,,! ,,logic ,,( ,,mod]n ,,physics ,,by ,p4 ,w4 ,,bridgman ,,hollis ,,pr(essor ,,( ,,ma!matics ,,& ,,natural ,,hi/ory ,,9 ,,h>v>d ,,univ]sity ,,new ,,york ,,! ,,macmillan ,,company ,,copyright1 #aibg1 ,by ,,! ,,macmillan ,,company4 ,,preface ,?is excursion into ! field ( fundam5tal criticism by "o ^: activities h hi!rto be5 conf9$ almo/ entirely to exp]im5t is n evid5ce ( s5ile decay1 z might be cynically assum$4 ,i h always1 ?r\gh\t all my exp]im5tal "w1 felt an imp]ative ne$ ( a bett] und]/&+ ( ! f\ndations ( our physical ?\ght & h = a long "t made m or less unsy/ematic attempts to rea* su* an und]/&+4 ,only n[1 h[ev]1 has a half sabbatical ye> giv5 me leisure to attempt a m or less ord]ly exposition4 ,9 spite ( previ\s writ+s on ! broad fundam5tals by ,clif=d1 ,/allo1 ,ma*1 & ,po9c>1 to m5tion only a few1 ,i believe a new essay ( ?is critical "* ne$s no apology4 ,= entirely ap>t f ! "q ( :e!r _m ( ! po9ts ( view ( ^! essays c be ma9ta9$1 ! discov]y ( new facts 9 ! doma9 ( relativity & quantum !ory has %ift$ ! c5t] ( int]e/ & emphasis4 ,all ! q rec5t activity ) ! new quantum me*anics seems to call = a new exam9ation ( fundam5tal matt]s :i* %all recognize1 at lea/ by implication1 ! exi/5ce ( ! special ph5om5a ( ! quantum doma94 ,h[ev]1 ! necessity = re-exam9ation does n mean at all t _m ( ! results ( previ\s criticism may n /ill be accept$2 "s ( ^! results h become s ?or\ghly incorporat$ into physical ?9k+ t we c assume !m )\t m5tion4 ,?us ! fundam5tal attitude ( ?is essay is empiricism1 :i* is n[ ju/ifi$ z ! attitude ( ! physici/ 9 l>ge "p by ! inquiry into ! physiological orig9 ( our concepts ( space1 "t1 & me*anics ) :i* ! previ\s essays 7 l>gely conc]n$4 ,none ( ! previ\s essays h consci\sly or imm$iately affect$ ! details ( ?is2 9 fact ,i h n read any ( !m )9 sev]al ye>s4 ,if passages "h recall passages already writt51 x is because ! ideas h be5 assimilat$ & ! precise orig9 =gott52 x is probably wor? :ile to let su* passages /& )\t revision1 because su* ideas ga9 9 plausibility ?r\gh hav+ be5 f\nd acceptable to indep5d5t ?\ght4 ,i am mu* indebt$ to ,pr(essor ,r4 ,f4 ,alfr$ ,ho]nl ( ! ,dep>tm5t ( ,philosophy ( ,johannesburg ,univ]sity1 ,s\? ,africa1 = sugge/+ sev]al modifications to make ! text m acceptable to a philosoph]1 & slight amplifications = ! b5efit ( read]s n famili> ) all ! details ( rec5t te*nical developm5ts 9 physics4 ,,introduction ,"o ( ! mo/ notewor?y movem5ts 9 rec5t physics is a *ange ( attitude t[>d :at may be call$ ! int]pretative aspect ( physics4 ,x is be+ increas+ly recogniz$1 bo? 9 ! writ+s & ! conv]sation ( physici/s1 t ! _w ( exp]im5t is n und]/&able )\t "s exam9ation ( ! purpose ( physics & ( ! nature ( its fundam5tal concepts4 ,x is no new ?+ to attempt a m critical und]/&+ ( ! nature ( physics1 b until rec5tly all su* attempts h be5 reg>d$ ) a c]ta9 suspicion or ev5 sometimes contempt4 ,! av]age physici/ is likely to deprecate 8 own conc]n ) su* que/ions1 & is incl9$ to dismiss ! speculations ( fell[ physici/s ) ! epi!t metaphysical4 ,?is attitude has no d\bt _h a c]ta9 ju/ification 9 ! utt] un9telligibility to ! physici/ ( _m metaphysical speculations & ! /]ility ( su* speculations 9 yield+ physical results4 ,h[ev]1 ! gr[+ reaction favor+ a bett] und]/&+ ( ! int]pretative fundam5tals ( physics is n a p5dulum sw+ ( ! fa%ion ( ?\ght t[>d metaphysics1 orig9at+ 9 ! upheaval ( moral values produc$ by ! great w>1 or any?+ ( ! sort1 b is a reaction absolutely =c$ ^u u by a rapidly increas+ array ( cold exp]im5tal facts4 ,?is reaction1 or r new movem5t1 0 )\t d\bt initiat$ by ! re/rict$ !ory ( relativity ( ,e9/e94 ,be=e ,e9/e91 an ev] increas+ numb] ( exp]im5tal facts conc]n+ bodies 9 rapid motion requir$ increas+ly complicat$ modifications 9 our nave notions 9 ord] to pres]ve self-consi/5cy1 until ,e9/e9 %[$ t ev]y?+ c\ld be re/or$ aga9 to a wond]ful simplicity by a slight *ange 9 "s ( our fundam5tal concepts4 ,! concepts :i* 7 mo/ obvi\sly t\*$ by ,e9/e9 7 ^? ( space & "t1 & mu* ( ! writ+ consci\sly inspir$ by ,e9/e9 has be5 conc]n$ ) ^! concepts4 ,b t exp]im5t compels a critique ( mu* m ?an ! concepts ( space & "t is made increas+ly evid5t by all ! new facts be+ discov]$ 9 ! quantum realm4 ,! situation pres5t$ to u by ^! new quantum facts is tw(old4 ,9 ! fir/ place1 all ^! exp]im5ts are conc]n$ ) ?+s s small z to be =ev] beyond ! possibility ( direct exp]i5ce1 s t we h ! problem ( translat+ ! evid5ce ( exp]im5t into o!r language4 ,?us we obs]ve an emission l9e 9 a spectroscope & may inf] an electron jump+ f "o en]gy level to ano!r 9 an atom4 ,9 ! second place1 we h ! problem ( und]/&+ ! translat$ exp]im5tal evid5ce4 ,n[ ( c\rse e "o kn[s t ?is problem is mak+ u ! greate/ difficulty4 ,! exp]im5tal facts are s utt]ly diff]5t f ^? ( our ord9>y exp]i5ce t n only d we app>5tly h to give up g5]alizations f pa/ exp]i5ce z broad z ! field equations ( electrodynamics1 = in/ance1 b x is ev5 be+ que/ion$ :e!r our ord9>y =ms ( ?\ght are applicable 9 ! new doma92 x is (t5 sugge/$1 = example1 t ! concepts ( space & "t break d[n4 ,! situation is rapidly becom+ acute4 ,s9ce ,i began writ+ ?is essay1 !re has be5 a /rik+ increase 9 critical activity inspir$ by ! new quantum me*anics ( #aibe-bf1 & x is common to he> expositions ( ! new ideas prefac$ by analysis ( :at exp]im5t really gives to u or :at our fundam5tal concepts really mean4 ,! *ange 9 ideas is n[ s rapid t a numb] ( ! /atem5ts ( ?is essay are already antiquat$ z expressions ( ! be/ curr5t op9ion2 h[ev] ,i h all[$ ^! /atem5ts to /&1 s9ce ! fundam5tal argum5ts are 9 n[ise affect$ & we h no reason to ?9k t pres5t be/ op9ions are 9 any way f9al4 ,we h ! impression ( be+ 9 an important =mative p]iod2 if we are1 ! complexion ( physics = a long "t 9 ! future w be det]m9$ by our pres5t attitude t[>d fundam5tal que/ions ( int]pretation4 ,to meet ?is situation x seems to me t some?+ m is ne$$ ?an ! h&-to-m\? philosophy t is n[ gr[+ up to meet special em]g5cies1 some?+ approa*+ m closely to a sy/ematic philosophy ( all physics :i* %all cov] ! exp]im5tal doma9s already consolidat$ z well z ^? :i* are n[ mak+ u s mu* tr\ble4 ,x is ! attempt ( ?is essay to give a m or less inclusive critique ( all physics4 ,our problem is ! d\ble "o ( und]/&+ :at we are try+ to d & :at our ideals %\ld be 9 physics1 & ( und]/&+ ! nature ( ! /ructure ( physics z x n[ exi/s4 ,^! two ends are toge!r fur!r$ by an analysis ( ! fundam5tal concepts ( physics2 an und]/&+ ( ! concepts we h[ h discloses ! pres5t /ructure ( physics & a realization ( :at ! concepts %\ld be involves ! ideals ( physics4 ,?is essay w be l>gely conc]n$ ) ! fundam5tal concepts2 x w appe> t almo/ all ! concepts c pr(it f re-exam9ation4 ,! mat]ial ( ?is essay is l>gely obta9$ by obs]vation ( ! actual curr5ts ( op9ion 9 physics2 mu* ( :at ,i h to say is m or less common prop]ty & d\btless e read] w f9d passages t he w feel h be5 tak5 out ( 8 own m\?4 ,on c]ta9 broad t5d5cies 9 pres5t day physics1 h[ev]1 ,i h put my own int]pretation1 & x is m ?an likely t ?is int]pretation w be unacceptable to _m4 ,b ev5 if n acceptable1 ,i hope t ! /imulus ( combatt+ ! ideas (f]$ "h may be ( value4 ,c]ta9 limitations w h to be set to our inquiry 9 ord] to keep x )9 manageable compass4 ,x is ( c\rse ! m]e/ truism t all our exp]im5tal k & our und]/&+ ( nature is impossible & non-exi/5t ap>t f our own m5tal processes1 s t /rictly speak+ no aspect ( psy*ology or epi/emology is )\t p]t95ce4 ,=tunately we %all be able to get along ) a m or less naive attitude t[>d _m ( ^! matt]s4 ,we %all accept z significant our common s5se judgm5t t !re is a _w ext]nal to u1 & %all limit z f> z possible our inquiry to ! behavior & int]pretation ( ?is ext]nal _w4 ,we %all rule out inquiries into our /ates ( consci\sness z su*4 ,9 spite1 h[ev]1 ( ! be/ int5tions1 we %all n be able to elim9ate completely consid]ations savor+ ( ! metaphysical1 because x is evid5t t ! nature ( our ?9k+ me*anism ess5tially colors any picture t we c =m ( nature1 & we %all h to recognize t unavoidable *>act]i/ics ( any outlook ( ours are impos$ 9 ?is way4 ,,cont5ts ,preface ,introduction ,,*apt] ,i4 ,,broad ,,po9ts ,,( ,,view ,new ,k9ds ( ,exp]i5ce ,always ,possible ,! ,op]ational ,"* ( ,concepts ,e9/e9's ,contribution 9 ,*ang+ ,our ,attitude t[>d ,concepts ,detail$ ,discussion ( ! ,concept ( ,l5g? ,! ,relative ,"* ( ,k ,mean+less ,que/ions ,g5]al ,comm5ts on ! ,op]ational ,po9t ( ,view ,,ii4 ,,o!r ,,g5]al ,,consid]ations ,! ,approximate ,"* ( ,empirical ,k ,explanations & ,me*anisms ,models & ,con/ructs ,! ,rle ( ,ma!matics 9 ,physics ,,iii4 ,,detail$ ,,consid]ation ,,( ,,v>i\s ,,concepts ,,( ,,physics ,! ,concept ( ,space ,! ,concept ( ,"t ,! ,causality ,concept ,! ,concept ( ,id5tity ,! ,concept ( ,velocity ,! ,concepts ( ,=ce & ,mass ,! ,concept ( ,en]gy ,! ,concepts ( ,!rmodynamics ,electrical ,concepts ,! ,nature ( ,light & ! ,concepts ( ,relativity ,o!r ,relativity ,concepts ,rotational ,motion & ,relativity ,quantum ,concepts ,,iv4 ,,special ,,views ,,( ,,nature ,! ,simplicity ( ,nature ,det]m9ism ,on ! ,possibility ( ,describ+ ,nature ,completely 9 ,t]ms ( ,analysis ,a ,glimpse ,ahead ,,index ,,! ,,logic ,,( ,,mod]n ,,physics ,,*apt] ,i ,,broad ,,po9ts ,,( ,,view ,,:atev] may be "o's op9ion z to our p]man5t acceptance ( ! analytical details ( ,e9/e9's re/rict$ & g5]al !ories ( relativity1 !re c be no d\bt t ?r\gh ^! !ories physics is p]man5tly *ang$4 ,x 0 a great %ock to discov] t classical concepts1 accept$ unque/ion+ly1 7 inadequate to meet ! actual situation1 & ! %ock ( ?is discov]y has result$ 9 a critical attitude t[>d our :ole conceptual /ructure :i* mu/ at lea/ 9 "p be p]man5t4 ,reflection on ! situation aft] ! ev5t %[s t x %\ld n h ne$$ ! new exp]im5tal facts :i* l$ to relativity to conv9ce u ( ! inadequacy ( our previ\s concepts1 b t a suffici5tly %rewd analysis %\ld h prep>$ u = at lea/ ! possibility ( :at ,e9/e9 did4 ,look+ n[ to ! future1 our ideas ( :at ext]nal nature is w always be subject to *ange z we ga9 new exp]im5tal k1 b !re is a "p ( our attitude to nature :i* %\ld n be subject to future *ange1 namely t "p :i* re/s on ! p]man5t basis ( ! "* ( our m9ds4 ,x is precisely "h1 9 an improv$ und]/&+ ( our m5tal relations to nature1 t ! p]man5t contribution ( relativity is to be f\nd4 ,we %\ld n[ make x our bus9ess to und]/& s ?or\ghly ! "* ( our p]man5t m5tal relations to nature t ano!r *ange 9 our attitude1 su* z t due to ,e9/e91 %all be =ev] impossible4 ,x 0 p]haps excusable t a revolution 9 m5tal attitude %\ld occur once1 because aft] all physics is a "y sci5ce1 & physici/s h be5 v busy1 b x w\ld c]ta9ly be a reproa* if su* a revolution %\ld ev] prove necess>y aga94 ,,new ,,k9ds ,,( ,,exp]i5ce ,,always ,,possible ,! fir/ lesson ( our rec5t exp]i5ce ) relativity is m]ely an int5sification & emphasis ( ! lesson :i* all pa/ exp]i5ce has also taught1 namely1 t :5 exp]im5t is pu%$ into new doma9s1 we mu/ be prep>$ = new facts1 ( an entirely diff]5t "* f ^? ( our =m] exp]i5ce4 ,?is is taught n only by ! discov]y ( ^? unsuspect$ prop]ties ( matt] mov+ ) high velocities1 :i* inspir$ ! !ory ( relativity1 b also ev5 m emphatically by ! new facts 9 ! quantum doma94 ,to a c]ta9 ext5t1 ( c\rse1 ! recognition ( all ?is does n involve a *ange ( =m] attitude2 ! fact has always be5 = ! physici/ ! "o ultimate ?+ f :i* !re is no appeal1 & 9 ! face ( :i* ! only possible attitude is a humility almo/ religi\s4 ,! new feature 9 ! pres5t situation is an int5sifi$ conviction t 9 reality new ord]s ( exp]i5ce d exi/1 & t we may expect to meet !m cont9ually4 ,we h already enc\nt]$ new ph5om5a 9 go+ to high velocities1 & 9 go+ to small scales ( magnitude3 we may simil>ly expect to f9d !m1 = example1 9 deal+ ) relations ( cosmic magnitudes1 or 9 deal+ ) ! prop]ties ( matt] ( enorm\s d5sities1 su* z is suppos$ to exi/ 9 ! />s4 ,impli$ 9 ?is recognition ( ! possibility ( new exp]i5ce beyond our pres5t range1 is ! recognition t no elem5t ( a physical situation1 no matt] h[ app>5tly irrelevant or trivial1 may be dismiss$ z )\t effect on ! f9al result until prov$ to be )\t effect by actual exp]im5t4 ,! attitude ( ! physici/ mu/ !re=e be "o ( pure empiricism4 ,he recognizes no a priori pr9ciples :i* det]m9e or limit ! possibilities ( new exp]i5ce4 ,exp]i5ce is det]m9$ only by exp]i5ce4 ,?is practically means t we mu/ give up ! dem& t all nature be embrac$ 9 any =mula1 ei!r simple or complicat$4 ,x may p]haps turn out ev5tually t z a matt] ( fact nature c be embrac$ 9 a =mula1 b we mu/ s organize our ?9k+ z n to dem& x z a necessity4 ,,! ,,op]ational ,,"* ,,( ,,concepts ,e9/e9's ,contribution 9 ,*ang+ ,our ,attitude ,t[>d ,concepts ,recogniz+ ! ess5tial unpr$ictability ( exp]im5t beyond our pres5t range1 ! physici/1 if he is to escape cont9ually revis+ 8 attitude1 mu/ use 9 describ+ & correlat+ nature concepts ( su* a "* t our pres5t exp]i5ce does n exact ho/ages ( ! future4 ,n[ "h x seems to me is ! greate/ contribution ( ,e9/e94 ,al?\gh he himself does n explicitly /ate or emphasize x1 ,i believe t a /udy ( :at he has done w %[ t he has ess5tially modifi$ our view ( :at ! concepts useful 9 physics are & %\ld be4 ,hi!rto _m ( ! concepts ( physics h be5 def9$ 9 t]ms ( _! prop]ties4 ,an excell5t example is af=d$ by ,newton's concept ( absolute "t4 ,! foll[+ quotation f ! ,s*olium 9 ,book ,i ( ! ,pr9cipia is illum9at+3 ,i d n def9e ,"t1 ,space1 ,place or ,motion1 z be+ well kn[n to all4 ,only ,i mu/ obs]ve t ! vulg> conceive ^? quantities "u no o!r notions b f ! relation !y be> to s5sible objects4 ,& !nce arise c]ta9 prejudices1 = ! remov+ ( :i*1 x w be conv5i5t to di/+ui% !m into ,absolute & ,relative1 ,true & ,app>5t1 ,ma!matical & ,common4 7,i7 ,absolute1 ,true1 & ,ma!matical ,"t1 ( itself1 & f its own nature fl[s equably )\t reg>d to any?+ ext]nal1 & by ano!r "n is call$ ,duration4 ,n[ !re is no assurance :atev] t !re exi/s 9 nature any?+ ) prop]ties l ^? assum$ 9 ! def9ition1 & physics1 :5 r$uc$ to concepts ( ?is "*1 becomes z purely an ab/ract sci5ce & z f> remov$ f reality z ! ab/ract geometry ( ! ma!maticians1 built on po/ulates4 ,x is a task = exp]im5t to discov] :e!r concepts s def9$ correspond to any?+ 9 nature1 & we mu/ always be prep>$ to f9d t ! concepts correspond to no?+ or only p>tially correspond4 ,9 p>ticul>1 if we exam9e ! def9ition ( absolute "t 9 ! light ( exp]im5t1 we f9d no?+ 9 nature ) su* prop]ties4 ,! new attitude t[>d a concept is entirely diff]5t4 ,we may illu/rate by consid]+ ! concept ( l5g?3 :at d we mean by ! l5g? ( an object8 ,we evid5tly "k :at we mean by l5g? if we c tell :at ! l5g? ( any & e object is1 & = ! physici/ no?+ m is requir$4 ,to f9d ! l5g? ( an object1 we h to p]=m c]ta9 physical op]ations4 ,! concept ( l5g? is !re=e fix$ :5 ! op]ations by :i* l5g? is measur$ are fix$3 t is1 ! concept ( l5g? involves z mu* z & no?+ m ?an ! set ( op]ations by :i* l5g? is det]m9$4 ,9 g5]al1 we mean by any concept no?+ m ?an a set ( op]ations2 ! concept is synonym\s ) ! correspond+ set ( op]ations4 ,if ! concept is physical1 z ( l5g?1 ! op]ations are actual physical op]ations1 namely1 ^? by :i* l5g? is measur$2 or if ! concept is m5tal1 z ( ma!matical cont9uity1 ! op]ations are m5tal op]ations1 namely ^? by :i* we det]m9e :e!r a giv5 aggregate ( magnitudes is cont9u\s4 ,x is n int5d$ to imply t !re is a h>d & fa/ division betwe5 physical & m5tal concepts1 or t "o k9d ( concept does n always conta9 an elem5t ( ! o!r2 ?is classification ( concept is n important = our future consid]ations4 ,we mu/ dem& t ! set ( op]ations equival5t to any concept be a unique set1 = o!rwise !re are possibilities ( ambiguity 9 practical applications :i* we _c admit4 ,apply+ ?is idea ( concept to absolute "t1 we d n und]/& ! mean+ ( absolute "t unless we c tell h[ to det]m9e ! absolute "t ( any concrete ev5t1 i4e41 unless we c measure absolute "t4 ,n[ we m]ely h to exam9e any ( ! possible op]ations by :i* we measure "t to see t all su* op]ations are relative op]ations4 ,!re=e ! previ\s /atem5t t absolute "t does n exi/ is replac$ by ! /atem5t t absolute "t is mean+less4 ,& 9 mak+ ?is /atem5t we are n say+ some?+ new ab\t nature1 b are m]ely br++ to light implications already conta9$ 9 ! physical op]ations us$ 9 measur+ "t4 ,x is evid5t t if we adopt ?is po9t ( view t[>d concepts1 namely t ! prop] def9ition ( a concept is n 9 t]ms ( its prop]ties b 9 t]ms ( actual op]ations1 we ne$ run no dang] ( hav+ to revise our attitude t[>d nature4 ,= if exp]i5ce is always describ$ 9 t]ms ( exp]i5ce1 !re mu/ always be correspond5ce betwe5 exp]i5ce & our description ( x1 & we ne$ nev] be emb>rass$1 z we 7 9 attempt+ to f9d 9 nature ! prototype ( ,newton's absolute "t4 ,fur!rmore1 if we rememb] t ! op]ations to :i* a physical concept are equival5t are actual physical op]ations1 ! concepts c be def9$ only 9 ! range ( actual exp]im5t1 & are undef9$ & mean+less 9 regions z yet unt\*$ by exp]im5t4 ,x foll[s t /rictly speak+ we _c make /atem5ts at all ab\t regions z yet unt\*$1 & t :5 we d make su* /atem5ts1 z we inevitably %all1 we are mak+ a conv5tionaliz$ extrapolation1 ( ! loos5ess ( :i* we mu/ be fully consci\s1 & ! ju/ification ( :i* is 9 ! exp]im5t ( ! future4 ,!re probably is no /atem5t ei!r 9 ,e9/e9 or o!r writ]s t ! *ange describ$ above 9 ! use ( concept has be5 self-consci\sly made1 b t su* is ! case is prov$1 ,i believe1 by an exam9ation ( ! way concepts are n[ h&l$ by ,e9/e9 & o!rs4 ,= ( c\rse ! true mean+ ( a t]m is to be f\nd by obs]v+ :at a man does ) x1 n by :at he says ab\t x4 ,we may %[ t ?is is ! actual s5se 9 :i* concept is com+ to be us$ by exam9+ 9 p>ticul> ,e9/e9's treatm5t ( simultaneity4 ,be=e ,e9/e91 ! concept ( simultaneity 0 def9$ 9 t]ms ( prop]ties4 ,x 0 a prop]ty ( two ev5ts1 :5 describ$ ) respect to _! relation 9 "t1 t "o ev5t 0 ei!r be=e ! o!r1 or aft] x1 or simultane\s ) x4 ,simultaneity 0 a prop]ty ( ! two ev5ts alone & no?+ else2 ei!r two ev5ts 7 simultane\s or !y 7 n4 ,! ju/ification = us+ ?is t]m 9 ?is way 0 t x seem$ to describe ! behavior ( actual ?+s4 ,b ( c\rse exp]i5ce !n 0 re/rict$ to a n>r[ range4 ,:5 ! range ( exp]i5ce 0 broad5$1 z by go+ to high velocities1 x 0 f\nd t ! concepts no long] appli$1 because !re 0 no c\nt]p>t 9 exp]i5ce = ?is absolute relation betwe5 two ev5ts4 ,e9/e9 n[ subject$ ! concept ( simultaneity to a critique1 :i* consi/$ ess5tially 9 %[+ t ! op]ations :i* enable two ev5ts to be describ$ z simultane\s involve measurem5ts on ! two ev5ts made by an obs]v]1 s t simultaneity is1 !re=e1 n an absolute prop]ty ( ! two ev5ts & no?