r di/urb+ to reflect t1 if ?is !ory is true1 any numb] ( ! objects we see 9 ! heav5s may be m]ely gho/s4 ,!y are l gho/s 9 _! habit ( revisit+ ! sc5es ( _! pa/ life4 ,suppose a /> _h explod$ at a c]ta9 place1 z />s sometimes w4 ,e ?\s& million ye>s its gho/ w\ld return to ! sc5e ( ! disa/] & explode aga9 9 ! same place4 ,!re is1 h[ev]1 consid]able d\bt :e!r rays ( light c\ld p]=m ! j\rney ) suffici5t accuracy to produce a cle> image4 ,"s w\ld be /opp$ by matt] on ! way1 "s w\ld be turn$ out ( ! /raight c\rse by pass+ ne> heavy bodies1 z 9 ! eclipse obs]vations describ$ 9 ,*apt] ,,ix1 & = "o reason or ano!r _! return w\ld n be punctual & exact4 ,!re are v>i\s reasons = d\bt+ :e!r ,e9/e9's univ]se c be q "r4#ab ,"s ( ^! are r complicat$4 ,b !re is "o objection :i* is easily appreciat$3 9 ,e9/e9's !ory1 absolute space & "t re-ent] by ano!r door4 ,! gho/ly sun is =m$ 9 ! 8place0 :]e x 0 a ?\s& million ye>s ago4 ,bo? ! 8place0 & ! p]iod ( "t are 9 a s5se absolute4 ,we saw z e>ly z ,*apt] ,i t 8place0 is a vague & popul> notion1 incapable ( sci5tific precision4 ,x seems h>dly wor? :ile to g ?r\gh su* a va/ intellectual labor if ! errors we set out to correct are to reappe> at ! end4 #ab ,see ,edd+ton1 ,space1 ,"t & ,gravitation1 p4 #afb;ff4 ,de ,sitt]'s _w is ev5 odd] ?an ,e9/e9's1 because "t goes mad z well z space4 ,i despair ( expla9+1 9 non-ma!matical language1 ! p>ticul> =m ( lunacy ) :i* "t is afflict$1 b "s ( its manife/ations c be describ$4 ,an obs]v] 9 ?is _w1 if he obs]ves a numb] ( clocks1 ea* ( :i* is p]fectly accurate f its own po9t ( view1 w ?9k t di/ant clocks are go+ sl[ z comp>$ ) ^? 9 8 neighborhood4 ,!y w seem to g sl[] & sl[]1 until1 at a di/ance ( "o qu>t] ( ! circumf]5ce ( ! univ]se1 !y w seem to h /opp$ altoge!r4 ,t region w seem to our obs]v] a sort ( lotus l&1 :]e no?+ is ev] done4 ,he w n be able to h any cognizance ( ?+s f>!r (f1 because no light waves c get across ! b\nd>y4 ,n t !re is any real b\nd>y3 ! p :o live 9 :at our obs]v] takes to be lotus l& live j z bu/l+ a life z he does1 b get ! impression t he is et]nally /&+ /ill4 ,z a matt] ( fact1 y w\ld nev] become aw>e ( ! lotus l&1 because x w\ld take an inf9ite "t = light to travel f x to y4 ,y c\ld become aw>e ( places j %ort ( x1 b x w\ld rema9 itself always j beyond y\r k54 ,!re w n be ! gho/ly suns ( ,e9/e9's _w1 because light _c travel s f>4 ,"o ( ! odde/ ?+s ab\t ?is /ate ( affairs is t empirical evid5ce = or aga9/ x is possible1 & t !re is actually "s slight evid5ce 9 its favor4 ,if all 8clocks0 are sl[$ d[n at a great di/ance f ! obs]v]1 ?is w apply to ! p]iodic motions ( atoms1 & !re=e to ! light :i* !y emit4 ,consequ5tly all rays ( light emitt$ by di/ant objects ought1 :5 !y rea* u1 to look r m r$ or less violet ?an :5 !y />t$4 ,?is c be te/$ by ! spectroscope4 ,we c comp>e a kn[n l9e1 z x appe>s 9 ! spectrum ( a spiral nebula1 ) ! same l9e z x appe>s 9 a t]re/rial laboratory4 ,we f9d1 z a matt] ( fact1 t 9 a l>ge majority ( spiral nebul !re is a consid]able displacem5t ( spectral l9es t[>ds ! r$4 ,! spiral nebul are ! mo/ di/ant objects we c see3 ,edd+ton /ates t _! di/ances 8may p]haps be ( ! ord] ( a million light-ye>s40 7,a light-ye> is ! di/ance light travels 9 a ye>47 ,! usual int]pretation ( a %ift+ ( spectral l9es t[>ds ! r$ is t x is a 8,doppl] effect10 due to ! fact t ! s\rce ( light is mov+ away f u4 ,b "o w\ld expect to f9d ! nebul j z (t5 mov+ t[>ds u z mov+ away f u1 if no?+ op]at$ b ! law ( *ances4 ,if ! _w is su* z ,de ,sitt] says x is1 ! spectral l9es ( ! spiral nebul w be displac$ t[>ds ! r$ ow+ to ! sl[+ d[n ( di/ant clocks1 ev5 if 9 fact !y are n mov+ away f u4 ,?is1 = :at x is wor?1 is an argum5t 9 favor ( ,de ,sitt]4 ,! same facts af=d ano!r argum5t 9 favor ( ,de ,sitt]1 = ano!r reason4 ,if1 at a giv5 mom5t1 a body is at re/ relatively to ! obs]v]1 & at a di/ance f him1 x w 79 ! abs5ce ( c\nt]act+ causes7 n rema9 at re/ f 8 po9t ( view1 b w beg9 to move away f him1 & w cont9ue to move away fa/] & fa/]2 ! fur!r x is f him1 ! m its retreat w be accel]at$4 ,= bodies :i* are n too di/ant f ea* o!r1 gravitation may ov]come ?is t5d5cy2 b z ?is t5d5cy increases ) ! di/ance1 :ile gravitation dim9i%es1 we %\ld expect to f9d v di/ant bodies rec$+ f u if ,de ,sitt]'s !ory is "r4 ,?us we h two reasons = ! displacem5t ( spectral l9es 9 spiral nebul3 "o1 ! sl[+ d[n ( "t2 ! o!r1 ! movem5t away f u :i* we %\ld expect at di/ances too great = gravitation to be s5sible4 ,h[ev]1 x _c be said t ! argum5t1 on ei!r gr\nd1 is v /rong4 ,edd+ton gives a li/ ( =ty-"o spiral nebul1 ( :i* five h _! spectral l9es %ift$ t[>ds ! violet1 n t[>ds ! r$4 ,?us ! mat]ial is nei!r v copi\s nor q h>moni\s4 ,e9/e9's & ,de ,sitt]'s hypo!ses d n exhau/ ! possibilities ( a f9ite _w3 !y are m]ely ! two simple/ =ms ( su* a _w4 ,!re are argum5ts aga9/ ea*1 & x h>dly seems probable t ei!r is q true4 ,b x does seem probable t some?+ m or less analog\s is true4 ,if ! univ]se is f9ite1 x is !oretically conceivable t !re %\ld be a complete inv5tory ( x4 ,we may be com+ to ! end ( :at physics c d 9 ! way ( /ret*+ ! imag9ation & sy/ematiz+ ! _w4 ,! p]iod s9ce ,galileo has be5 ess5tially ! p]iod ( physics1 z ! age ( ! ,greeks 0 ! p]iod ( geometry4 ,x may be t physics w lose its attractions ?r\gh success3 if ! fundam5tal laws ( physics come to be fully kn[n1 adv5tur\s & inquir+ intellects w turn to o!r fields4 ,?is may alt] pr(\ndly ! :ole texture ( human life1 s9ce our pres5t absorption 9 ma*9]y & indu/rialism is ! reflection 9 ! practical _w ( ! !ori/'s int]e/ 9 physical laws4 ,b su* speculations are ev5 m ra% ?an ^? ( ,de ,sitt]1 & ,i d n wi% to lay any /ress ^u !m4 ,,*apt] ,,xii3 ,,conv5tions ,,& ,,natural ,,laws ,"o ( ! mo/ difficult matt]s 9 all controv]sy is to di/+ui% disputes ab\t words f disputes ab\t facts3 x ought n to be difficult1 b 9 practice x is4 ,?is is q z true 9 physics z 9 o!r subjects4 ,9 ! sev5te5? c5tury !re 0 a t]rific debate z to :at 8=ce0 is2 to u n[1 x 0 obvi\sly a debate z to h[ ! ^w 8=ce0 %\ld be def9$1 b at ! "t x 0 ?\ght to be mu* m4 ,"o ( ! purposes ( ! me?od ( t5sors1 :i* is employ$ 9 ! ma!matics ( relativity1 is to elim9ate :at is purely v]bal 79 an ext5d$ s5se7 9 physical laws4 ,x is ( c\rse obvi\s t :at dep5ds on ! *oice ( co-ord9ates is 8v]bal0 9 ! s5se conc]n$4 ,a man punt+ walks along ! boat1 b keeps a con/ant position ) ref]5ce to ! riv] b$ s long z he does n pick up 8 pole4 ,! ,lilliputians might debate endlessly :e!r he is walk+ or /&+ /ill3 ! debate w\ld be z to words1 n z to facts4 ,if we *oose co-ord9ates fix$ relatively to ! boat1 he is walk+2 if we *oose co-ord9ates fix$ relatively to ! riv] b$1 he is /&+ /ill4 ,we want to express physical laws 9 su* a way t x %all be obvi\s :5 we are express+ ! same law by ref]5ce to two diff]5t sy/ems ( co-ord9ates1 s t we %all n be misl$ into suppos+ we h diff]5t laws :5 we only h "o law 9 diff]5t words4 ,?is is accompli%$ by ! me?od ( t5sors4 ,"s laws :i* seem plausible 9 "o language _c be translat$ into ano!r2 ^! are impossible z laws ( nature4 ,! laws t c be translat$ into any co-ord9ate language h c]ta9 *>act]i/ics3 ?is is a sub/antial help 9 look+ = su* laws ( nature z ! !ory ( relativity c admit to be possible4 ,comb9$ ) :at we "k ( ! actual motions ( bodies1 x enables u to decide :at mu/ be ! correct expression ( ! law ( gravitation3 logic & exp]i5ce comb9e 9 equal proportions 9 obta9+ ?is expression4 ,b ! problem ( arriv+ at g5u9e laws ( nature is n to be solv$ by ! me?od ( t5sors alone2 a good1 deal ( c>eful ?