+ else1 b mu/ also involve ! relation ( ! ev5ts to ! obs]v]4 ,until !re=e we h exp]im5tal pro( to ! contr>y1 we mu/ be prep>$ to f9d t ! simultaneity ( two ev5ts dep5ds on _! relation to ! obs]v]1 & 9 p>ticul> on _! velocity4 ,e9/e91 9 ?us analyz+ :at is involv$ 9 mak+ a judgm5t ( simultaneity1 & 9 seiz+ on ! act ( ! obs]v] z ! ess5ce ( ! situation1 is actually adopt+ a new po9t ( view z to :at ! concepts ( physics %\ld be1 namely1 ! op]ational view4 ,( c\rse ,e9/e9 actually w5t mu* fur!r ?an ?is1 & f\nd precisely h[ ! op]ations = judg+ simultaneity *ange :5 ! obs]v] moves1 & obta9$ quantitative expressions = ! effect ( ! motion ( ! obs]v] on ! relative "t ( two ev5ts4 ,we may notice1 p>5!tically1 t !re is mu* fre$om ( *oice 9 select+ ! exact op]ations2 ^? :i* ,e9/e9 *ose 7 det]m9$ by conv5i5ce & simplicity ) relation to light beams4 ,entirely ap>t f ! precise quantitative relations ( ,e9/e9's !ory1 h[ev]1 ! important po9t = u is t if we _h adopt$ ! op]ational po9t ( view1 we w\ld1 be=e ! discov]y ( ! actual physical facts1 h se5 t simultaneity is ess5tially a relative concept1 & w\ld h left room 9 our ?9k+ = ! discov]y ( su* effects z 7 lat] f\nd4 ,detail$ ,discussion ( ! ,concept ( ,l5g? ,we may n[ ga9 fur!r famili>ity ) ! op]ational attitude t[>d a concept & "s ( its implications by exam9+ f ?is po9t ( view ! concept ( l5g?4 ,our task is to f9d ! op]ations by :i* we measure ! l5g? ( any concrete physical object4 ,we beg9 ) objects ( our commone/ exp]i5ce1 su* z a h\se or a h\se lot4 ,:at we d is suffici5tly indicat$ by ! foll[+ r\gh description4 ,we />t ) a measur+ rod1 lay x on ! object s t "o ( its ends co9cides ) "o end ( ! object1 m>k on ! object ! position ( ! o!r end ( ! rod1 !n move ! rod along 9 a /raight l9e ext5sion ( its previ\s position until ! fir/ end co9cides ) ! previ\s position ( ! second end1 repeat ?is process z (t5 z we c1 & call ! l5g? ! total numb] ( times ! rod 0 appli$4 ,?is proc$ure1 app>5tly s simple1 is 9 practice exce$+ly complicat$1 & d\btless a full description ( all ! precautions t mu/ be tak5 w\ld fill a l>ge treatise4 ,we mu/1 = example1 be sure t ! temp]ature ( ! rod is ! /&>d temp]ature at :i* its l5g? is def9$1 or else we mu/ make a correction = x2 or we mu/ correct = ! gravitational di/ortion ( ! rod if we measure a v]tical l5g?2 or we mu/ be sure t ! rod is n a magnet or is n subject to electrical =ces4 ,all ^! precautions w\ld occur to e physici/4 ,b we mu/ also g fur!r & specify all ! details by :i* ! rod is mov$ f "o position to ! next on ! object--its precise pa? ?r\gh space & its velocity & accel]ation 9 gett+ f "o position to ano!r4 ,practically ( c\rse1 precautions su* z ^! are n m5tion$1 b ! ju/ification is 9 our exp]i5ce t v>iations ( proc$ure ( ?is k9d are )\t effect on ! f9al result4 ,b we always h to recognize t all our exp]i5ce is subject to error1 & t at "s "t 9 ! future we may h to specify m c>efully ! accel]ation1 = example1 ( ! rod 9 mov+ f "o position to ano!r1 if exp]im5tal accuracy %\ld be s increas$ z to %[ a measurable effect4 ,9 pr9ciple ! op]ations by :i* l5g? is measur$ %\ld be uniquely specifi$4 ,if we h m ?an "o set ( op]ations1 we h m ?an "o concept1 & /rictly !re %\ld be a sep>ate "n to correspond to ea* diff]5t set ( op]ations4 ,s mu* = ! l5g? ( a /ation>y object1 :i* is complicat$ en\gh4 ,n[ suppose we h to measure a mov+ /reet c>4 ,! simple/1 & :at we may call ! nave proc$ure1 is to bo>d ! c> ) our met] /ick & repeat ! op]ations we w\ld apply to a /ation>y body4 ,notice t ?is proc$ure r$uces to t already adopt$ 9 ! limit+ case :5 ! velocity ( ! /reet c> vani%es4 ,b "h !re may be new que/ions ( detail4 ,h[ %all we jump on to ! c> ) our /ick 9 h&8 ,%all we run & jump on f beh9d1 or %all we let x pick u up f 9 front8 ,or p]haps does n[ ! mat]ial ( :i* ! /ick is compos$ make a diff]5ce1 al?\gh previ\sly x did n8 ,all ^! que/ions mu/ be answ]$ by exp]im5t4 ,we believe f pres5t evid5ce t x makes no diff]5ce h[ we jump on to ! c>1 or ( :at mat]ial ! rod is made1 & t ! l5g? ( ! c> f\nd 9 ?is way w be ! same z if x 7 at re/4 ,b ! exp]im5ts are m difficult1 & we are n s sure ( our conclusions z be=e4 ,n[ !re are v obvi\s limitations to ! proc$ure j giv54 ,if ! /reet c> is go+ too fa/1 we c n bo>d x directly1 b mu/ use devices1 su* z gett+ on f a mov+ automobile2 &1 m important /ill1 !re are limitations to ! velocity t c be giv5 to /reet c>s or to met] /icks by any practical means 9 our control1 s t ! mov+ bodies :i* c be measur$ 9 ?is way are re/rict$ to a l[ range ( velocity4 ,if we want to be able to measure ! l5g? ( bodies mov+ ) high] velocities su* z we f9d exi/+ 9 nature 7/>s or ca?ode p>ticles71 we mu/ adopt ano!r def9ition & o!r op]ations = measur+ l5g?1 :i* also r$uce to ! op]ations already adopt$ 9 ! /atic case4 ,?is is precisely :at ,e9/e9 did4 ,s9ce ,e9/e9's op]ations 7 diff]5t f our op]ations above1 8 l5g? does n mean ! same z our l5g?4 ,we mu/ accord+ly be prep>$ to f9d t ! l5g? ( a mov+ body measur$ by ! proc$ure ( ,e9/e9 is n ! same z t above2 ?is ( c\rse is ! fact1 & ! trans=mation =mulas ( relativity give ! precise connection betwe5 ! two l5g?s4 ,e9/e9's proc$ure = measur+ ! l5g? ( bodies 9 motion 0 dictat$ n only by ! consid]ation t x mu/ be applicable to bodies ) high velocities1 b also by ma!matical conv5i5ce1 9 t ,e9/e9 describes ! _w ma!matically by a sy/em ( cord9ate geometry1 & ! l5g? ( an object is connect$ simply ) quantities 9 ! analytic equations4 ,x is ( int]e/ to describe briefly ,e9/e9's actual op]ations = measur+ ! l5g? ( a body 9 motion2 x w %[ h[ op]ations :i* may be simple f a ma!matical po9t ( view may appe> complicat$ f a physical viewpo9t4 ,! obs]v] :o is to measure ! l5g? ( a mov+ object mu/ fir/ ext5d ov] 8 entire plane ( ref]5ce 7= simplicity ! problem is consid]$ two-dim5sional7 a sy/em ( "t coord9ates1 i4e41 at ea* po9t ( 8 plane ( ref]5ce !re mu/ be a clock1 & all ^! clocks mu/ be syn*roniz$4 ,at ea* clock an obs]v] mu/ be situat$4 ,n[ to f9d ! l5g? ( ! mov+ object at a specifi$ in/ant ( "t 7x is a subject = lat] inve/igation to f9d :e!r its l5g? is a function ( "t71 ! two obs]v]s :o happ5 to co9cide 9 position ) ! two ends ( ! object at ! specifi$ "t on _! clocks are requir$ to f9d ! di/ance betwe5 _! two positions by ! proc$ure = measur+ ! l5g? ( a /ation>y object1 & ?is di/ance is by def9ition ! l5g? ( ! mov+ object 9 ! giv5 ref]5ce sy/em4 ,?is proc$ure = measur+ ! l5g? ( a body 9 motion h5ce involves ! idea ( simultaneity1 ?r\gh ! simultane\s position ( ! two ends ( ! rod1 & we h se5 t ! op]ations by :i* simultaneity are det]m9$ are relative1 *ang+ :5 ! motion ( ! sy/em *anges4 ,we h5ce are prep>$ to f9d a *ange 9 ! l5g? ( a body :5 ! velocity ( ! measur+ sy/em *anges1 & ?is 9 fact is :at happ5s4 ,! precise num]ical dep5d5ce is work$ out by ,e9/e91 & involves o!r consid]ations1 9 :i* we are n int]e/$ at pres5t4 ,! two sorts ( l5g?1 ! naive "o & t ( ,e9/e91 h c]ta9 features 9 common4 ,9 ei!r case 9 ! limit1 z ! velocity ( ! measur+ sy/em approa*es z]o1 ! op]ations approa* ^? = measur+ ! l5g? ( a /ation>y object4 ,?is1 ( c\rse1 is a requirem5t 9 any good def9ition1 impos$ by consid]ations ( conv5i5ce1 & x is too obvi\s a matt] to ne$ elaboration4 ,ano!r feature is t ! op]ations equival5t to ei!r concept bo? involve ! motion ( ! sy/em1 s t we mu/ recognize ! possibility t ! l5g? ( a mov+ object may be a function ( its velocity4 ,x is a matt] ( exp]im5t1 unpr$ictable until tri$1 t )9 ! limits ( pres5t exp]im5tal error ! naive l5g? is n affect$ by motion1 & ,e9/e9's l5g? is4 ,s f>1 we h ext5d$ ! concept ( l5g? 9 only "o way beyond ! range ( ord9>y exp]i5ce1 namely to high velocities4 ,! ext5sion may obvi\sly be made 9 o!r directions4 ,let u inquire :at are ! op]ations by :i* we measure ! l5g? ( a v l>ge object4 ,9 practice we probably fir/ meet ! desirability ( a *ange ( proc$ure 9 measur+ l>ge pieces ( l&4 ,"h our proc$ure dep5ds on measurem5ts ) a surveyor's !odolite4 ,?is involves ext5d+ ov] ! surface ( ! l& a sy/em ( coord9ates1 />t+ f a base l9e measur$ ) a tape 9 ! conv5tional way1 sight+ on di/ant po9ts f ! extremities ( ! l9e1 & measur+ ! angles4 ,n[ 9 ?is ext5sion we h made "o v ess5tial *ange3 ! angles betwe5 ! l9es connect+ di/ant po9ts are n[ angles betwe5 beams ( light4 ,we assume t a beam ( light travels 9 a /raight l9e4 ,fur!rmore1 we assume 9 ext5d+ our sy/em ( triangulation ov] ! surface ( ! e>? t ! geometry ( light beams is ,euclidean4 ,we d ! be/ we c to *eck ! assumptions1 b at mo/ c nev] get m ?an a p>tial *eck4 ,?us ,gauss#a *eck$ :e!r ! angles ( a l>ge t]re/rial triangle add to two "r angles & f\nd agreem5t )9 exp]im5tal error4 ,we n[ "k f ! exp]im5ts ( ,mi*elson#b t if 8 measurem5ts _h be5 accurate en\gh he w\ld n h got a *eck1 b w\ld h _h an excess or defect accord+ to ! direction 9 :i* ! beam ( light travell$ ar\nd ! triangle ) respect to ! rotation ( ! e>?4 ,b if ! geometry ( light beams is ,euclidean1 !n n only mu/ ! angles ( a triangle add to two "r angles1 b !re are def9ite relations betwe5 ! l5g?s ( ! sides & ! angles1 & to *eck ^! relations ! sides %\ld be measur$ by ! old proc$ure ) a met] /ick4 ,su* a *eck on a l>ge scale has nev] be5 attempt$1 & is n feasible4 ,x seems1 !n1 t our *ecks on ! ,euclidean "* ( optical space are all ( re/rict$ "*4 ,we h app>5tly prov$ t up to a c]ta9 scale ( magnitude optical space is ,euclidean ) respect to measures ( angle1 b ?is may n necess>ily involve t space is also ,euclidean ) respect to measures ( l5g?1 s t space ne$ n be completely ,euclidean4 ,!re is a fur!r mo/ important re/riction 9 t our /udies ( non-,euclidean geometry h %[n t ! p]c5tage excess ( ! angles ( a non-,euclidean triangle ov] #ahj may dep5d on ! magnitude ( ! triangle1 s t x may well be t we h n detect$ ! non-,euclidean "* ( space simply because our measurem5ts h n be5 on a l>ge en\gh scale4 ,footnote #a3 ,c4 ,f4 ,gauss1 ,gesammelte ,w]ke1 especially vol4 ,,iv4 ,footnote #b3 ,see a discussion ( ! !ory ( ?is exp]im5t by ,l4 ,silb]/e91 ,j\r4 ,opt4 ,soc4 ,am]4 #e1 #bia-cjg4 #aiba4 ,we ?us see t ! concept ( l5g? has und]gone a v ess5tial *ange ( "* ev5 )9 ! range ( t]re/rial measurem5ts1 9 t we h sub/itut$ = :at ,i may call ! tactual concept an optical concept1 complicat$ by an assumption ab\t ! nature ( our geometry4 ,f a v direct concept we h come to a v indirect concept ) a mo/ complicat$ set ( op]ations4 ,/rictly speak+1 l5g? :5 measur$ 9 ?is way by light beams %\ld be call$ by ano!r "n1 s9ce ! op]ations are diff]5t4 ,! practical ju/ification = reta9+ ! same "n is t )9 our pres5t exp]im5tal limits a num]ical diff]5ce betwe5 ! results ( ! two sorts ( op]ations has n be5 detect$4 ,we are /ill worse (f :5 we make ! ext5sion to sol> & /ell> di/ances4 ,"h space is entirely optical 9 "*1 & we nev] h an opportunity ( ev5 p>tially comp>+ tactual ) optical space4 ,no direct measures ( l5g? h ev] be5 made1 nor c we ev5 measure ! ?ree angles ( a triangle & s *eck our assumption t ! use ( ,euclidean geometry 9 ext5d+ ! concept ( space is ju/ifi$4 ,we nev] h "u obs]vation m ?an two angles ( a triangle1 z :5 we measure ! di/ance ( ! moon by obs]vation f ! two ends ( ! e>?'s diamet]4 ,to ext5d to /ill great] di/ance our measures ( l5g?1 we h to make /ill fur!r assumptions1 su* z t inf]5ces f ! ,newtonian laws ( me*anics are valid4 ,! accuracy ( our inf]5ces ab\t l5g?s f su* measurem5ts is n high4 ,a/ronomy is usually reg>d$ z a sci5ce ( extraord9>ily high accuracy1 b its accuracy is v re/rict$ 9 "*1 namely to ! measurem5t ( angles4 ,x is probably safe to say t no a/ronomical di/ance1 except p]haps t ( ! moon1 is kn[n ) an accuracy great] ?an #j4a4 ,:5 we pu% our e/imates to di/ances beyond ! conf9es ( ! sol> sy/em 9 :i* we are assi/$ by ! laws ( me*anics1 we are r$uc$ 9 ! fir/ place to measurem5ts ( p>allax1 :i* at be/ h a q inf]ior accuracy1 & :i* fur!rmore fail entirely outside a r re/rict$ range4 ,= great] /ell> di/ances we are driv5 to o!r & mu* r\gh] e/imates1 re/+ = in/ance on ! ext5sion to great di/ances ( connections f\nd )9 ! range ( p>allax betwe5 brightness & spectral type ( a />1 or on su* assumptions z t1 because a gr\p ( />s looks z if x 7 all toge!r 9 space & _h a common orig91 x actually is s4 ,?us at great] & great] di/ances n only does exp]im5tal accuracy become less1 b ! v nature ( ! op]ations by :i* l5g? is to be det]m9$ becomes indef9ite1 s t ! di/ances ( ! mo/ remote /ell> objects z e/imat$ by diff]5t obs]v]s or by diff]5t me?ods may be v div]g5t4 ,a p>ticul> consequ5ce ( ! inaccuracy ( ! a/ronomical measures ( great di/ances is t ! "q ( :e!r l>ge scale space is ,euclidean or n is m]ely academic4 ,we ?us see t 9 ! ext5sion f t]re/rial to great /ell> di/ances ! concept ( l5g? has *ang$ completely 9 "*4 ,to say t a c]ta9 /> is #aje light ye>s di/ant is actually & conceptually an entire diff]5t k9d ( ?+ f say+ t a c]ta9 goal po/ is #ajj met]s di/ant4 ,because ( our conviction t ! "* ( our exp]i5ce may *ange :5 ! range ( ph5om5a *anges1 we feel ! importance ( su* a "q z :e!r ! space ( di/ances ( #aje light ye>s is ,euclidean or n1 & are correspond+ly dissatisfi$ t at pres5t !re seems no way ( giv+ mean+ to x4 ,we enc\nt] difficulties simil> to ^? above1 & are also compell$ to modify our proc$ures1 :5 we g to small di/ances4 ,d[n to ! scale ( microscopic dim5sions a fairly /raight=w>d ext5sion ( ! ord9>y measur+ proc$ure is suffici5t1 z :5 we measure a l5g? 9 a micromet] eyepiece ( a microscope4 ,?is is ( c\rse a comb9ation ( tactual & optical measurem5ts1 & c]ta9 assumptions1 ju/ifi$ z f> z possible by exp]i5ce1 h to be made ab\t ! behavior ( light beams4 ,^! assumptions are ( a q diff]5t "* f ^? :i* give u conc]n on ! a/ronomical scale1 because "h we meet difficulty f int]f]5ce effects due to ! f9ite scale ( ! /ructure ( light1 & are n conc]n$ ) a possible curvature ( light beams 9 ! long rea*es ( space4 ,ap>t f ! matt] ( conv5i5ce1 we might also measure small di/ances by ! tactual me?od4 ,z ! dim5sions become small]1 c]ta9 difficulties become increas+ly important t 7 negligible on a l>g] scale4 ,9 c>ry+ out physically ! op]ations equival5t to our concepts1 !re are a ho/ ( practical precautions to be tak5 :i* c\ld be explicitly enum]at$ ) difficulty1 b ( :i* nev]!less any practical physici/ is consci\s4 ,suppose1 = example1 we measure l5g? tactually by a comb9ation ( ,johanss5 gauges4 ,9 pil+ ^! toge!r1 we mu/ be sure t !y are clean1 & are ?us 9 actual contact4 ,p>ticles ( me*anical dirt fir/ engage our att5tion4 ,!n z we g to small] dim5sions we p]haps h to pay att5tion to adsorb$ films ( moi/ure1 !n at /ill small] dim5sions to adsorb$ films ( gas1 until f9ally we h to "w 9 a vacuum1 :i* mu/ be ! m ne>ly complete ! small] ! dim5sions4 ,ab\t ! "t t we discov] ! necessity = a complete vacuum1 we discov] t ! gauges !mselves are atomic 9 /ructure1 t !y h no def9ite b\nd>ies1 & !re=e no def9ite l5g?1 b t ! l5g? is a hazy ?+1 v>y+ rapidly 9 "t betwe5 c]ta9 limits4 ,we treat ?is situation z be/ we c by tak+ a "t av]age ( ! app>5t positions ( ! b\nd>ies1 assum+ t along ) ! decrease ( dim5sions we h acquir$ a correspond+ extravagant increase 9 nimbl5ess4 ,b z ! dim5sions get small] cont9ually1 ! difficulties due to ?is haz9ess increase indef9itely 9 p]c5tage effect1 & we are ev5tually driv5 to give up altoge!r4 ,we h made ! discov]y t !re are ess5tial physical limitations to ! op]ations :i* def9$ ! concept ( l5g?4 ,we p]haps d n reg>d ! sub/itution ( optical = tactual space on ! a/ronomical scale z compell$ by ! same sort ( physical necessity1 because ,i suppose ! possible ev5tual l&+ ( m5 9 ! moon w always be "o ( ! dreams ( humanity4 ,at ! same "t t we h come to ! end ( our rope ) our ,johanss5 gauge proc$ure1 our companion ) ! microscope has be5 enc\nt]+ difficulties due to ! f9ite wave l5g? ( light2 ?is difficulty he has be5 able to m9imize by us+ light ( progressively %ort] wave l5g?s1 b he has ev5tually _h to /op on rea*+ ,x-rays4 ,( c\rse ?is optical proc$ure ) ! microscope is m conv5i5t1 & is !re=e adopt$ 9 practice4 ,let u n[ see :at is impli$ 9 our concept ( l5g? ext5d$ to ultramicroscopic dim5sions4 ,:at1 = in/ance1 is ! mean+ ( ! /atem5t t ! di/ance betwe5 ! planes ( atoms 9 a c]ta9 cry/al is #c x #aj-h cm48 ,:at we w\ld l to mean is t x #ajh ( ^! planes pil$ on top ( ea* o!r give a ?ickness ( #a cm42 b ( c\rse su* a mean+ is n ! actual "o4 ,! actual mean+ may be f\nd by exam9+ ! op]ations by :i* we arriv$ at ! numb] #c x #aj-h4 ,z a matt] ( fact1 #c x #aj-h 0 ! numb] obta9$ by solv+ a g5]al equation d]iv$ f ! wave !ory ( light1 into :i* c]ta9 num]ical data obta9$ by exp]im5ts ) ,x-rays _h be5 sub/itut$4 ,?us n only has ! "* ( ! concept ( l5g? *ang$ f tactual to optical1 b we h gone mu* fur!r 9 committ+ ourselves to a def9ite optical !ory4 ,if ?is 7 ! :ole /ory1 we w\ld be mo/ uncom=table ) respect to ?is bran* ( physics1 because we are s unc]ta9 ( ! correctness ( our optical !ories1 b actually a numb] ( *ecks c be appli$ :i* greatly re/ore our confid5ce4 ,= in/ance1 f ! d5sity ( ! cry/al & ! grat+ space1 ! weight ( ! individual atoms may be comput$1 & ^! weights may !n be comb9$ ) measurem5ts ( ! dim5sions ( o!r sorts ( cry/al into :i* ! same atoms ent] to give values ( ! d5sities ( ^! cry/als1 :i* may be *eck$ aga9/ exp]im5t4 ,all su* *ecks h succe$$ )9 limits ( accuracy :i* are fairly high4 ,x is important to notice t1 9 spite ( ! *ecks1 ! "* ( ! concept is *ang+1 & beg9s to involve su* ?+s z ! equations ( optics & ! assumption ( ! cons]vation ( mass4 ,we are n cont5t1 h[ev]1 to /op ) dim5sions ( atomic ord]1 b h to pu% on to ! electron ) a diamet] ( ! ord] ( #aj-ah cm4 ,:at is ! possible mean+ ( ! /atem5t t ! diamet] ( an electron is #aj-ah cm48 ,aga9 ! only answ] is f\nd by exam9+ ! op]ations by :i* ! numb] #aj-ah 0 obta9$4 ,?is numb] came by solv+ c]ta9 equations d]iv$ f ! field equations ( electrodynamics1 into :i* c]ta9 num]ical data obta9$ by exp]im5t _h be5 sub/itut$4 ,! concept ( l5g? has !re=e n[ be5 s modifi$ z to include t !ory ( electricity embodi$ 9 ! field equations1 &1 mo/ important1 assumes ! correctness ( ext5d+ ^! equations f ! dim5sions 9 :i* !y may be v]ifi$ exp]im5tally into a region 9 :i* _! correctness is "o ( ! mo/ important & problematical ( pres5t-day que/ions 9 physics4 ,to f9d :e!r ! field equations are correct on a small scale1 we mu/ v]ify ! relations dem&$ by ! equations betwe5 ! electric & magnetic =ces & ! space coord9ates1 to det]m9e :i* involves measurem5t ( l5g?s4 ,b if ^! space coord9ates _c be giv5 an indep5d5t mean+ ap>t f ! equations1 n only is ! attempt$ v]ification ( ! equations impossible1 b ! "q itself is mean+less4 ,if we /ick to ! concept ( l5g? by itself1 we are l&$ 9 a vici\s circle4 ,z a matt] ( fact1 ! concept ( l5g? disappe>s z an indep5d5t ?