\ght is want$ 9 addition4 ,"s ( ?is has be5 done1 especially by ,edd+ton2 mu* rema9s to be done4 ,to take a simple illu/ration3 ,suppose1 z 9 ! hypo!sis ( ! ,fitzg]ald contraction1 t l5g?s 9 "o direction 7 %ort] ?an 9 ano!r4 ,let u assume t a foot rule po9t+ nor? is only half z long z ! same foot rule po9t+ ea/1 & t ?is is equally true ( all o!r bodies4 ,does su* an hypo!sis h any mean+8 ,if y h a fi%+ rod fifte5 feet long :5 x is po9t+ we/1 & y !n turn x to ! nor?1 x w /ill measure fifte5 feet1 because y\r foot rule w h %runk too4 ,x won't 8look0 any %ort]1 because y\r eye w h be5 affect$ 9 ! same way4 ,if y are to f9d out ! *ange1 x _c be by ord9>y measurem5t2 x mu/ be by "s su* me?od z ! ,mi*elson-,morley exp]im5t1 9 :i* ! velocity ( light is us$ to measure l5g?s4 ,!n y /ill h to decide :e!r x is simpl] to suppose a *ange ( l5g? or a *ange 9 ! velocity ( light4 ,! exp]im5tal fact w\ld be t light takes long] to trav]se :at y\r foot rule decl>es to be a giv5 di/ance 9 "o direction ?an 9 ano!r--or1 z 9 ! ,mi*elson-,morley exp]im5t1 t x ought to take long] b doesn't4 ,y c adju/ y\r measures to su* a fact 9 v>i\s ways2 9 any way y *oose to adopt1 !re w be an elem5t ( conv5tion4 ,?is elem5t ( conv5tion survives 9 ! laws t y arrive at aft] y h made y\r decision z to measures1 & (t5 x takes subtle & elusive =ms4 ,to elim9ate ! elem5t ( conv5tion is1 9 fact1 extraord9>ily difficult2 ! m ! subject is /udi$1 ! great] ! difficulty is se5 to be4 ,a m important example is ! "q ( ! size & %ape ( ! electron4 ,we f9d exp]im5tally t all electrons are ! same size1 & t !y are symmetrical 9 all directions4 ,h[ f> is ?is a g5u9e fact asc]ta9$ by exp]im5t1 & h[ f> is x a result ( our conv5tions ( measurem5t8 ,we h "h a numb] ( diff]5t comp>isons to make3 7#a7 betwe5 diff]5t directions 9 reg>d to "o electron at "o "t2 7#b7 9 reg>d to "o electron at diff]5t times2 7#c7 9 reg>d to two electrons at ! same "t4 ,we c !n arrive at ! comp>ison ( two electrons at diff]5t times1 by comb9+ 7#b7 & 7#c74 ,we may dismiss any hypo!sis :i* w\ld affect all electrons equally2 = example1 x w\ld be useless to suppose t 9 "o region ( space-"t !y 7 all l>g] ?an 9 ano!r4 ,su* a *ange w\ld affect our measur+ appliances j z mu* z ! ?+s measur$1 & w\ld !re=e produce no discov]able ph5om5a4 ,?is is z mu* z to say t x w\ld be no *ange at all4 ,b ! fact t two electrons h ! same mass1 = in/ance1 _c be reg>d$ z purely conv5tional4 ,giv5 suffici5t m9ut5ess & accuracy1 we c\ld comp>e ! effects ( two diff]5t electrons ^u a ?ird2 if !y 7 equal "u l circum/ances1 we %\ld be able to inf] equality 9 a n purely conv5tional s5se4 ,! "q ( ! symmetry ( ! =ces ex]t$ by an electron--i4e41 t ^! =ces dep5d only ^u ! di/ance f ! electron1 & n ^u ! direction--is m complicat$4 ,edd+ton f9ally comes to ! conclusion t ?is1 too1 is a matt] ( conv5tion4 ,! argum5t is difficult & ,i h n fully und]/ood x2 b ,i feel "s hesitation 9 accept+ x z valid4 ,edd+ton describes ! process conc]n$ 9 ! m advanc$ portions ( ! !ory ( relativity z 8_w-build+40 ,! /ructure to be built is ! physical _w z we "k x2 ! economical ar*itect tries to con/ruct x ) ! smalle/ possible am\nt ( mat]ial4 ,?is is a "q = logic & ma!matics4 ,! great] our te*nical skill 9 ^! two subjects1 ! m real build+ we %all d1 & ! less we %all be cont5t ) m]e heaps ( /ones4 ,b be=e we c use 9 our build+ ! /ones t nature provides1 we h to hew !m into ! "r %apes3 ?is is all "p ( ! process ( budd+4 ,9 ord] t ?is may be possible1 ! raw mat]ial mu/ h "s /ructure 7:i* we may conceive z analog\s to ! gra9 9 timb]71 b almo/ any /ructure w d4 ,by successive ma!matical ref9em5ts1 we :ittle away our initial requirem5ts until !y am\nt to v little4 ,giv5 ?is necess>y m9imum ( /ructure 9 ! raw mat]ial1 we f9d t we c con/ruct f x a ma!matical expression :i* w h ! prop]ties t are ne$$ = describ+ ! _w we p]ceive--9 p>ticul>1 ! prop]ties ( cons]vation :i* are *>act]i/ic ( mom5tum & en]gy 7or mass74 ,our raw mat]ial consi/$ m]ely ( ev5ts2 b :5 we f9d t we c build out ( x some?+ :i*1 z measur$1 w seem to be nev] creat$ or de/roy$1 x seems n surpris+ t we %\ld come to believe 9 8bodies40 ,^! are really m]e ma!matical con/ructions out ( ev5ts1 b ow+ to _! p]man5ce !y are practically important1 & our s5ses 7:i* 7 presumably develop$ by biological ne$s7 are adapt$ = notic+ !m1 r ?an ! crude cont9uum ( ev5ts :i* is !oretically m fundam5tal4 ,f ?is po9t ( view1 x is a/oni%+ h[ little ( ! real _w is reveal$ by physical sci5ce3 our k is limit$1 n only by ! conv5tional elem5t1 b also by ! selectiv5ess ( our p]ceptual app>atus4 ,we assume t !re is an 8int]val0 betwe5 two ev5ts1 9 ! s5se expla9$ 9 ,*apt] ,,vii1 b we no long] assume t we c unambigu\sly comp>e ! l5g? ( an int]val 9 "o region ) ! l5g? ( an int]val 9 ano!r4 ,x is assum$ by ,weyl1 :o introduc$ ?is limitation1 t we c comp>e a numb] ( small int]vals :i* all />t f ! same po9t2 also t1 9 a v small j\rney1 our measur+ rod w n alt] its l5g? mu*1 s t !re w only be a small error if we comp>e l5g?s 9 neighbor+ places by ! usual me?ods4 ,weyl f\nd t1 by dim9i%+ our assumptions z to int]val 9 ?is way1 x 0 possible to br+ electromagnetism & gravitation into "o sy/em4 ,! ma!matics ( ,weyl's !ory is complicat$1 & ,i %all n attempt to expla9 x4 ,= ! pres5t1 ,i am conc]n$ ) a diff]5t consequ5ce ( 8 !ory4 ,if l5g?s 9 diff]5t regions _c be comp>$ directly1 !re is an elem5t ( conv5tion 9 ! indirect comp>isons :i* we actually make4 ,?is elem5t w be at fir/ unrecogniz$1 b w be su* z to simplify to ! utmo/ ! expression ( ! laws ( nature4 ,9 p>ticul>1 conditions ( symmetry may be entirely creat$ by conv5tions z to measurem5t1 & !re is no reason to suppose t !y repres5t any prop]ty ( ! real _w4 ,! law ( gravitation itself1 accord+ to ,edd+ton1 may be reg>d$ z express+ conv5tions ( measurem5t4 8,! conv5tions ( measurem5t10 he says1 8introduce an isotropy#ac & homog5eity into measur$ space :i* ne$ n orig9ally h any c\nt]p>t 9 ! relation-/ructure :i* is be+ survey$4 ,?is isotropy & homog5eity is exactly express$ by ,e9/e9's law ( gravitation40#ad #ac 8,isotropy0 means be+ simil> 9 all directions--e4g41 t a foot rule is z long :5 x po9ts nor? z :5 x po9ts ea/4 #ad ,ma!matical ,!ory ( ,relativity1 p4 #bch4 ,! limitations ( k introduc$ by ! selectiv5ess ( our p]ceptual app>atus may be illu/rat$ by ! inde/ructibility ( matt]4 ,?is has be5 gradually discov]$ by exp]im5t1 & seem$ a well-f\nd$ empirical law ( nature4 ,n[ x turns out t1 f our orig9al space-"t cont9uum1 we c con/ruct a ma!matical expression :i* w h prop]ties caus+ x to appe> inde/ructible4 ,! /atem5t t matt] is inde/ructible !n ceases to be a proposition ( physics1 & becomes in/ead a proposition ( l+ui/ics & psy*ology4 ,z a proposition ( l+ui/ics3 8,matt]0 is ! "n ( ! ma!matical expression 9 "q4 ,z a proposition ( psy*ology3 ,our s5ses are su* t we notice :at is r\ghly ! ma!matical expression 9 "q1 & we are l$ ne>] & ne>] to x z we ref9e ^u our crude p]ceptions by sci5tific obs]vation4 ,?is is mu* less ?an physici/s us$ to ?9k !y knew ab\t matt]4 ,! read] may say3 ,:at !n is left ( physics8 ,:at d we really "k ab\t ! _w ( matt]8 ,"h we may di/+ui% ?ree dep>tm5ts ( physics4 ,!re is fir/ :at is includ$ )9 ! !ory ( relativity1 g5]aliz$ z widely z possible4 ,next1 !re are laws :i* _c be br\ght )9 ! scope ( relativity4 ,?irdly1 !re is :at may be call$ geography4 ,let u consid] ea* ( ^! 