+1 & fuses 9 a complicat$ way ) o!r concepts1 all ( :i* are !mselves alt]$ !reby1 ) ! result t ! total numb] ( concepts us$ 9 describ+ nature at ?is level is r$uc$ 9 numb]4 ,a precise analysis ( ! situation is difficult1 & ,i suppose has nev] be5 attempt$1 b ! g5]al "* ( ! situation is evid5t4 ,until at lea/ a p>tial analysis is attempt$1 ,i d n see h[ any mean+ c be atta*$ to su* que/ions z :e!r space is ,euclidean 9 ! small scale4 ,x is int]e/+ to obs]ve t any increas$ accuracy 9 k ( l>ge scale ph5om5a mu/1 z f> z we n[ c see1 arise f an increase 9 ! accuracy ( measurem5t ( small ?+s1 t is1 9 ! measurem5t ( small angles or ! analysis ( m9ute diff]5ces ( wave l5g?s 9 ! spectra4 ,to "k ! v l>ge takes u into ! same field ( exp]im5t z to "k ! v small1 s t op]ationally ! l>ge & ! small h features 9 common4 ,?is some:at detail$ analysis ( ! concept ( l5g? br+s out features common to all our concepts4 ,if we deal ) ph5om5a outside ! doma9 9 :i* we orig9ally def9$ our concepts1 we may f9d physical h9drances to p]=m+ ! op]ations ( ! orig9al def9ition1 s t ! orig9al op]ations h to be replac$ by o!rs4 ,^! new op]ations are1 ( c\rse1 to be s *os5 t !y give1 )9 exp]im5tal error1 ! same num]ical results 9 ! doma9 9 :i* ! two sets ( op]ations may be bo? appli$2 b we mu/ recognize 9 pr9ciple t 9 *ang+ ! op]ations we h really *ang$ ! concept1 & t to use ! same "n = ^! diff]5t concepts ov] ! entire range is dictat$ only by consid]ations ( conv5i5ce1 :i* may sometimes prove to h be5 pur*as$ at too high a price 9 t]ms ( unambiguity4 ,we mu/ always be prep>$ "s day to f9d t an increase 9 exp]im5tal accuracy may %[ t ! two diff]5t sets ( op]ations :i* give ! same results 9 ! m ord9>y "p ( ! doma9 ( exp]i5ce1 lead to measurably diff]5t results 9 ! m unfamili> p>ts ( ! doma94 ,we mu/ rema9 aw>e ( ^! jo9ts 9 our conceptual /ructure if we hope to r5d] unnecess>y ! s]vices ( ! unborn ,e9/e9s4 ,! second feature common to all concepts br\ght out by ! detail$ discussion ( l5g? is t1 z we approa* ! exp]im5tally atta9able limit1 concepts lose _! individuality1 fuse toge!r1 & become few] 9 numb]1 z we h se5 t at dim5sions ( ! ord] ( ! diamet] ( an electron ! concepts ( l5g? & ! electric field vectors fuse into an amorph\s :ole4 ,n only does nature z exp]i5c$ by u become diff]5t 9 "* on its horizons1 b x becomes simpl]1 & !re=e our concepts1 :i* are ! build+ /ones ( our descriptions1 become few] 9 numb]4 ,?is seems to be an entirely natural /ate ( affairs4 ,h[ ! numb] ( concepts is (t5 kept =mally ! same z we approa* ! horizon w be discuss$ lat] 9 special cases4 ,a precise analysis ( our conceptual /ructure has nev] be5 attempt$1 except p]haps 9 v re/rict$ doma9s1 & x seems to me t !re is room "h = mu* important future "w4 ,su* an analysis is n to be attempt$ 9 ?is essay1 b only "s ( ! m important qualitative aspects are to be po9t$ out4 ,x w nev] be possible to give a clean-cut logical analysis ( ! conceptual situation1 = ! nature ( our concepts1 accord+ to our op]ational po9t ( view1 is ! same z ! nature ( exp]im5tal k1 :i* is (t5 hazy4 ,?us 9 ! transition regions :]e nature is gett+ simpl] & ! numb] ( op]ationally indep5d5t concepts *anges1 a c]ta9 haz9ess is inevitable1 = ! actual *ange 9 our conceptual /ructure 9 ^! transition regions is cont9u\s1 correspond+ to ! cont9uity ( our exp]im5tal k1 :]eas =mally ! numb] ( concepts %\ld be an integ]4 ,! ,relative ,"* ( ,k ,two o!r consequ5ces ( ! op]ational po9t ( view mu/ n[ be exam9$4 ,fir/ is ! consequ5ce t all our k is relative4 ,?is may be und]/ood 9 a g5]al or a m p>ticul> s5se4 ,! g5]al s5se is illu/rat$ 9 ,haldane's book on ! ,reign ( ,relativity4 ,relativity 9 ! g5]al s5se is ! m]e/ truism if ! op]ational def9ition ( concept is accept$1 = exp]i5ce is describ$ 9 t]ms ( concepts1 & s9ce our concepts are con/ruct$ ( op]ations1 all our k mu/ unescapably be relative to ! op]ations select$4 ,b k is also relative 9 a n>r[] s5se1 z :5 we say !re is no su* ?+ z absolute re/ 7or motion7 or absolute size1 b re/ & size are relative t]ms4 ,conclusions ( ?is k9d are involv$ 9 ! specific "* ( ! op]ations 9 t]ms ( :i* re/ or size are def9$4 ,an exam9ation ( ! op]ations by :i* we det]m9e :e!r a body is at re/ or 9 motion %[s t ! op]ations are relative op]ations3 re/ or motion is det]m9$ ) respect to "s o!r body select$ z ! /&>d4 ,9 say+ t !re is no su* ?+ z absolute re/ or motion we are n mak+ a /atem5t ab\t nature 9 ! s5se t might be suppos$1 b we are m]ely mak+ a /atem5t ab\t ! "* ( our descriptive processes4 ,simil>ly ) reg>d to size3 exam9ation ( ! op]ations ( ! measur+ process %[s t size is measur$ relative to ! fundam5tal measur+ rod4 ,! absolute !re=e disappe>s 9 ! orig9al mean+ ( ! ^w4 ,b ! absolute may usefully return ) an alt]$ mean+1 & we may say t a ?+ has absolute prop]ties if ! num]ical magnitude is ! same :5 measur$ ) ! same =mal proc$ure by all obs]v]s4 ,:e!r a giv5 prop]ty is absolute or n c be det]m9$ only by exp]im5t1 l&+ u 9 ! p>adoxical position t ! absolute is absolute only relative to exp]im5t4 ,9 "s cases1 ! mo/ sup]ficial obs]vation %[s t a prop]ty is n absolute1 z1 = example1 x is at once obvi\s t measur$ velocity *anges ) ! motion ( ! obs]v]4 ,b 9 o!r cases ! decision is m difficult4 ,?us ,mi*elson ?\ght he _h an absolute proc$ure = measur+ l5g?1 by ref]r+ to ! wave l5g? ( ! r$ cadmium l9e z /&>d2#c x requir$ difficult & accurate exp]im5t to %[ t ?is l5g? v>ies ) ! motion ( ! obs]v]4 ,ev5 !n1 by *ang+ ! def9ition ( ! l5g? ( a mov+ object1 we believe t l5g? might be made to re-assume its desir$ absolute "*4 ,footnote #c3 ,a4 ,a4 ,mi*elson1 ,light ,waves & ,_! ,uses1 ,univ]sity ( ,*icago ,press1 #aijc1 ,*ap4 ,v4 ,to /op ! discussion at ?is po9t might leave ! impression t ?is obs]vation ( ! relative "* ( k is ( only a v t5u\s & academic int]e/1 s9ce x appe>s to be conc]n$ mo/ly ) ! "* ( our descriptive processes1 & to say little ab\t ext]nal nature4 ,:at ?is means we leave to ! metaphysician to decide4 ,b ,i believe !re is a deep] significance to all ?is4 ,x mu/ be rememb]$ t all our argum5t />ts ) ! concepts z giv54 ,n[ ^! concepts involve physical op]ations2 9 ! discov]y ( :at op]ations may be usefully employ$ 9 describ+ nature is buri$ almo/ all physical exp]i5ce4 ,9 erect+ our /ructure ( physical sci5ce1 we are build+ on ! "w ( all ! ages4 ,!re is !n ?is purely physical significance 9 ! /atem5t t all motion is relative1 namely t no op]ations ( measur+ motion h be5 f\nd to be useful 9 describ+ simply ! behavior ( nature :i* are n op]ations relative to a s+le obs]v]2 9 mak+ ?is /atem5t we are /at+ some?+ ab\t nature4 ,x takes an enorm\s am\nt ( real physical exp]i5ce to discov] relations ( ?is sort4 ,! discov]y t ! numb] obta9$ by c\nt+ ! numb] ( times a /ick may be appli$ to an object c be simply us$ 9 describ+ natural ph5om5a 0 "o ( ! mo/ important & fundam5tal discov]ies ev] made by man4 ,mean+less ,que/ions ,ano!r consequ5ce ( ! op]ational "* ( our concepts1 almo/ a coroll>y ( t consid]$ above1 is t x is q possible1 nay ev5 disquiet+ly easy1 to inv5t expressions or to ask que/ions t are mean+less4 ,x con/itutes a great advance 9 our critical attitude t[>d nature to realize t a great _m ( ! que/ions t we uncritically ask are )\t mean+4 ,if a specific "q has mean+1 x mu/ be possible to f9d op]ations by :i* an answ] may be giv5 to x4 ,x w be f\nd 9 _m cases t ! op]ations _c exi/1 & ! "q !re=e has no mean+4 ,= in/ance1 x means no?+ to ask :e!r a /> is at re/ or n4 ,ano!r example is a "q propos$ by ,clif=d1 namely1 :e!r x is n possible t z ! sol> sy/em moves f "o "p ( space to ano!r ! absolute scale ( magnitude may be *ang+1 b 9 su* a way z to affect all ?+s equally1 s t ! *ange ( scale c nev] be detect$4 ,an exam9ation ( ! op]ations by :i* l5g? is measur$ 9 t]ms ( measur+ rods %[s t ! op]ations d n exi/ 7because ( ! nature ( our def9ition ( l5g?7 = answ]+ ! "q4 ,! "q c be giv5 mean+ only f ! po9t ( view ( "s imag9>y sup]ior be+ wat*+ f an ext]nal po9t ( vantage4 ,b ! op]ations by :i* su* a be+ measures l5g? are diff]5t f ! op]ations ( our def9ition ( l5g?1 s t ! "q acquires mean+ only by *ang+ ! significance ( our t]ms--9 ! orig9al s5se ! "q means no?+4 ,to /ate t a c]ta9 "q ab\t nature is mean+less is to make a significant /atem5t ab\t nature itself1 because ! fundam5tal op]ations are det]m9$ by nature1 & to /ate t nature _c be describ$ 9 t]ms ( c]ta9 op]ations is a significant /atem5t4 ,x mu/ be recogniz$1 h[ev]1 t !re is a s5se 9 :i* no s]i\s "q is entirely )\t mean+1 because d\btless ! que/ion] _h 9 m9d "s int5tion 9 ask+ ! "q4 ,b to give mean+ 9 ?is s5se to a "q1 "o mu/ inquire into ! mean+ ( ! concepts z us$ by ! que/ion]1 & x w (t5 be f\nd t ^! concepts c be def9$ only 9 t]ms ( fictiti\s prop]ties1 z ,newton's absolute "t 0 def9$ by its prop]ties1 s t ! mean+ to be ascrib$ to ! "q 9 ?is way has no connection ) reality4 ,i believe t x w enable u to make m significant & int]e/+ /atem5ts1 & !re=e w be m useful1 to adopt exclusively ! op]ational view1 & s admit ! possibility ( que/ions entirely )\t mean+4 ,?is matt] ( mean+less que/ions is a v subtle ?+ :i* may poison mu* m ( our ?\ght ?an t deal+ ) purely physical ph5om5a4 ,i believe t _m ( ! que/ions ask$ ab\t social & philosophical subjects w be f\nd to be mean+less :5 exam9$ f ! po9t ( view ( op]ations4 ,x w\ld d\btless conduce greatly to cl>ity ( ?\ght if ! op]ational mode ( ?9k+ 7 adopt$ 9 all fields ( inquiry z well z 9 ! physical4 ,j z 9 ! physical doma91 s 9 o!r doma9s1 "o is mak+ a significant /atem5t ab\t 8 subject 9 /at+ t a c]ta9 "q is mean+less4 ,9 ord] to emphasize ?is matt] ( mean+less que/ions1 ,i give "h a li/ ( que/ions1 ) :i* ! read] may amuse himself by f9d+ :e!r !y h mean+ or n4 7#a7 ,0 !re ev] a "t :5 matt] did n exi/8 7#b7 ,may "t h a beg9n+ or an end8 7#c7 ,:y does "t fl[8 7#d7 ,may space be b\nd$8 7#e7 ,may space or "t be discont9u\s8 7#f7 ,may space h a f\r? dim5sion1 n directly detectible1 b giv5 indirectly by inf]5ce8 7#g7 ,are !re p>ts ( nature =ev] beyond our detection8 7#h7 ,is ! s5sation :i* ,i call blue really ! same z t :i* my neighbor calls blue8 ,is x possible t a blue object may ar\se 9 him ! same s5sation t a r$ object does 9 me & vice v]sa8 7#i7 ,may !re be miss+ integ]s 9 ! s]ies ( natural numb]s z we "k !m8 7#aj7 ,is a univ]se possible 9 :i* #b #b #d8 7#aa7 ,:y does negative electricity attract positive8 7#ab7 ,:y does nature obey laws8 7#ac7 ,is a univ]se possible 9 :i* ! laws are diff]5t8 7#ad7 ,if "o "p ( our univ]se c\ld be completely isolat$ f ! re/1 w\ld x cont9ue to obey ! same laws8 7#ae7 ,c we be sure t our logical processes are valid8 ,,g5]al ,,comm5ts ,,on ,,! ,,op]ational ,,po9t ,,( ,,view ,to adopt ! op]ational po9t ( view involves mu* m ?an a m]e re/riction ( ! s5se 9 :i* we und]/& concept1 b means a f>-rea*+ *ange 9 all our habits ( ?\ght1 9 t we %all no long] p]mit ourselves to use z tools 9 our ?9k+ concepts ( :i* we _c give an adequate acc\nt 9 t]ms ( op]ations4 ,9 "s respects ?9k+ becomes simpl]1 because c]ta9 old g5]alizations & idealizations become incapable ( use2 = in/ance1 _m ( ! speculations ( ! e>ly natural philosoph]s become simply unreadable4 ,9 o!r respects1 h[ev]1 ?9k+ becomes mu* m difficult1 because ! op]ational implications ( a concept are (t5 v involv$4 ,= example1 x is mo/ difficult to grasp adequately all t is conta9$ 9 ! app>5tly simple concept ( "t1 & requires ! cont9ual correction ( m5tal t5d5cies :i* we h long unque/ion+ly accept$4 ,op]ational ?9k+ w at fir/ prove to be an unsocial virtue2 "o w f9d oneself p]petually unable to und]/& ! simple/ conv]sation ( "o's fri5ds1 & w make oneself univ]sally unpopul> by dem&+ ! mean+ ( app>5tly ! simple/ t]ms ( e argum5t4 ,possibly aft] e "o has s*ool$ himself to ?is bett] way1 !re w rema9 a p]man5t unsocial t5d5cy1 because d\btless mu* ( our pres5t conv]sation w !n become unnecess>y4 ,! socially optimi/ic may v5ture to hope1 h[ev]1 t ! ultimate effect w be to release "o's en]gies = m /imulat+ & int]e/+ int]*ange ( ideas4 ,n only w op]ational ?9k+ re=m ! social art ( conv]sation1 b all our social relations w be liable to re=m4 ,let any "o exam9e 9 op]ational t]ms any popul> pres5t-day discussion ( religi\s or moral que/ions to realize ! magnitude ( ! re=mation await+ u4 ,:]ev] we temporize or compromise 9 apply+ our !ories ( conduct to practical life we may suspect a failure ( op]ational ?9k+4 ,,*apt] ,,ii ,,o!r ,,g5]al ,,consid]ations ,,! ,,approximate ,,"* ,,( ,,empirical ,,k ,,al?\gh _m aspects ( ! processes by :i* we obta9 k ( ! ext]nal physical _w are mu* beyond ! scope ( our pres5t inquiry1 "o matt] mu/ be m5tion$ 9 detail because x tacitly und]lies all our discussion1 ! fact1 namely1 t all results ( measurem5t are only approximate4 ,t su* is true is evid5t aft] ! mo/ sup]ficial exam9ation ( any measur+ process2 any /atem5t ab\t num]ical relations betwe5 measur$ quantities mu/ always be subject to ! qualification t ! relation is valid only )9 limits4 ,fur!rmore1 all exp]i5ce seems to be ( ?is "*2 we nev] h p]fectly clean-cut k ( any?+1 b all our exp]i5ce is surr\nd$ by a twilight zone1 a p5umbra ( unc]ta9ty1 into :i* we h n yet p5etrat$4 ,?is p5umbra is z truly an unexplor$ region z any o!r region beyond exp]im5t1 su* z ! region ( high velocities1 = example1 & we mu/ hold no preconceiv$ notions z to :at w be f\nd )9 ! region4 ,! p5umbra is to be p5etrat$ by improv+ ! accuracy ( measurem5t4 ,)9 :at 0 at "o "t p5umbra has be5 f\nd ! displacem5t ( angul> position ( ! />s ne> ! edge ( ! sol> disc1 & )9 ! p5umbra z yet unp5etrat$ we look = su* effects z ! equival5ce ( mass & en]gy4 ,_m ( ! great discov]ies ( ! future w probably be made )9 ! p5umbra3 we h already m5tion$ t increas$ k ( ph5om5a ( a cosmic scale is to be obta9$ by increas+ ! accuracy ( measurem5t ( ! v small4 ,x is a g5]al consequ5ce ( ! approximate "* ( all measurem5t t no empirical sci5ce c ev] make exact /atem5ts4 ,?is 0 fairly obvi\s 9 ! case ( me*anics1 b x requir$ a ,gauss#d to conv9ce u t ! geometry 9 :i* we are int]e/$ z physici/s is an empirical subject1 & t "o _c say t actual space is ,euclidean1 b only t actual space approa*es to ideal ,euclidean space )9 a c]ta9 degree ( approximation4 ,i believe t we are compell$ to g /ill fur!r1 & recognize t ari?metic1 s f> z x purports to deal ) actual physical objects1 is also affect$ ) ! same p5umbra ( unc]ta9ty z all o!r empirical sci5ce4 ,a typical /atem5t ( empirical ari?metic is t #b objects plus #b objects makes #d objects4 ,?is /atem5t acquires physical mean+ only 9 t]ms ( c]ta9 physical op]ations1 & ^! op]ations mu/ be p]=m$ 9 "t4 ,footnote #d3 ,c4 ,f4 ,gauss1 ,gesammelte ,w]ke1 especially vols4 ,,iv & ,,viii4 ,n[ ! p5umbra gets into ?is situation ?r\gh ! concept ( object4 ,if ! /atem5t ( ari?metic is to be an exact /atem5t 9 ! ma!matical s5se ! object mu/ be a def9ite clean-cut ?+1 :i* pres]ves its id5tity 9 "t ) no p5umbra4 ,b ?is sort ( ?+ is nev] exp]i5c$1 & z f> z we "k does n correspond exactly to any?+ 9 exp]i5ce4 ,x is ( c\rse true t 9 mo/ exp]i5ce ! p5umbra is s v ?9 & snug-fitt+ t x requires special ef=t to recognize its pres5ce at all2 b scrut9y1 ,i believe1 %[s t x is always !re4 ,if our exp]i5ce _h be5 re/rict$ to ph5om5a 9 a vacuum1 & ! objects we 7 try+ to c\nt _h be5 sph]es ( a gas :i* exp& & int]p5etrate1 x is obvi\s t ! concept ( object z a ?+ ) id5tity w\ld h be5 mu* m difficult to =m4 ,or1 if our objects are tumbl]s ( wat]1 we discov] :5 our obs]vation rea*es a c]ta9 /age ( ref9em5t t ! am\nt ( wat] is cont9ually *ang+ by evaporation & cond5sation1 & we are bo!r$ by ! "q :e!r ! object is /ill ! same aft] x has wax$ & wan$4 ,com+ to solids1 we ev5tually discov] t ev5 solids evaporate1 or cond5se gases on !m1 & we see t an object ) id5tity is an ab/raction correspond+ exactly to no?+ 9 nature4 ,( c\rse ! p5umbra ( unc]ta9ty :i* surr\nds our ari?metical /atem5ts because ( ?is prop]ty ( physical objects is s exce$+ly t5u\s t practically we are n aw>e ( its exi/5ce1 & expect nev] to f9d undiscov]$ ph5om5a )9 ! p5umbra4 ,b 9 pr9ciple we mu/ recognize its pres5ce1 & mu/ fur!r recognize t all empirical sci5ce mu/ be ( ?is "*4 ,9 mo/ empirical sci5ces1 ! p5umbra is at fir/ prom95t1 & becomes less important & ?9n] z ! accuracy ( physical measurem5t is increas$4 ,9 me*anics1 = example1 ! p5umbra is at fir/ l a ?ick obscur+ veil at ! /age :]e we measure =ces only by our muscul> s5sations1 & gradually is att5uat$1 z ! precision ( measurem5ts increases4 ,b ) ! ari?metical concept ( an individual id5tifiable object x is ! exact rev]se2 a crude po9t ( view does n suspect ! exi/5ce ( ! p5umbra at all1 & we discov] x only by highly ref9+ our me?ods4 ,d\btless ari?metic owes its e>ly developm5t to ?is prop]ty4 ,we may n[ g /ill fur!r4 ,op]ations !mselves are1 ( c\rse1 d]iv$ f exp]i5ce1 & w\ld be expect$ also to h a nebul\s edge ( unc]ta9ty4 ,we h to ask su* que/ions z :e!r ! op]ations ( ari?metic are clean-cut ?+s4 ,is ! op]ation ( multiply+ #b objects by #b a def9ite op]ation1 ) no envelop+ haze8 ,all our physical exp]i5ce conv9ces u t if !re is a p5umbra ab\t ! concept ( op]ations ( ?is sort x is s t5u\s z to be negligible1 at lea/ = ! pres5t2 b ! "q af=ds an int]e/+ topic = speculation4 ,we also h to ask :e!r m5tal op]ations may simil>ly be envelop$ 9 a haze4 ,,explanations ,,& ,,me*anisms ,p]haps ! climax ( our task ( int]pret+ & correlat+ nature is rea*$ :5 we are able to f9d an explanation ( ph5om5a2 ) ! f9d+ ( ! explanation we are incl9$ to feel t our und]/&+ ( ! situation is complete4 ,we n[ h to ask :at is ! nature ( ! explanation :i* we set z ! goal ( our ef=ts4 ,! answ] is n easy to give1 & !re may be diff]5ce ( op9ion ab\t x4 ,we %all get ! be/ answ] to ?is1 z to s _m o!r que/ions1 by adopt+ ! op]ational po9t ( view1 & exam9+ :at we d 9 giv+ an explanation4 ,i believe t exam9ation w %[ t ! ess5ce ( an explanation consi/s 9 r$uc+ a situation to elem5ts ) :i* we are s famili> t we accept !m z a matt] ( c\rse1 s t our curiosity re/s4#e ,r$uc+ a situation to elem5ts means1 f ! op]ational po9t ( view1 discov]+ famili> correlations betwe5 ! ph5om5a ( :i* ! situation is compos$4 ,footnote #e3 ,! ultimate elem5ts ( explanation are analog\s to ! axioms ( =mal ma!matics4 ,!re is involv$ "h ! !sis t x is possible to analyze nature into correlations1 )\t1 h[ev]1 any assumption :atev] z to ! "* ( ^! correlations4 ,x seems to me t su* a !sis is ! mo/ g5]al t c be made if nature is to be intelligible at all4 ,?is !sis und]lies all ! consid]ations ( ?is essay1 & we %all n try to f9d any?