9 turn4 ,! !ory ( relativity1 ap>t f conv5tion1 tells u t ! ev5ts 9 ! univ]se h a f\r-dim5sional ord]1 & t1 betwe5 any two ev5ts :i* are ne> toge!r 9 ?is ord]1 !re is a relation call$ 8int]val10 :i* is capable ( be+ measur$ if suitable precautions are tak54 ,we make also an assumption z to :at happ5s :5 a little measur+ rod is c>ri$ r\nd a clos$ circuit 9 a c]ta9 mann]2 ! consequ5ces ( ?is assumption are su* z to make x highly probable t x is true4 ,beyond ?is1 !re is little 9 ! !ory ( relativity t c be reg>d$ z physical laws4 ,!re is a great deal ( ma!matics1 %[+ t c]ta9 ma!matically-con/ruct$ quantities mu/ behave l ! ?+s we p]ceive2 & !re is a sugge/ion ( a bridge betwe5 psy*ology & physics 9 ! !ory t ^! ma!matically-con/ruct$ quantities are :at our s5ses are adapt$ = p]ceiv+4 ,b nei!r ( ^! ?+s is physics 9 ! /rict s5se4 ,! "p ( physics :i* _c1 at pres5t1 be br\ght )9 ! scope ( relativity is l>ge & important4 ,!re is no?+ 9 relativity to %[ :y !re %\ld be electrons & protons2 relativity _c give any reason :y matt] %\ld exi/ 9 little lumps4 ,) ?is goes ! :ole !ory ( ! /ructure ( ! atom4 ,! !ory ( quanta also is q outside ! scope ( relativity4 ,relativity is1 9 a s5se1 ! mo/ extreme application ( :at may be call$ next-to-next me?ods4 ,gravitation is no long] reg>d$ z due to ! effect ( ! sun ^u a planet1 b z express+ *>act]i/ics ( ! region 9 :i* ! planet happ5s to be4 ,di/ance1 :i* us$ to be ?\ght to h a def9ite mean+ h[ev] f> ap>t two po9ts might be1 is n[ only def9ite = neighbor+ po9ts4 ,! di/ance betwe5 widely sep>at$ places dep5ds ^u ! r\te *os54 ,we may1 x is true1 def9e ! di/ance z ! geodesic di/ance1 b t c only be e/imat$ by add+ up little bits1 t is to say1 by ! me?od we use 9 e/imat+ ! l5g? ( a curve4 ,:at applies to di/ance applies equally to ! /raight l9e4 ,!re is no?+ 9 ! actual _w hav+ exactly ! prop]ties t /raight l9es 7 suppos$ to h2 ! ne>e/ approa* is ! track ( a light ray4 ,/raight l9es h to be replac$ by geodesics1 :i* are def9$ by :at !y d at ea* po9t1 n all at once1 l ,euclidean /raight l9es4 ,measurem5t1 9 ,weyl's !ory1 suff]s ! same fate4 ,we c only use a measur+ rod to give l5g?s 9 "o place3 :5 we move x to ano!r region1 !re is no kn[+ h[ x w alt]4 ,we d assume1 h[ev]1 t1 if x alt]s1 x alt]s bit by bit1 gradually1 cont9u\sly1 & n by sudd5 jumps4 ,p]haps ?is assumption is unju/ifi$4 ,x belongs to ! g5]al outlook ( relativity1 :i* is t ( cont9uity4 ,no d\bt x is ow+ to ?is outlook t relativity is unable to acc\nt = ! discont9uities 9 physics1 su* z quanta1 electrons & protons4 ,p]haps relativity w conqu] ^! doma9s :5 x le>ns to disp5se ) ! assumption ( cont9uity4 ,f9ally we come to geography1 9 :i* ,i include hi/ory4 ,! sep>ation ( hi/ory f geography re/s ^u ! sep>ation ( "t f space2 :5 we amalgamate ! two 9 space-"t1 we ne$ "o ^w to describe ! comb9ation ( geography & hi/ory4 ,= ! sake ( simplicity1 ,i %all use ! "o ^w geography 9 ?is ext5d$ s5se4 ,geography1 9 ?is s5se1 includes ev]y?+ t1 z a matt] ( crude fact1 di/+ui%es "o "p ( space-"t f ano!r4 ,"o "p is occupi$ by ! sun1 "o by ! e>?2 ! int]m$iate regions conta9 light waves1 b no matt] 7ap>t f a v little "h & !re74 ,!re is a c]ta9 degree ( !oretical connection betwe5 diff]5t geographical facts2 to e/abli% ?is is ! purpose ( physical laws4 ,x is ?\ght t a suffici5t k ( ! geographical facts ( ! sol> sy/em ?r\gh\t any f9ite "t1 h[ev] %ort1 w\ld enable an ideally compet5t physici/ to pr$ict ! future ( ! sol> sy/em s long z x rema9$ remote f o!r />s4 ,we are already 9 a position to calculate ! l>ge facts ab\t ! sol> sy/em backw>ds & =w>ds = va/ p]iods ( "t4 ,b 9 all su* calculations we ne$ a basis ( crude fact4 ,! facts are int]connect$1 b facts c only be inf]r$ f o!r facts1 n f g5]al laws alone4 ,?us ! facts ( geography h a c]ta9 indep5d5t /atus 9 physics4 ,no am\nt ( physical laws w enable u to inf] a physical fact unless we "k o!r facts z data = our inf]5ce4 ,& "h :5 ,i speak ( 8facts0 ,i am ?9k+ ( p>ticul> facts ( geography1 9 ! ext5d$ s5se 9 :i* ,i am us+ ! t]m4 ,9 ! !ory ( relativity1 we are conc]n$ ) /ructure1 n ) ! mat]ial ( :i* ! /ructure is compos$4 ,9 geography1 on ! o!r h&1 ! mat]ial is relevant4 ,if !re is to be any diff]5ce betwe5 "o place & ano!r1 !re mu/ ei!r be diff]5ces betwe5 ! mat]ial 9 "o place & t 9 ano!r1 or places :]e !re is mat]ial & places :]e !re is none4 ,! =m] ( ^! alt]natives seems ! m satisfactory4 ,we might try to say3 ,!re are electrons & protons1 & ! re/ is empty4 ,b 9 ! 8empty0 regions !re are light waves1 s t we _c say no?+ happ5s 9 !m4 ,"s p ma9ta9 t ! light waves take place 9 ! e!r1 o!rs are cont5t to say simply t !y take place2 b 9 any case ev5ts are occurr+ :]e !re are light waves4 ,t is all t we c really say = ! places :]e !re is matt]1 s9ce matt] has turn$ out to be a ma!matical con/ruction built out ( ev5ts4 ,we may say1 !re=e1 t !re are ev5ts ev]y:]e 9 space-"t1 b !y mu/ be ( a some:at diff]5t k9d accord+ z we are deal+ ) a region :]e !re is an electron or proton or ) ! sort ( region we %\ld ord9>ily call empty4 ,b z to ! intr9sic nature ( ^! ev5ts we c "k no?+1 except :5 !y happ5 to be ev5ts 9 our own lives4 ,our own p]ceptions & feel+s mu/ be "p ( ! crude mat]ial ( ev5ts :i* physics arranges into a patt]n--or r1 :i* physics f9ds to be arrang$ 9 a patt]n4 ,z reg>ds ev5ts :i* d n =m "p ( our own lives1 physics tells u ! patt]n ( !m1 b is q unable to tell u :at !y are l 9 !mselves4 ,nor does x seem possible t ?is %\ld be discov]$ by any o!r me?od4 ,,*apt] ,,xiii3 ,,! ,,abolition ,,( 8,,=ce0 ,9 ! ,newtonian sy/em1 bodies "u ! action ( no =ces move 9 /raight l9es ) uni=m velocity2 :5 bodies d n move 9 ?is way1 _! *ange ( motion is ascrib$ to a 8=ce40 ,"s =ces seem intelligible to our imag9ation3 ^? ex]t$ by a rope or /r+1 by bodies collid+1 or by any k9d ( obvi\s pu%+ or pull+4 ,z expla9$ 9 an e>li] *apt]1 our app>5t imag9ative und]/&+ ( ^! processes is q fallaci\s2 all t x really means is t pa/ exp]i5ce enables u to =esee m or less :at is go+ to happ5 )\t ! ne$ ( ma!matical calculations4 ,b ! 8=ces0 involv$ 9 gravitation & 9 ! less famili> =ms ( electrical action d n seem 9 ?is way 8natural0 to our imag9ation4 ,x seems odd t ! e>? c float 9 ! void3 ! natural ?+ to suppose is t x mu/ fall4 ,t is :y x has to be support$ on an elephant1 & ! elephant on a tortoise1 accord+ to "s e>ly speculators4 ,! ,newtonian !ory1 9 addition to action at a di/ance1 introduc$ two o!r imag9ative novelties4 ,! fir/ 01 t gravitation is n always & ess5tially direct$ :at we %\ld call 8d[nw>ds10 i4e41 t[>ds ! c5t] ( ! e>?4 ,! second 01 t a body go+ r\nd & r\nd 9 a circle ) uni=m velocity is n 8mov+ uni=mly0 9 ! s5se 9 :i* t phrase is appli$ to ! motion ( bodies "u no =ces1 b is p]petually be+ turn$ out ( ! /raight c\rse t[>ds ! c5t] ( ! circle1 :i* requires a =ce pull+ x 9 t direction4 ,h5ce ,newton arriv$ at ! view t ! planets are attract$ to ! sun by a =ce1 :i* is call$ gravitation4 ,?is :ole po9t ( view1 z we h se51 is sup]s$$ by relativity4 ,!re are no long] su* ?