+ m g5]al4 ,we %all1 h[ev]1 recognize t any assumption z to ! "* ( ! correlations con/itutes a special hypo!sis :i* may re/rict ! future1 & t !re=e ^! special hypo!ses are to be subject$ to special exam9ation4 ,we return to ?is matt] 9 m detail 9 discuss+ ! causality concept1 :i* is closely relat$ to ! concept ( explanation4 ,9 ?is view ( explanation !re is no implication t ! elem5t is ei!r a small] or a l>g] scale ?+ ?an ! ph5om5on be+ expla9$2 ?us we may expla9 ! prop]ties ( a gas 9 t]ms ( its con/itu5t molecules1 or p]haps "s day we %all become s famili> ) ! idea ( a non-,euclidean space t we %all expla9 7in/ead ( describe7 ! gravitational attraction ( a /one by ! e>? 9 t]ms ( a space-"t curvature impos$ by all ! re/ ( ! matt] 9 ! univ]se4 ,if ?is is accept$ z ! true nature ( explanation1 we see t an explanation is n an absolute sort ( ?+1 b :at is satisfactory = "o man w n be = ano!r4 ,! savage is satisfi$ by expla9+ ! ?und]/orm z ! caprici\s act ( an angry god4 ,! physici/ dem&s m1 & requires t ! famili> elem5ts to :i* we r$uce a situation be su* t we c intuitively pr$ict _! behavior4 ,?us ev5 if ! physici/ believ$ 9 ! exi/5ce ( ! angry god1 he w\ld n be satisfi$ ) ?is explanation ( ! ?und]/orm because he is n s well acqua9t$ ) angry gods z to be able to pr$ict :5 ang] is foll[$ by a /orm4 ,he w\ld h to "k :y ! god _h become angry1 & :y mak+ a ?und]/orm eas$ 8 ire4 ,b ev5 ) ?is additional qualification1 sci5tific explanation is obvi\sly /ill a relative affair--relative to ! elem5ts or axioms to :i* we make r$uction & :i* we accept z ultimate4 ,^! elem5ts dep5d to a c]ta9 ext5t on ! purpose 9 view1 & also on ! range ( our previ\s physical exp]i5ce4 ,if we are expla9+ ! action ( a ma*9e1 we are satisfi$ to r$uce ! action to ! pu% & pull ( ! v>i\s memb]s ( ! ma*9e1 x be+ accept$ z an ultimate t ^! memb]s transmit pu%es or pulls4 ,b ! physici/ :o has ext5d$ 8 exp]im5tal k fur!r1 may want to expla9 h[ ! memb]s transmit pu%es or pulls 9 t]ms ( ! action on ea* o!r ( ! electrons 9 _! orbits 9 ! atoms4 ,! "* ( our explanatory /ructure w dep5d on ! "* ( our exp]im5tal k1 & w *ange z ?is *anges4 ,=mally1 !re is no limit to ! process ( explanation1 because we c always ask :at is ! explanation ( ! elem5ts 9 t]ms ( :i* we h giv5 ! la/ explanation4 ,b ! po9t ( view ( op]ations %[s t ?is is m]e =malism :i* ends only 9 mean+less j>gon1 = we soon arrive at ! limit ( our exp]im5tal k1 & beyond ?is ! op]ations involv$ 9 ! concepts ( our explanations become impossible & ! concepts become mean+less4 ,z we ext5d exp]im5tal k & pu% our explanations fur!r & fur!r1 we see t ! explanatory sequ5ce may be t]m9at$ 9 sev]al possible ways4 ,9 ! fir/ place1 we may nev] pu% our exp]im5ts beyond a /age into :i* ! elem5ts ) :i* we are already famili> d n ent]4 ,9 ?is case explanation is v simple3 x involves no?+ ess5tially new1 b m]ely ! dis5tanglem5t ( complexities4 ,! k9etic !ory ( gases1 9 expla9+ ! !rmal prop]ties ( a gas 9 t]ms ( ord9>y me*anical prop]ties ( ! molecules1 sugge/s su* a situation4 ,or1 secondly1 our exp]im5ts may br+ u into contact ) situations novel to u1 9 :i* we c recognize no famili> elem5ts1 or at lea/ mu/ recognize t !re is some?+ 9 addition to ! famili> elem5ts4 ,su* a situation con/itutes an explanatory crisis & explanation has to /op by def9ition4 ,or ?irdly1 we may try to =ce our explanations into a pr$et]m9$ mold1 by =mally erect+ or inv5t+ beyond ! range ( pres5t exp]im5t ultimates m or less l elem5ts already famili> to u1 & seek to expla9 all pres5t exp]i5ce 9 t]ms ( ^! *os5 ultimates4 ,leav+ = ! pres5t ! ?ird possibility1 :i* is )9 our control to accept or reject1 & is a =mal matt]1 x is m]ely a "q ( exp]im5tal fact :i* ( ! fir/ two possibilities corresponds to ! actual /ate ( affairs4 ,! mo/ p]functory exam9ation ( ! pres5t /ate ( physics %[s t we are n[ fac+ ! second ( ^! possibilities1 & t 9 ! new exp]im5tal facts ( relativity1 & 9 all quantum ph5om5a1 we are confront$ ) an explanatory crisis4 ,x has (t5 be5 emphasiz$ t ,e9/e9's !ory ( gravitation does n seek at all to give an explanation ( gravitational ph5om5a1 b m]ely describes & correlates ^! ph5om5a 9 comp>atively simple ma!matical language4 ,no m attempt is made to r$uce ! gravitational attraction betwe5 ! e>? & ! sun to simple t]ms ?an 0 made by ,newton4 ,9 ! realm ( quantum ph5om5a x is ( c\rse ! m]e/ commonplace t our old ideas ( me*anics & electrodynamics h fail$1 s t x is a matt] ( ! greate/ conc]n to f9d h[ _m1 or inde$ :e!r any1 elem5ts ( ! old situations c be c>ri$ ov] into ! new4 ,an exam9ation ( _m ( ! s-call$ explanations ( quantum !ory con/itutes at once a ju/ification ( ! def9ition ( explanation giv5 above1 & ( ! /atem5t t 9 quantum ph5om5a we are at an explanatory crisis4 ,= ! endeavor ( all ^! quantum explanations is to f9d 9 e new or m complicat$ situation ! same elem5ts :i* h already be5 met 9 simpl] situations1 & :i* are !re=e relatively m famili>4 ,= example1 _m quantum ph5om5a are made to involve ! emission ( en]gy :5 an electron jumps f "o orbit to ano!r4 ,b always ! elem5ts to :i* r$uction is made are !mselves quantum ph5om5a1 & ^! are /ill s new & unfamili> t we feel an in/9ctive ne$ = explanation 9 o!r t]ms4 ,we seek to und]/& :y ! electron emits :5 x jumps4 ,! explanatory crisis :i* n[ confronts u 9 relativity & quantum ph5om5a is b a repetition ( :at has occurr$ _m "t 9 ! pa/4 ,a simil> crisis confront$ ,prome!us :5 he discov]$ fire1 & ! fir/ man :o obs]v$ a /raw /ick+ to a piece ( rubb$ amb]1 or a susp5d$ lode/one seek+ ! nor? />4 ,e kitt5 is confront$ ) su* a crisis at ! end ( n9e days4 ,:5ev] exp]i5ce takes u into new & unfamili> realms1 we are to be at lea/ prep>$ = a new crisis4 ,n[ :at are we to d 9 su* a crisis8 ,x seems to me t ! only s5sible c\rse is to d exactly :at ! kitt5 does1 namely1 to wait until we h amass$ s mu* exp]i5ce ( ! new k9d t x is p]fectly famili> to u1 & !n to resume ! process ( explanation ) elem5ts f our new exp]i5ce includ$ 9 our li/ ( axioms4 ,n only w obs]vation %[ t ?is is :at is n[ actually be+ done ) respect to quantum & gravitational ph5om5a1 b x is 9 h>mony ) ! entire _s ( our outlook on nature4 ,all our k is 9 t]ms ( exp]i5ce2 we %\ld n expect or desire to erect an explanatory /ructure diff]5t 9 "* f t ( exp]i5ce4 ,our exp]i5ce is f9ite2 on ! conf9es ( ! exp]im5tally atta9able x becomes hazy1 & ! concepts 9 t]ms ( :i* we describe x fuse toge!r & lose indep5d5t mean+4 ,fur!rmore1 at e ext5sion ( our exp]im5tal range we mu/ be prep>$ to f9d1 & z a matt] ( fact we h (t5 f\nd1 t we enc\nt] ph5om5a ( an entirely novel "* = :i* previ\s exp]i5ce has giv5 u no prep>ation4 ,! explanatory /ructure propos$ above has all ^! prop]ties2 x is f9ite1 be+ t]m9at$ by ! edge ( exp]im5t1 ! f9al /ages ( our explanations are hazy 9 t x becomes m & m difficult to di/+ui% elem5ts ( famili> exp]i5ce1 & e n[ & !n we mu/ admit new elem5ts into our explanations4 ,! fir/ /ep 9 resum+ our explanatory progress1 aft] we h be5 confront$ ) su* a crisis1 is to seek = v>i\s sorts ( correlation betwe5 ! elem5ts ( our new exp]i5ce1 9 ! confid5t expectation t ^! elem5ts w ev5tually become s famili> to u t !y may be us$ z ! ultimates ( a new explanation4 ,?is is exactly :at is n[ happ5+ 9 quantum !ory4 ,diametrically oppos$ to ! views above1 !re is ano!r ideal ( ! explanatory process :i* is held by _m physici/s1 & :i* has be5 m5tion$ above z ! ?ird possible way 9 :i* ! explanatory sequ5ce may be t]m9at$1 namely1 ! endeavor to devise beyond ! limit ( pres5t exp]im5t a /ructure built ( elem5ts l "s ( ^? ( our pres5t exp]i5ce1 9 ! action ( :i* we endeavor to f9d ! explanation ( ph5om5a 9 ! pres5t range4 ,n[ a program su* z ?is1 z a s]i\s program = ! f9al correlation ( nature1 is entirely oppos$ to ! _s ( ! consid]ations exp\nd$ "h4 ,!re is no w>rant :atev] 9 exp]i5ce = ! conviction t z we p5etrate deep] & deep] we %all f9d ! elem5ts ( previ\s exp]i5ce repeat$1 al?\gh sometimes we d f9d su* repetitions1 z 9 ! behavior ( gases4 ,yet ?is has be5 ! attitude ( _m em95t physici/s1 = example1 ,f>aday & ,maxwell1 9 seek+ to expla9 di/ant electrical action by ! propagation ?r\gh a m$ium ( a me*anical pu% or pull1 or by ,h]tz1 :o s\ght 9 all ph5om5a ! effect ( conceal$ masses ) ord9>y me*anical in]tia4 ,al?