+s z 8/raight l9es0 9 ! old geometrical s5se4 ,!re are 8/raighte/ l9es10 or geodesics1 b ^! involve "t z well z space4 ,a light ray pass+ ?r\gh ! sol> sy/em does n describe ! same orbit z a comet1 f a geometrical po9t ( view2 nev]!less ea* moves 9 a geodesic4 ,! :ole imag9ative picture is *ang$4 ,a poet might say t wat] runs d[n hill because x is attract$ to ! sea1 b a physici/ or an ord9>y mortal w\ld say t x moves z x does1 at ea* po9t1 because ( ! nature ( ! gr\nd at t po9t1 )\t reg>d to :at lies ahead ( x4 ,j z ! sea does n cause ! wat] to run t[>ds x1 s ! sun does n cause ! planets to move r\nd x4 ,! planets move r\nd ! sun because t is ! easie/ ?+ to d--9 ! te*nical s5se ( 8lea/ action40 ,x is ! easie/ ?+ to d because ( ! nature ( ! region 9 :i* !y are1 n because ( an influ5ce emanat+ f ! sun4 ,! suppos$ necessity ( attribut+ gravitation to a 8=ce0 attract+ ! planets t[>ds ! sun has aris5 f ! det]m9ation to pres]ve ,euclidean geometry at all co/s4 ,if we suppose t our space is ,euclidean1 :5 9 fact x is n1 we %all h to call 9 physics to rectify ! errors ( our geometry4 ,we %all f9d bodies n mov+ 9 :at we insi/ ^u reg>d+ z /raight l9es1 & we %all dem& a cause = ?is behavior4 ,edd+ton has /at$ ?is matt] ) admirable lucidity4 ,he supposes a physici/ :o has assum$ ! =mula = int]val :i* is us$ 9 ! special !ory ( relativity--a =mula :i* /ill supposes t ! obs]v]'s space is ,euclidean4 ,he cont9ues3 ,s9ce int]vals c be comp>$ by exp]im5tal me?ods1 he ought soon to discov] t 8 7=mula = ! int]val7 _c be reconcil$ ) obs]vational results1 & s realize 8 mi/ake4 ,b ! m9d does n s readily get rid ( an obsession4 ,x is m likely t our obs]v] w cont9ue 9 8 op9ion1 & attribute ! discrepancy ( ! obs]vations to "s influ5ce :i* is pres5t & affects ! behavior ( 8 te/-bodies4 ,he w1 s to speak1 introduce a sup]natural ag5cy :i* he c blame = ! consequ5ces ( 8 mi/ake4444 ,! "n giv5 to any ag5cy :i* causes deviation f uni=m motion 9 a /raight l9e is =ce accord+ to ! ,newtonian def9ition ( =ce4 ,h5ce ! ag5cy invok$ ?r\gh our obs]v]'s mi/ake is describ$ z a 8field ( =ce40444 ,a field ( =ce repres5ts ! discrepancy betwe5 ! natural geometry ( a co-ord9ate sy/em & ! ab/ract geometry arbitr>ily ascrib$ to x4#ae #ae ,ma!matical ,!ory ( ,relativity1 pp4 #cg-ch4 ,italics 9 ! orig9al4 ,if p 7 to le>n to conceive ! _w 9 ! new way1 )\t ! old notion ( 8=ce10 x w\ld alt] n only _! physical imag9ation1 b probably also _! morals & politics4 ,! latt] effect w\ld be q illogical1 b is none ! less probable on t acc\nt4 ,9 ,newton's !ory ( ! sol> sy/em1 ! sun seems l a mon>* ^: behe/s ! planets h to obey4 ,9 ,e9/e9's _w !re is m individualism & less gov]nm5t ?an 9 ,newton's4 ,!re is also f> less hu/le3 we h se5 t laz9ess is ! fundam5tal law ( ,e9/e9's univ]se4 ,! ^w 8dynamic0 has come to mean1 9 newspap] language1 8en]getic & =ceful02 b if x meant 8illu/rat+ ! pr9ciples ( dynamics10 x ought to be appli$ to ! p 9 hot climates :o sit "u banana trees wait+ = ! fruit to drop into _! m\?s4 ,i hope t j\rnali/s1 9 future1 :5 !y speak ( a 8dynamic p]sonality10 w mean a p]son :o does :at is lea/ tr\ble at ! mom5t1 )\t ?9k+ ( remote consequ5ces4 ,if ,i c contribute to ?is result1 ,i %all n h writt5 9 va94 ,x has be5 cu/om>y = p to draw argum5ts f ! laws ( nature z to :at we ought to d4 ,su* argum5ts seem to me a mi/ake3 to imitate nature may be m]ely slavi%4 ,b if nature1 z portray$ by ,e9/e91 is to be our model1 x w\ld seem t ! an>*i/s w h ! be/ ( ! argum5t4 ,! physical univ]se is ord]ly1 n because !re is a c5tral gov]nm5t1 b because e body m9ds its own bus9ess4 ,no two p>ticles ( matt] ev] come into contact2 :5 !y get too close1 !y bo? move (f4 ,if a man 7 _h up = knock+ ano!r man d[n1 he w\ld be sci5tifically correct 9 plead+ t he _h nev] t\*$ him4 ,:at happ5$ 0 t !re 0 a hill 9 space-"t 9 ! region ( ! o!r man's nose1 & x fell d[n ! hill4 ,! abolition ( 8=ce0 seems to be connect$ ) ! sub/itution ( sight = t\* z ! s\rce ( physical ideas1 z expla9$ 9 ,*apt] ,i4 ,:5 an image 9 a look+ glass moves1 we d n ?9k t some?+ has pu%$ x4 ,9 places :]e !re are two l>ge mirrors opposite to ea* o!r1 y may see innum]able reflections ( ! same object4 ,suppose a g5tleman 9 a top-hat is /&+ betwe5 ! mirrors1 !re may be tw5ty or ?irty top-hats 9 ! reflections4 ,suppose n[ somebody comes & knocks (f ! g5tleman's hat ) a /ick3 all ! o!r tw5ty or ?irty top-hats w tumble d[n at ! same mom5t4 ,we ?9k t a =ce is ne$$ to knock (f ! 8real0 top-hat1 b we ?9k ! rema9+ tw5ty or ?irty tumble (f1 s to speak1 ( !mselves1 or out ( a m]e passion = imitation4 ,let u try to ?9k out ?is matt] a little m s]i\sly4 ,obvi\sly some?+ happ5s :5 an image 9 a look+ glass moves4 ,f ! po9t ( view ( sight1 ! ev5t seems j z real z if x 7 n 9 a mirror4 ,b no?+ has happ5$ f ! po9t ( view ( t\* or he>+4 ,:5 ! 8real0 top-hat falls1 x makes a noise2 ! tw5ty or ?irty reflections fall )\t a s\nd4 ,if x falls on y\r toe1 y feel x2 b we believe t ! tw5ty or ?irty p 9 ! mirrors feel no?+1 ?\gh top-hats fall on _! toes too4 ,b all ?is is equally true ( ! a/ronomical _w4 ,x makes no noise1 because s\nd _c travel across a vacuum4 ,s f> z we "k1 x causes no 8feel+s10 because !re is no "o on ! spot to 8feel0 x4 ,! a/ronomical _w1 !re=e1 seems h>dly m 8real0 or 8solid0 ?an ! _w 9 ! look+ glass1 & has j z little ne$ ( 8=ce0 to make x move4 ,! read] may feel t ,i am indulg+ 9 idle sophi/ry4 8,aft] all10 he may say1 8! image 9 ! mirror is ! reflection ( some?+ solid1 & ! top-hat 9 ! mirror only falls (f because ( ! =ce appli$ to ! real top-hat4 ,! top-hat 9 ! mirror _c indulge 9 behavior ( its own2 x has to copy ! real "o4 ,?is %[s h[ diff]5t ! image is f ! sun & ! planets1 because !y are n oblig$ to be p]petually imitat+ a prototype4 ,s y _h bett] give up pret5d+ t an image is j z real z "o ( ! heav5ly bodies40 ,!re is1 ( c\rse1 "s tru? 9 ?is2 ! po9t is to discov] exactly :at tru?4 ,9 ! fir/ place1 images are n 8imag9>y40 ,:5 y see an image1 c]ta9 p]fectly real light waves rea* y\r eye2 & if y hang a clo? ov] ! mirror1 ^! light waves cease to exi/4 ,!re is1 h[ev]1 a purely optical diff]5ce betwe5 an 8image0 & a 8real0 ?+4 ,! optical diff]5ce is b\nd up ) ?is "q ( imitation4 ,:5 y hang a clo? ov] ! mirror1 x makes no diff]5ce to ! 8real0 object2 b :5 y move ! 8real0 object away1 ! image vani%es also4 ,?is makes u say t ! light rays :i* make ! image are only reflect$ at ! surface ( ! mirror1 & d n really come f a po9t beh9d x1 b f ! 8real0 object4 ,we h "h an example ( a g5]al pr9ciple ( great importance4 ,mo/ ( ! ev5ts 9 ! _w are n isolat$ occurr5ces1 b memb]s ( gr\ps ( m or less simil> ev5ts1 :i* are su* t ea* gr\p is connect$ 9 an assignable mann] ) a c]ta9 small region ( space-"t4 ,?is is ! case ) ! light rays :i* make u see bo? ! object & its reflection 9 ! mirror3 !y all emanate f ! object z a c5t]4 ,if y put an opaque globe r\nd ! object at a c]ta9 di/ance1 ! object & its reflection are invisible at any po9t outside ! globe4 ,we h se5 t gravitation1 al?\gh no long] reg>d$ z an action at a di/ance1 is /ill connect$ ) a c5t]3 !re is1 s to speak1 a hill symmetrically arrang$ ab\t its summit1 & ! summit is ! place :]e we conceive ! body to be :i* is connect$ ) ! gravitational field we are consid]+4 ,= simplicity1 common s5se lumps toge!r all ! ev5ts :i* =m "o gr\p 9 ! above s5se4 ,:5 two p see ! same object1 two diff]5t ev5ts occur1 b !y are ev5ts belong+ to "o gr\p & connect$ ) ! same c5t]4 ,j ! same applies :5 two p 7z we say7 he> ! same noise4 ,& s ! reflection 9 a mirror is less 8real0 ?an ! object reflect$1 ev5 f an optical po9t ( view1 because light rays d n spread 9 all directions f ! place :]e ! image seems to be1 b only 9 directions 9 front ( ! mirror1 & only s long z ! object reflect$ rema9s 9 position4 ,?is illu/rates ! usefulness ( gr\p+ connect$ ev5ts ab\t a c5t] 9 ! way we h be5 consid]+4 ,:5 we exam9e ! *anges 9 su* a gr\p ( objects1 we f9d t !y are ( two k9ds3 !re are ^? :i* affect only "s memb] ( ! gr\p1 & ^? :i* make connect$ alt]ations 9 all ! memb]s ( ! gr\p4 ,if y put a c&le 9 front ( a mirror1 & !n hang black clo? ov] ! mirror1 y alt] only ! reflection ( ! c&le z se5 f v>i\s places4 ,if y %ut y\r eyes1 y alt] its appe>ance to y1 b n its appe>ance else:]e4 ,if y put a r$ globe r\nd x at a di/ance ( a foot1 y alt] its appe>ance at any di/ance great] ?an a foot1 b n at any di/ance less ?an a foot4 ,9 all ^! cases1 y d n reg>d ! c&le itself z hav+ *ang$2 9 fact1 9 all ( !m1 y f9d t !re are gr\ps ( *anges connect$ ) a diff]5t c5t] or ) a numb] ( diff]5t c5t]s4 ,:5 y %ut y\r eyes1 = in/ance1 y\r eyes1 n ! c&le1 look diff]5t to any o!r obs]v]3 ! c5t] ( ! *anges t occur is 9 y\r eyes4 ,b :5 y bl[ out ! c&le1 its appe>ance ev]y:]e is *ang$2 9 ?is case y say t ! *ange has happ5$ to ! c&le4 ,! *anges t happ5 to an object are ^? t affect ! :ole gr\p ( ev5ts :i* c5t] ab\t ! object4 ,all ?is is only an int]pretation ( common s5se1 & an attempt to expla9 :at we mean by say+ t ! image ( ! c&le 9 ! mirror is less 8real0 ?an ! c&le4 ,!re is no connect$ gr\p ( ev5ts situat$ all r\nd ! place :]e ! image seems to be1 & *anges 9 ! image c5t] ab\t ! c&le1 n ab\t a po9t beh9d ! mirror4 ,?is gives a p]fectly v]ifiable mean+ to ! /atem5t t ! image is 8only0 a reflection4 ,& at ! same "t x enables u to reg>d ! heav5ly bodies1 al?\gh we c only see & n t\* !m1 z m 8real0 ?an an image 9 a look+ glass4 ,we c n[ beg9 to int]pret ! common s5se notion ( "o body hav+ an 8effect0 ^u ano!r1 :i* we mu/ d if we are really to und]/& :at is meant by ! abolition ( 8=ce40 ,suppose y come into a d>k room & swit* on ! electric light3 ! appe>ance ( ev]y?+ 9 ! room is *ang$4 ,s9ce ev]y?+ 9 ! room is visible because x reflects ! electric light1 ?is case is really analog\s to t ( ! image 9 ! mirror2 ! electric light is ! c5t] f :i* all ! *anges emanate4 ,9 ?is case1 ! 8effect0 is expla9$ by :at we h already said4 ,! m important case is :5 ! effect is a movem5t4 ,suppose y let loose a tig] 9 ! middle ( a ,bank ,holiday cr[d3 !y w\ld all move1 & ! tig] w\ld be ! c5t] ( _! v>i\s movem5ts4 ,a p]son :o c\ld see ! p b n ! tig] w\ld inf] t !re 0 some?+ repulsive at t po9t4 ,we say 9 ?is case t ! tig] has an effect ^u ! p1 & we might describe ! tig]'s action ^u !m z ( ! nature ( a repulsive =ce4 ,we "k1 h[ev]1 t !y fly because ( some?+ :i* happ5s to !m1 n m]ely because ! tig] is :]e he is4 ,!y fly because !y c see & he> him1 t is to say1 because c]ta9 waves rea* _! eyes & e>s4 ,if ^! waves c\ld be made to rea* !m )\t !re be+ any tig]1 !y w\ld fly j z fa/1 because ! neighborhood w\ld seem to !m j z unpleasant4 ,let u n[ apply simil> consid]ations to ! sun's gravitation4 ,! 8=ce0 ex]t$ by ! sun only diff]s f t ex]t$ by ! tig] 9 be+ attractive in/ead ( repulsive4 ,in/ead ( act+ ?r\gh waves ( light or s\nd1 ! sun acquires its app>5t p[] ?r\gh ! fact t !re are modifications ( space-"t all r\nd ! sun4 ,l ! noise ( ! tig]1 !y are m int5se ne> _! s\rce2 z we travel away !y gr[ less & less4 ,to say t ! sun 8causes0 ^! modifications ( space-"t is to add no?+ to our k4 ,:at we "k is t ! modifications proce$ accord+ to a c]ta9 rule1 & t !y are gr\p$ symmetrically ab\t ! sun z c5t]4 ,! language ( cause & effect adds only a numb] ( q irrelevant imag9+s1 connect$ ) w1 muscul> t5sion1 & su* matt]s4 ,:at we c m or less asc]ta9 is m]ely ! =mula accord+ to :i* space-"t is modifi$ by ! pres5ce ( gravitat+ matt]4 ,m correctly3 we c asc]ta9 :at k9d ( space-"t is ! pres5ce ( gravitat+ matt]4 ,:5 space-"t is n accurately ,euclidean 9 a c]ta9 region1 b has a non-,euclidean "* :i* gr[s m & m m>k$ z we approa* a c]ta9 c5t]1 & :51 fur!r1 ! dep>ture f ,euclid obeys a c]ta9 law1 we describe ?is /ate ( affairs briefly by say+ t !re is gravitat+ matt] at ! c5t]4 ,b ?is is only a comp5di\s acc\nt ( :at we "k4 ,:at we "k is ab\t ! places :]e ! gravitat+ matt] is n1 n ab\t ! place :]e x is4 ,! language ( cause & effect 7( :i* 8=ce0 is a p>ticul> case7 is ?us m]ely a conv5i5t %or?& = c]ta9 purposes2 x does n repres5t any?+ t is g5u9ely to be f\nd 9 ! physical _w4 ,& h[ ab\t matt]8 ,is matt] also no m ?an a conv5i5t %or?&8 ,?is "q1 h[ev]1 be+ a l>ge "o1 dem&s a sep>ate *apt]4 ,,*apt] ,,xiv3 ,,:at ,,is ,,matt]8 ,! "q 8,:at is matt]80 is ( ! k9d t is ask$ by metaphysicians1 & answ]$ 9 va/ books ( incr$ible obscurity4 ,b ,i am n ask+ ! "q z metaphysician3 ,i am ask+ x z a p]son :o wants to f9d out :at is ! moral ( mod]n physics1 & m especially ( ! !ory ( relativity4 ,x is obvi\s f :at we h le>n$ ( t !ory t matt] _c be conceiv$ q z x us$ to be4 ,i ?9k we c n[ say m or less :at ! new conception mu/ be4 ,!re 7 two traditional conceptions ( matt]1 bo? ( :i* h _h advocates ev] s9ce sci5tific speculation began4 ,!re 7 ! atomi/s1 :o ?\ght t matt] consi/$ ( t9y lumps :i* c\ld nev] be divid$2 ^! 7 suppos$ to hit ea* o!r & !n b\nce (f 9 v>i\s ways4 ,aft] ,newton1 !y 7 no long] suppos$ actually to come into contact ) ea* o!r1 b to attract & repel ea* o!r1 & move 9 orbits r\nd ea* o!r4 ,!n !re 7 ^? :o ?\ght t !re is matt] ( "s k9d ev]y:]e1 & t a true vacuum is impossible4 ,desc>tes held ?is view1 & attribut$ ! motions ( ! planets to vortices 9 ! e!r4 ,! ,newtonian !ory ( gravitation caus$ ! view t !re is matt] ev]y:]e to fall into discr$it1 ! m s z light 0 ?\ght by ,newton & 8 disciples to be due to actual p>ticles travel+ f ! s\rce ( ! light4 ,b :5 ?is view ( light 0 disprov$1 & x 0 %[n t light consi/$ ( waves1 ! e!r 0 reviv$ s t !re %\ld be some?+ to undulate4 ,! e!r became /ill m respectable :5 x 0 f\nd to play ! same "p 9 electromagnetic ph5om5a z 9 ! propagation ( light4 ,x 0 ev5 hop$ t atoms might turn out to be a mode ( motion ( ! e!r4 ,at ?is /age1 ! atomic view ( matt] 01 on ! :ole1 gett+ ! wor/ ( x4 ,leav+ relativity aside = ! mom5t1 mod]n physics has provid$ pro( ( ! atomic /ructure ( ord9>y matt]1 :ile n disprov+ ! argum5ts 9 favor ( ! e!r1 to :i* no su* /ructure is attribut$4 ,! result 0 a sort ( compromise betwe5 ! two views1 ! "o apply+ to :at 0 call$ 8gross0 matt]1 ! o!r to ! e!r4 ,!re c be no d\bt ab\t electrons & protons1 ?\gh1 z we %all see %ortly1 !y ne$ n be conceiv$ z atoms 7 conceiv$ traditionally4 ,z = ! e!r1 its /atus is v curi\s3 _m physici/s /ill ma9ta9 t1 )\t x1 ! propagation ( light & o!r electromagnetic waves w\ld be inconceivable1 b except 9 ?is way x is difficult to see :at purpose x s]ves4 ,! tru? is1 ,i ?9k1 t relativity dem&s ! ab&onm5t ( ! old conception ( 8matt]10 :i* is infect$ by ! metaphysics associat$ ) 8sub/ance10 & repres5ts a po9t ( view n really necess>y 9 deal+ ) ph5om5a4 ,?is is :at we mu/ n[ inve/igate4 ,9 ! old view1 a piece ( matt] 0 some?+ :i* surviv$ all ?r\gh "t1 :ile nev] be+ at m ?an "o place at a giv5 "t4 ,?is way ( look+ at ?+s is obvi\sly connect$ ) ! complete sep>ation ( space & "t 9 :i* p =m]ly believ$4 ,:5 we sub/itute space-"t = space & "t1 we %all naturally expect to d]ive ! physical _w f con/itu5ts :i* are z limit$ 9 "t z 9 space4 ,su* con/itu5ts are :at we call 8ev5ts40 ,an ev5t does n p]si/ & move1 l ! traditional piece ( matt]2 x m]ely exi/s = its little mom5t & !n ceases4 ,a piece ( matt] w ?us be resolv$ into a s]ies ( ev5ts4 ,j z1 9 ! old view1 an ext5d$ body 0 compos$ ( a numb] ( p>ticles1 s1 n[1 ea* p>ticle1 be+ ext5d$ 9 "t1 mu/ be reg>d$ z compos$ ( :at we may call 8ev5t-p>ticles40 ,! :ole s]ies ( ^! ev5ts makes up ! :ole hi/ory ( ! p>ticle1 & ! p>ticle is reg>d$ z be+ its hi/ory1 n "s metaphysical entity to :i* ! ev5ts happ54 ,?is view is r5d]$ necess>y by ! fact t relativity compels u to place "t & space m on a level ?an !y 7 9 ! old] physics4 ,?is ab/ract requirem5t mu/ be br\ght into relation ) ! kn[n facts ( ! physical _w4 ,n[ :at are ! kn[n facts8 ,let u take x z conc$$ t light consi/s ( waves travel+ ) ! receiv$ velocity4 ,we !n "k a great deal ab\t :at goes on 9 ! p>ts ( space-"t :]e !re is no matt]2 we "k1 t is to say1 t !re are p]iodic occurr5ces 7light waves7 obey+ c]ta9 laws4 ,^! light waves />t f atoms1 & ! mod]n !ory ( ! /ructure ( ! atoms enables u to "k a great deal ab\t ! circum/ances "u :i* !y />t1 & ! reasons :i* det]m9e _! wave l5g?s4 ,we c f9d out n only h[ "o light wave travels1 b h[ its s\rce moves relatively to ourselves4 ,b :5 ,i say ?is ,i am assum+ t we c recognise a s\rce ( light z ! same at two slightly diff]5t times4 ,?is is1 h[ev]1 ! v ?+ :i* _h to be inve/igat$4 ,we saw1 9 ! prec$+ *apt]1 h[ a gr\p ( connect$ ev5ts c be =m$1 all relat$ to ea* o!r by a law1 & all rang$ ab\t a c5t] 9 space-"t4 ,su* a gr\p ( ev5ts w be ! arrival1 at v>i\s places1 ( ! light waves emitt$ by a brief fla% ( light4 ,we d n ne$ to suppose t any?+ p>ticul> is happ5+ at ! c5t]2 c]ta9ly we d n ne$ to suppose t we "k :at is happ5+ !re4 ,:at we "k is t1 z a matt] ( geometry1 ! gr\p ( ev5ts 9 "q are rang$ ab\t a c5t]1 l wid5+ ripples on a pool :5 a fly has t\*$ x4 ,we c hypo!tically inv5t an occurr5ce :i* is to h happ5$ at ! c5t]1 & set =? ! laws by :i* ! consequ5t di/urbance is transmitt$4 ,?is hypo!tical occurr5ce w !n appe> to common s5se z ! 8cause0 ( ! di/urbance4 ,x w also c\nt z "o ev5t 9 ! biography ( ! p>ticle ( matt] :i* is suppos$ to occupy ! c5t] ( ! di/urbance4 ,n[ we f9d n only t "o light wave travels outw>d f a c5t] accord+ to a c]ta9 law1 b also t1 9 g5]al1 x is foll[$ by o!r closely simil> light waves4 ,! sun1 = example1 does n *ange its appe>ance sudd5ly2 ev5 if a cl\d passes across x dur+ a high w9d1 ! transition is gradual1 ?\gh swift4 ,9 ?is way a gr\p ( occurr5ces connect$ ) a c5t] at "o po9t ( space-"t is br\ght into relation ) o!r v simil> gr\ps ^: c5t]s are at neighbor+ po9ts ( space-"t4 ,= ea* ( ^! o!r gr\ps common s5se inv5ts simil> hypo!tical occurr5ces to occupy _! c5t]s1 & says t all ^! hypo!tical occurr5ces are "p ( "o hi/ory2 t is to say1 x inv5ts a hypo!tical 8p>ticle0 to :i* ! hypo!tical occurr5ces are to h occurr$4 ,x is only by ?is d\ble use ( hypo!sis1 p]fectly unnecess>y 9 ea* case1 t we arrive at any?+ t c be call$ 8matt]0 9 ! old s5se ( ! ^w4 ,if we are to avoid unnecess>y hypo!ses1 we %all say t an electron at a giv5 mom5t is ! v>i\s di/urbances 9 ! surr\nd+ m$ium :i*1 9 ord9>y language1 w\ld be said to be 8caus$0 by x4 ,b we %all n take ^! di/urbances at :at is1 = u1 ! mom5t 9 "q1 s9ce t w\ld make !m dep5d ^u ! obs]v]2 we %all in/ead travel outw>d f ! electron ) ! velocity ( light1 & take ! di/urbance we f9d 9 ea* place z we rea* x4 ,! closely simil> set ( di/urbances1 ) v ne>ly ! same c5t]1 :i* is f\nd exi/+ slightly e>li] or slightly lat]1 w be def9$ z be+ ! electron at a slightly e>li] or slightly lat] mom5t4 ,9 ?is way1 we pres]ve all ! laws ( physics1 )\t hav+ rec\rse to unnecess>y hypo!ses or inf]r$ entities1 & we rema9 9 h>mony ) ! g5]al pr9ciple ( economy :i* has enabl$ ! !ory ( relativity to cle> away s mu* useless lumb]4 ,common s5se imag9es t :5 x sees a table x sees a table4 ,?is is a gross delusion4 ,:5 common s5se sees a table1 c]ta9 light waves rea* its eyes1 & ^! are ( a sort :i*1 9 its previ\s exp]i5ce1 has be5 associat$ ) c]ta9 s5sations ( t\*1 z well z ) o!r p's te/imony t !y also saw ! table4 ,b none ( ?is ev] br\ght u to ! table itself4 ,! light waves caus$ occurr5ces 9 our eyes1 & ^! caus$ occurr5ces 9 ! optic n]ve1 & ^! 9 turn caus$ occurr5ces 9 ! bra94 ,any "o ( ^!1 happ5+ )\t ! usual prelim9>ies1 w\ld h caus$ u to h ! s5sations we call 8see+ ! table10 ev5 if !re _h be5 no table4 7,( c\rse1 if matt] 9 g5]al is to be int]pret$ z a gr\p ( occurr5ces1 ?is mu/ apply also to ! eye1 ! optic n]ve1 & ! bra947 ,z to ! s5se ( t\* :5 we press ! table ) our f+]s1 t is an electric di/urbance 9 ! electrons & protons ( our f+] tips1 produc$1 accord+ to mod]n physics1 by ! proximity ( ! electrons & protons 9 ! table4 ,if ! same di/urbance 9 our f+] tips arose 9 any o!r way1 we %\ld h ! same s5sations1 9 spite ( !re be+ no table4 ,! te/imony ( o!rs is obvi\sly a second-h& affair4 ,a witness 9 a law c\rt1 if ask$ :e!r he _h se5 "s occurr5ce1 w\ld n be all[$ to reply t he believ$ s because ( ! te/imony ( o!rs to t effect4 ,9 any case1 te/imony consi/s ( s\nd waves & dem&s psy*ological z well z physical int]pretation2 its connection ) ! object is !re=e v indirect4 ,= all ^! reasons1 :5 we say t a man 8sees a table10 we use a highly abbreviat$ =m ( expression1 conceal+ complicat$ & difficult inf]5ces1 ! validity ( :i* may well be op5 to "q4 ,b we are 9 dang] ( becom+ entangl$ 9 psy*ological que/ions1 :i* we mu/ avoid if we c4 ,let u !re=e return to ! purely physical po9t ( view4 ,:at ,i wi% to sugge/ may be put z foll[s4 ,ev]y?+ t occurs else:]e1 ow+ to ! exi/5ce ( an electron1 c be explor$ exp]im5tally1 at lea/ 9 !ory1 unless x occurs 9 c]ta9 conceal$ ways4 ,b :at occurs )9 ! electron 7if any?+ occurs !re7 x is absolutely impossible to "k3 !re is no conceivable app>atus by :i* we c\ld obta9 ev5 a glimpse ( x4 ,an electron is kn[n by its 8effects40 ,b ! ^w 8effects0 belongs to a view ( causation :i* w n fit mod]n physics1 & 9 p>ticul> w n fit relativity4 ,all t we h a "r to say is t c]ta9 gr\ps ( occurr5ces happ5 toge!r1 t is to say1 9 neighbor+ p>ts ( space-"t4 ,a giv5 obs]v] w reg>d "o memb] ( ! gr\p z e>li] ?an ! o!r1 b ano!r obs]v] may judge ! "t ord] diff]5tly4 ,& ev5 :5 ! "t ord] is ! same = all obs]v]s1 all t we really h is a connection betwe5 ! two ev5ts1 :i* works equally backw>ds & =w>ds4 ,x is n true t ! pa/ det]m9es ! future 9 "s s5se o!r ?an t 9 :i* ! future det]m9es ! pa/3 ! app>5t diff]5ce is only due to our ignorance1 because we "k less ab\t ! future ?an ab\t ! pa/4 ,?is is a m]e accid5t3 !re might be be+s :o w\ld rememb] ! future & h to inf] ! pa/4 ,! feel+s ( su* be+s 9 ^! matt]s w\ld be ! exact opposite ( our own1 b no m fallaci\s4 ,! moral ( ?is is t1 if an electron is only kn[n by its 8effects10 !re is no reason to suppose t any?+ exi/s except ! 8effects40 ,9 s f> z ^! 8effects0 consi/ ( light waves & o!r electromagnetic di/urbances1 we may say t :at is call$ 8empty space0 consi/s ( regions :]e ^! di/urbances are propagat$ freely4 ,e su* di/urbance1 we f9d1 has a c5t]1 & :5 we get v ne> ! c5t] 7?\gh /ill at a f9ite di/ance f x7 we f9d t ! law ( propagation ( ! di/urbance ceases to be valid4 ,?is region )9 :i* ! law does n hold is call$ 8matt]02 x w be an electron or proton accord+ to circum/ances4 ,! region s def9$ is f\nd to move relatively to o!r su* regions1 & its movem5ts foll[ ! kn[n laws ( dynamics4 ,s f>1 ?is !ory provides = electromagnetic ph5om5a & ! motions ( matt]2 & x does s )\t assum+ t 8matt]0 is any?+ b sy/ems ( electromagnetic ph5om5a4 ,9 ord] to c>ry out ! !ory fully1 x w\ld no d\bt be necess>y to introduce _m complications4 ,b x seems fairly cle> t all ! facts & laws ( physics c be int]pret$ )\t assum+ t 8matt]0 is any?+ m ?an gr\ps ( ev5ts1 ea* ev5t be+ ( ! sort :i* we %\ld naturally reg>d z 8caus$0 by ! matt] 9 "q4 ,?is does n involve any *ange 9 ! symbols or =mul ( physics3 x is m]ely a "q ( int]pretation ( ! symbols4 ,?is latitude 9 int]pretation is a *>act]i/ic ( ma!matical physics4 ,:at we "k is c]ta9 v ab/ract logical relations1 :i* we express 9 ma!matical =mul2 we "k also t1 at c]ta9 po9ts1 we arrive at results :i* are capable ( be+ te/$ exp]im5tally4 ,take1 = example1 ! eclipse obs]vations by :i* ,e9/e9's !ory z to ! b5d+ ( light 0 e/abli%$4 ,! actual obs]vation consi/$ 9 ! c>eful measurem5t ( c]ta9 di/ances on c]ta9 photographic plates4 ,! =mul :i* 7 to be v]ifi$ 7 conc]n$ ) ! c\rse ( light 9 pass+ ne> ! sun4 ,al?\gh ! "p ( ^! =mul :i* gives ! obs]v$ result mu/ always be int]pret$ 9 ! same way1 ! o!r "p ( !m may be capable ( a great v>iety ( int]pretations4 ,! =mul giv+ ! motions ( ! planets are almo/ exactly ! same 9 ,e9/e9's !ory z 9 ,newton's1 b ! mean+ ( ! =mul is q diff]5t4 ,x may be said g5]ally t1 9 ! ma!matical treatm5t ( nature1 we c be f> m c]ta9 t our =mul are approximately correct ?an we c be z to ! correctness ( ?is or t int]pretation ( !m4 ,& s 9 ! case ) :i* ?is *apt] is conc]n$3 ! "q z to ! nature ( an electron or a proton is by no means answ]$ :5 we "k all t ma!matical physics has to say z to ! laws ( its motion & ! laws ( its int]action ) ! environm5t4 ,a def9ite & conclusive answ] to our "q is n possible j because a v>iety ( answ]s are compatible ) ! tru? ( ma!matical physics4 ,nev]!less "s answ]s are pref]able to o!rs1 because "s h a great] probability 9 _! favor4 ,we h be5 seek+1 9 ?is *apt]1 to def9e matt] s t !re mu/ be su* a ?+ if ! =mul ( physics are true4 ,if we _h made our def9ition su* z to secure t a p>ticle ( matt] %\ld be :at "o ?9ks ( z sub/antial1 a h>d1 def9ite lump1 we %\ld n h be5 sure t any su* ?+ exi/s4 ,t is :y our def9ition1 ?\gh x may seem complicat$1 is pref]able f ! po9t ( view ( logical economy & sci5tific caution4 ,,*apt] ,,xv3 ,,philosophical ,,consequ5ces ,! philosophical consequ5ces ( relativity are nei!r s great nor s />tl+ z is sometimes ?\ght4 ,x ?r[s v little light on "t-honor$ controv]sies1 su* z t betwe5 realism & idealism4 ,"s p ?9k t x supports ,kant's view t space & "t are 8subjective0 & are 8=ms ( intuition40 ,i ?9k su* p h be5 misl$ by ! way 9 :i* writ]s on relativity speak ( 8! obs]v]40 ,x is natural to suppose t ! obs]v] is a human be+1 or at lea/ a m9d2 b he is j z likely to be a photographic plate or a clock4 ,t is to say1 ! odd results z to ! diff]5ce betwe5 "o 8po9t ( view0 & ano!r are conc]n$ ) 8po9t ( view0 9 a s5se applicable to physical in/rum5ts j z mu* z to p ) p]ceptions4 ,! 8subjectivity0 conc]n$ 9 ! !ory ( relativity is a physical subjectivity1 :i* w\ld exi/ equally if !re 7 no su* ?+s z m9ds or s5ses 9 ! _w4 ,moreov]1 x is a /rictly limit$ subjectivity4 ,! !ory does n say t ev]y?+ is relative2 on ! contr>y1 x gives a te*nique = di/+ui%+ :at is relative f :at belongs to a physical occurr5ce 9 its own "r4 ,if we are go+ to say t ! !ory supports ,kant ab\t space & "t1 we %all h to say t x refutes him ab\t space-"t4 ,9 my view1 nei!r /atem5t is correct4 ,i see no reason :y1 on su* issues1 philosoph]s %\ld n all /ick to ! views !y previ\sly held4 ,!re 7 no conclusive argum5ts on ei!r side be=e1 & !re are none n[2 to hold ei!r view %[s a dogmatic r ?an a sci5tific temp]4 ,nev]!less1 :5 ! ideas involv$ 9 ,e9/e9's "w h become famili>1 z !y w :5 !y are taught 9 s*ools1 c]ta9 *anges 9 our habits ( ?\ght are likely to result1 & to h great importance 9 ! long run4 ,"o ?+ :i* em]ges is t physics tells u mu* less ab\t ! physical _w ?an we ?\ght x did4 ,almo/ all ! 8great pr9ciples0 ( traditional physics turn out to be l ! 8great law0 t !re are always ?ree feet to a y>d2 o!rs turn out to be d[nright false4 ,! cons]vation ( mass may s]ve to illu/rate bo? ^! mis=tunes to :i* a 8law0 is liable4 ,mass us$ to be def9$ z 8quantity ( matt]10 & z f> z exp]im5t %[$ x 0 nev] increas$ or dim9i%$4 ,b ) ! great] accuracy ( mod]n measurem5ts1 curi\s ?+s 7 f\nd to happ54 ,9 ! fir/ place1 ! mass z measur$ 0 f\nd to increase ) ! velocity2 ?is k9d ( mass 0 f\nd to be really ! same ?+ z en]gy4 ,?is k9d ( mass is n con/ant = a giv5 body1 b ! total am\nt ( x 9 ! univ]se is cons]v$1 or at lea/ obeys a law v closely analog\s to cons]vation4 ,?is law itself1 h[ev]1 is to be reg>d$ z a truism1 ( ! nature ( ! 8law0 t !re are ?ree feet to a y>d2 x results f our me?ods ( measurem5t1 & does n express a g5u9e prop]ty ( matt]4 ,! o!r k9d ( mass1 :i* we may call 8prop] mass10 is t :i* is f\nd to be ! mass by an obs]v] mov+ ) ! body4 ,?is is ! ord9>y t]re/rial case1 :]e ! body we are weigh+ is n fly+ ?r\gh ! air4 ,! 8prop] mass0 ( a body is v ne>ly con/ant1 b n q1 & ! total am\nt ( 8prop] mass0 9 ! _w is n q con/ant4 ,"o w\ld suppose t if y h f\r "o-p\nd weights1 & y put !m all toge!r into ! scales1 !y w toge!r weigh f\r p\nds4 ,?is is a fond delusion3 !y weigh r less1 ?\gh n en\gh less to be discov]$ by ev5 ! mo/ c>eful measurem5ts4 ,9 ! case ( f\r hydrog5 atoms1 h[ev]1 :5 !y are put toge!r to make "o helium atom1 ! defect is noticeable2 ! helium atom weighs measurably less ?an f\r sep>ate hydrog5 atoms4 ,broadly speak+1 traditional physics has collaps$ into two portions1 truisms & geography4 ,!re are1 h[ev]1 new] portions ( physics1 su* z ! !ory ( quanta1 :i* d n come "u ?is head1 b appe> to give g5u9e k ( laws rea*$ by exp]im5t4 ,! _w :i* ! !ory ( relativity pres5ts to our imag9ation is n s mu* a _w ( 8?+s0 9 8motion0 z a _w ( ev5ts4 ,x is true t !re are /ill electrons & protons :i* p]si/1 b ^! 7z we saw 9 ! prec$+ *apt]7 are really to be conceiv$ z /r+s ( connect$ ev5ts1 l ! successive notes ( a song4 ,x is ev5ts t are ! /uff ( relativity physics4 ,betwe5 two ev5ts :i* are n too remote f ea* o!r !re is1 9 ! g5]al !ory z 9 ! special !ory1 a measurable relation call$ 8int]val10 :i* appe>s to be ! physical reality ( :i* lapse ( "t & di/ance 9 space are two m or less confus$ repres5tations4 ,betwe5 two di/ant ev5ts1 !re is n any "o def9ite int]val4 ,b !re is "o way ( mov+ f "o ev5t to ano!r :i* makes ! sum ( all ! little int]vals along ! r\te great] ?an by any o!r r\te4 ,?is r\te is call$ a 8geodesic10 & x is ! r\te :i* a body w *oose if left to itself4 ,! :ole ( relativity physics is a mu* m /ep-by-/ep matt] ?an ! physics & geometry ( =m] days4 ,euclid's /raight l9es h to be replac$ by light rays1 :i* d n q come up to ,euclid's /&>d ( /raightness :5 !y pass ne> ! sun or any o!r v heavy body4 ,! sum ( ! angles ( a triangle is /ill ?\ght to be two "r angles 9 v remote regions ( empty space1 b n :]e !re is matt] 9 ! neighborhood4 ,we1 :o _c leave ! e>?1 are incapable ( rea*+ a place :]e ,euclid is true4 ,propositions :i* us$ to be prov$ by reason+ h n[ become ei!r conv5tions1 or m]ely approximate tru?s v]ifi$ by obs]vation4 ,x is a curi\s fact--( :i* relativity is n ! only illu/ration--t1 z reason+ improves1 its claims to ! p[] ( prov+ facts gr[ less & less4 ,logic us$ to be ?\ght to tea* u h[ to draw inf]5ces2 n[1 x tea*es u r h[ n to draw inf]5ces4 ,animals & *ildr5 are t]ribly prone to inf]5ce3 a horse is surpris$ beyond measure if y take an unusual turn+4 ,:5 m5 began to reason1 !y tri$ to ju/ify ! inf]5ces t !y _h drawn un?9k+ly 9 e>li] days4 ,a great deal ( bad philosophy & bad sci5ce result$ f ?is prop5sity4 8,great pr9ciples10 su* z ! 8uni=mity ( nature10 ! 8law ( univ]sal causation10 & s on1 are attempts to bol/] up our belief t :at has (t5 happ5$ be=e w happ5 aga91 :i* is no bett] f\nd$ ?an ! horse's belief t y w take ! turn+ y usually take4 ,x is n altoge!r easy to see :at is to replace ^! pseudo-pr9ciples 9 ! practice ( sci5ce2 b p]haps ! !ory ( relativity gives u a glimpse ( ! k9d ( ?+ we may expect4 ,causation1 9 ! old s5se1 no long] has a place 9 !oretical physics4 ,!re is1 ( c\rse1 some?+ else :i* takes its place1 b ! sub/itute appe>s to h a bett] empirical f\ndation ?an ! old pr9ciple :i* x has sup]s$$4 ,! collapse ( ! notion ( "o all-embrac+ "t1 9 :i* all ev5ts ?r\gh\t ! univ]se c be dat$1 mu/ 9 ! long run affect our views z to cause & effect1 evolution1 & _m o!r matt]s4 ,= in/ance1 ! "q :e!r1 on ! :ole1 !re is progress 9 ! univ]se1 may dep5d ^u our *oice ( a measure ( "t4 ,if we *oose "o out ( a numb] ( equally good clocks1 we may f9d t ! univ]se is progress+ z fa/ z ! mo/ optimi/ic ,am]ican ?9ks x is2 if we *oose ano!r equally good clock1 we may f9d t ! univ]se is go+ f bad to worse z fa/ z ! mo/ melan*oly ,slav c\ld imag9e4 ,?us optimism & pessimism are nei!r true nor false1 b dep5d ^u ! *oice ( clocks4 ,! effect ( ?is ^u a c]ta9 type ( emotion is deva/at+4 ,! poet speaks ( ,"o f>-(f div9e ev5t ,to :i* ! :ole creation moves4 ,b if ! ev5t is suffici5tly f> (f1 & ! creation moves suffici5tly quickly1 "s p>ts w judge t ! ev5t has already happ5$1 :ile o!rs w judge t x is /ill 9 ! future4 ,?is spoils ! poetry4 ,! second l9e ought to be3 ,to :i* "s p>ts ( ! creation move1 :ile o!rs move away f x4 ,b ?is won't d4 ,i sugge/ t an emotion :i* c be de/roy$ by a little ma!matics is nei!r v g5u9e nor v valuable4 ,b ?is l9e ( argum5t w\ld lead to a criticism ( ! ,victorian ,age1 :i* lies outside my !me4 ,:at we "k ab\t ! physical _w1 ,i repeat1 is mu* m ab/ract1 ?an 0 =m]ly suppos$4 ,betwe5 bodies !re are occurr5ces1 su* z light waves2 ( ! laws ( ^! occurr5ces1 we "k some?+--j s mu* z c be express$ 9 ma!matical =mul--b ( _! nature we "k no?+4 ,( ! bodies !mselves1 z we saw 9 ! prec$+ *apt]1 we "k s little t we _c ev5 be sure t !y are any?+3 !y may be m]ely gr\ps ( ev5ts 9 o!r places1 ^? ev5ts :i* we %\ld naturally reg>d z _! effects4 ,we naturally int]pret ! _w pictorially2 t is to say1 we imag9e t :at goes on is m or less l :at we see4 ,b 9 fact ?is lik5ess c only ext5d to c]ta9 =mal logical prop]ties express+ /ructure1 s t all we c "k is c]ta9 g5]al *>act]i/ics ( its *anges4 ,p]haps an illu/ration may make ! matt] cle>4 ,betwe5 a piece ( or*e/ral music z play$1 & ! same piece ( music z pr9t$ 9 ! score1 !re is a c]ta9 resemblance1 :i* may be describ$ z a resemblance 9 /ructure4 ,! resemblance is ( su* a sort t1 :5 y "k ! rules1 y c inf] ! music f ! score or ! score f ! music4 ,b suppose y _h be5 /one deaf f bir?1 b _h liv$ among musical p4 ,y c\ld und]/&1 if y _h le>n$ to speak & to d lip-read+1 t ! musical scores repres5t$ some?+ q diff]5t f !mselves 9 intr9sic quality1 ?\gh simil> 9 /ructure4#af ,! value ( music w\ld be completely unimag9able to y1 b y c\ld inf] all its ma!matical *>act]i/ics1 s9ce !y are ! same z ^? ( ! score4 ,n[ our k ( nature is some?+ l ?is4 ,we c read ! scores1 & inf] j s mu* z our /one-deaf p]son c\ld h inf]r$ ab\t music4 ,b we h n ! advantages :i* he d]iv$ f association ) musical p4 ,we _c "k :e!r ! music repres5t$ by ! scores is beautiful or hide\s2 p]haps1 9 ! la/ analysis1 we _c be q sure t ! scores repres5t any?+ b !mselves4 ,b ?is is a d\bt :i* ! physici/1 9 8 pr(essional capacity1 _c p]mit himself to ent]ta94 #af ,= ! def9ition ( 8/ructure10 see ! pres5t au?or's ,introduction to ,ma!matical ,philosophy4 ,assum+ ! utmo/ t c be claim$ = physics1 x does n tell u :at x is t *anges1 or :at are its v>i\s /ates2 x only tells u su* ?+s z t *anges foll[ ea* o!r p]iodically1 or spread ) a c]ta9 spe$4 ,ev5 n[ we are probably n at ! end ( ! process ( /ripp+ away :at is m]ely imag9ation1 9 ord] to rea* ! core ( true sci5tific k4 ,! !ory ( relativity has accompli%$ a v great deal 9 ?is respect1 & 9 do+ s has tak5 u ne>] & ne>] to b>e /ructure1 :i* is ! ma!matician's goal--n because x is ! only ?+ 9 :i* he is int]e/$ z a human be+1 b because x is ! only ?+ t he c express 9 ma!matical =mul4 ,b f> z we h travel$ 9 ! direction ( ab/raction1 x may be t we %all h to travel fur!r /ill4 ,9 ! prec$+ *apt]1 ,i sugge/$ :at may be call$ a m9imum def9ition ( matt]1 t is to say1 "o 9 :i* matt] has1 s to speak1 z little 8sub/ance0 z is compatible ) ! tru? ( physics4 ,9 adopt+ a def9ition ( ?is k9d1 we are play+ = safety3 our t5u\s matt] w exi/1 ev5 if some?+ m beefy also exi/s4 ,we tri$ to make our def9ition ( matt]1 l ,isabella's gruel 9 ,jane ,au/51 8?91 b n too ?940 ,we %all1 h[ev]1 fall into error if we ass]t positively t matt] is no?+ m ?an ?is4 ,leibniz ?\ght t a piece ( matt] is really a colony ( s\ls4 ,!re is no?+ to %[ t he 0 wrong1 ?\gh !re is also no?+ to %[ t he 0 "r3 we "k no m ab\t x ei!r way ?an we d ab\t ! flora & fauna ( ,m>s4 ,to ! non-ma!matical m9d1 ! ab/ract "* ( our physical k may seem unsatisfactory4 ,f an arti/ic or imag9ative po9t ( view1 x is p]haps regrettable1 b f a practical po9t ( view x is ( no consequ5ce4 ,ab/raction1 difficult z x is1 is ! s\rce ( practical p[]4 ,a f9anci]1 ^: deal+s ) ! _w are m ab/ract ?an ^? ( any o!r 8practical0 man1 is also m p[]ful ?an any o!r practical man4 ,he c deal 9 :eat or cotton )\t ne$+ ev] to h se5 ei!r3 all he ne$s to "k is :e!r !y w g up or d[n4 ,?is is ab/ract ma!matical k1 at lea/ z comp>$ to ! k ( ! agriculturi/4 ,simil>ly ! physici/1 :o kn[s no?+ ( matt] except c]ta9 laws ( its movem5ts1 nev]!less kn[s en\gh to enable him to manipulate x4 ,aft] work+ ?r\gh :ole /r+s ( equations1 9 :i* ! symbols /& = ?+s ^: intr9sic nature c nev] be kn[n to u1 he arrives at la/ at a result :i* c be int]pret$ 9 t]ms ( our own p]ceptions1 & utiliz$ to br+ ab\t desir$ effects 9 our own lives4 ,:at we "k ab\t matt]1 ab/ract & s*ematic z x is1 is en\gh1 9 pr9ciple1 to tell u ! rules accord+ to :i* x produces p]ceptions & feel+s 9 ourselves2 & x is ^u ^! rules t ! practical uses ( physics dep5d4 ,! f9al conclusion is t we "k v little1 & yet x is a/oni%+ t we "k s mu*1 & /ill m a/oni%+ t s little k c give u s mu* p[]4 ,,! ,,end