\gh z a g5]al pr9ciple ?is program seems to be absolutely )\t ju/ification1 nev]!less x may be ju/ifi$ if ! specific "* ( ! physical facts seems to indicate a repetition at l[] levels ( elem5ts famili> high] up4 ,h]tz und\bt$ly _h ?is ju/ification1 z did also ,maxwell to a c]ta9 ext5t1 9 ! discov]y t ! g5]al equations ( electrodynamics are ( ! same =m z ! g5]aliz$ ,lagrangean equations ( me*anics4 ,= ,f>aday1 h[ev]1 !re seems no su* ju/ification2 ! urge to ?is sort ( ?+ 9 ,f>aday came f an uncritical acceptance ( 8 own temp]am5tal reactions4 ,f a less s]i\s po9t ( view x may1 h[ev]1 be q ju/ifi$ to make su* a work+ hypo!sis z t 9 ! action ( electrical =ces may be discov]$ ! same elem5ts ) :i* we are famili> 9 ! ev]yday exp]i5ces ( me*anics4 ,= su* a hypo!sis (t5 enables u to make p>tial correlations :i* sugge/ new exp]im5tal te/s1 & ?us gives ! /imulus to an ext5sion ( our exp]im5tal horizon4 ,_m physici/s recognize ! t5tative "* ( su* attempt$ explanations1 b o!rs app>5tly take !m m s]i\sly1 z = example ,"l ,kelv9 9 8 cont9u\s life-long attempts to f9d a me*anical explanation ( all physical ph5om5a4 ,?is quotation f ,kelv9 is illum9at+4 ,i nev] satisfy myself until ,i c make a me*anical model ( a ?+4 ,if ,i c make a me*anical model1 ,i c und]/& x4 ,z long z ,i _c make a me*anical model all ! way ?r\gh1 ,i _c und]/& x4444 ,b ,i want to und]/& light z well z ,i c )\t introduc+ ?+s t we und]/& ev5 less (4 ,s mu* = g5]al consid]ations on ! nature ( explanation4 ,com+ n[ to great] detail1 _m explanations involve :at may be describ$ z a me*anism4 ,x is difficult to *>act]ize exactly :at we mean by me*anism1 b x seems to be associat$ ) an attitude ( m9d t /rives to realize ! ?ird ( ! possibilities m5tion$ above4 ,z a matt] ( fact1 ! me*anism s\ght = is usually ( a p>ticul> type1 9 t ! ultimate elem5ts select$ are me*anical elem5ts4 ,?is po9t ( view is p>ticul>ly *>act]i/ic ( ! ,engli% s*ool ( physici/s4 ,al?\gh me*anism usually implies me*anical elem5ts1 we may %[ by specific examples t we d actually use ! ^w 9 a broad] significance4 ,if1 = example1 we c\ld devise )9 ! core ( an atom a revolv+ sy/em ( electrical *>ges1 act+ on ea* o!r ) ! ord9>y inv]se squ>e =ces ( electro/atics1 su* t e n[ & !n ! sy/em becomes un/able & breaks up1 we %\ld d\btless say t we _h f\nd a me*anism = expla9+ radioactive dis9tegration4 ,h[ev]1 ! =mulation ( a precise def9ition ( me*anism is ( second>y conc]n to u2 we are prim>ily int]e/$ 9 und]/&+ ! attitude ( m9d t feels a me*anism is necess>y4 ,a typical example ( su* an urge to a me*anism is af=d$ by ! gravitational action betwe5 di/ant bodies4 ,to _m m9ds ! concept ( action at a di/ance is absolutely abhorr5t1 n to be tol]at$ = an in/ant4 ,su* an intol]able situation is avoid$ by ! inv5tion ( a m$ium fill+ all space1 :i* transmits a =ce f "o body to ! o!r ?r\gh ! successive action on ea* o!r ( its contigu\s p>ts4 ,or ! dilemma ( action at a di/ance may be avoid$ 9 o!r ways1 z by ,boscovit* 9 ! eighte5? c5tury1 :o1 9 ord] to expla9 gravitation1 fill$ space ) a triply inf9ite horde ( inf9itesimal projectiles4 ,n[ ( c\rse x is a matt] = exp]im5t to decide :e!r any physical reality c be ascrib$ to a m$ium :i* makes gravitation possible by ! action ( its adjac5t p>ts1 b ,i c see no ju/ification :atev] = ! attitude :i* refuses on purely a priori gr\nds to accept action at a di/ance z a possible axiom or ultimate ( explanation4 ,x is difficult to conceive any?+ m sci5tifically bigot$ ?an to po/ulate t all possible exp]i5ce con=ms to ! same type z t ) :i* we are already famili>1 & !re=e to dem& t explanation use only elem5ts famili> 9 ev]yday exp]i5ce4 ,su* an attitude bespeaks an unimag9ativ5ess1 a m5tal obtus5ess & ob/9acy1 :i* might be expect$ to h exhau/$ _! pragmatic ju/ification at a l[] plane ( m5tal activity4 ,al?\gh x w probably be fairly easy to give intellectual ass5t to ! /rictures ( ! la/ p>agraph1 ,i believe _m w discov] 9 !mselves a long+ = me*anical explanation :i* has all ! t5acity ( orig9al s94 ,! discov]y ( su* a desire ne$ n occasion any p>ticul> al>m1 because x is easy to see h[ ! dem& = ?is sort ( explanation has _h its orig9 9 ! enorm\s prepond]ance ( ! me*anical 9 our physical exp]i5ce4 ,b nev]!less1 j z ! old monks /ruggl$ to subdue ! fle%1 s mu/ ! physici/ /ruggle to subdue ?is sometimes ne>ly irresi/ible1 b p]fectly unju/ifiable desire4 ,"o ( ! l>ge purposes ( ?is exposition w be atta9$ if x c>ries ! conviction t ?is long+ is unju/ifiable1 & is wor? mak+ ! ef=t to subdue4 ,! situation ) respect to action at a di/ance is typical ( ! g5]al situation4 ,i believe ! ess5ce ( ! explanatory process is su* t we mu/ be prep>$ to accept z an ultimate = our explanations ! m]e /atem5t ( a correlation betwe5 ph5om5a or situations ) :i* we are suffici5tly famili>4 ,?us1 9 quantum !ory1 !re is no reason :y we %\ld n be will+ to accept z an ultimate ! fundam5tal fact t :5 an electron jumps radiation is emitt$1 provid$ always t we c give indep5d5t mean+ 9 t]ms ( op]ations to ! jump+ ( an electron4 ,if !re is no exp]im5t sugge/+ o!r & int]m$iate ph5om5a1 we ought to be able to re/ intellectually satisfi$ ) ?is4 ,( c\rse x is q a diff]5t matt]1 & entirely ju/ifi$1 to imag9e :at ! assumption ( f9] details 9 ! process w\ld involve exp]im5tally1 & !n to seek = ^! possible new exp]im5tal facts4 ,x is a consequ5ce ( ?is view t any correlation is adapt$ to be an absolutely f9al elem5t ( explanation1 & c nev] be sup]s$$ by ! discov]y ( new exp]im5tal facts1 if ! correlation is by def9ition beyond ! rea* ( fur!r exp]im5t4 ,su* a possibility1 = example1 is conta9$ 9 a correlation betwe5 ! num]ical magnitude ( ! gravitational con/ant & ! total mass ( ! univ]se4 ,some?+ ( ?is sort may be well attempt$ by ^? :o desire _! explanations to take a =mally f9al %ape4 ,we %all return to ?is subject lat]4 ,! in/9ctive dem& = a me*anism is =tifi$ by obs]vation ( ! _m important cases 9 :i* me*anisms h be5 discov]$ or inv5t$4 ,h[ev]1 ! significance ( su* successful attempts mu/ be subject to mo/ c>eful scrut9y4 ,! matt] has be5 discuss$ by ,po9c>1#f :o %[$ t n only is x always possible to f9d a me*ani/ic explanation ( any ph5om5on 7,h]tz's program 0 a p]fectly possible "o71 b !re are always an inf9ite numb] ( su* explanations4 ,?is is v unsatisfactory4 ,footnote #f3 ,h5ri ,po9c>4 ,wiss5s*aft & ,hypo!se1 ,translat$ into ,g]man by ,f4 & ,l4 ,l9demann1 ,teubn]1 ,leipzig1 #aijf4 ,see especially p4 #bag4 ,we want to be able to f9d ! real me*anism4 ,n[ an exam9ation ( specific propos$ me*anisms w %[ t mo/ me*anisms are m complicat$ ?an ! simple physical ph5om5on :i* !y are inv5t$ to expla91 9 t !y h m indep5d5tly v>iable attributes ?an ! ph5om5on has be5 yet prov$ to h4 ,an example is af=d$ by ! me*anical models inv5t$ to facilitate ! /udy ( ! prop]ties ( simple inductive electrical circuits4 ,! great numb] ( su* models :i* h be5 propos$ is suffici5t indication ( _! possible inf9ite numb]4 ,b if ! me*anism has m indep5d5tly v>iable attributes ?an ! orig9al ph5om5on1 x is obvi\s t ! "q is )\t mean+ :e!r ! me*anism is ! real "o or n1 = 9 ! me*anism !re mu/ be simple motions or comb9ations ( motions :i* h no c\nt]p>t 9 features ( ! orig9al ph5om5on z yet discov]$4 ,obvi\sly1 !n1 ! op]ations d n exi/ by :i* we may set up a "o to "o correspond5ce betwe5 ! prop]ties ( ! me*anism & ! natural ph5om5on1 & ! "q ( reality has no mean+4 ,if1 !n1 a me*anism is to be tak5 s]i\sly z actually correspond+ to reality1 we mu/ dem& t x h no m degrees ( fre$om ?an ! orig9al ph5om5on1 & we mu/ also be sure t ! ph5om5on has no undiscov]$ features4 ,physical exp]i5ce %[s t su* conditions are mo/ difficult to meet1 & inde$ ! probability is t !y are impossible4 ,a me*anism ) m indep5d5tly v>iable attributes ?an ! ph5om5on may prove to be a v useful tool ( ?\ght1 & !re=e wor? inv5t+ & /udy+1 b x is to be reg>d$ no m s]i\sly ?an is a mnemonic device1 or any o!r artifice by :i* a man =ces 8 m9d to give him bett] s]vice4 ,!re is ano!r possible program ( explanation1 ! conv]se ( t consid]$ above1 namely1 to expla9 all famili> facts ( ord9>y exp]i5ce 9 t]ms ( less famili> facts f\nd at a deep] level4 ,! mo/ /rik+ example ( ?is is ! rec5t attempt to give a complete electrical explanation ( ! univ]se4 ,! orig9al attempt 0 to expla9 electrical effects 9 me*anical t]ms2 ?is attempt fail$4 ,at ab\t ! same "t ! exi/5ce ( ! electron 0 exp]im5tally e/abli%$1 s t x 0 evid5t t electricity is a v fundam5tal con/itu5t ( matt]4 ,! program ( explanation 0 rev]s$1 & an electrical explanation s\ght = all me*anical ph5om5a1 includ+ 9 p>ticul> me*anical mass4 ,b ?is attempt has also fail$2 we recognize t "p ( mass may be non-electrical 9 "*1 we po/ulate non-electrical =ces inside ! electron1 & fur!r1 we usually po/ulate = electrons & protons ! prop]ty ( imp5etrability1 a prop]ty d]iv$ f exp]i5ce on a high] scale ( magnitude4 ,a program ( ?is g5]al sort is likely to be reg>d$ ) consid]able sympa?y1 & inde$ ! *ances ( success seem mu* great] ?an d ^? ( ! conv]se program1 = 9 our exp]i5ce l>ge scale ph5om5a are m (t5 built up f & analyz$ into small scale ph5om5a ?an ! conv]se4 ,b z a matt] ( pr9ciple we mu/ aga9 recognize t ! only appeal is to exp]im5t1 & t we h to ask j "o "q3 ,is x true1 z a matt] ( fact1 t all l>ge scale ph5om5a c be built up ( elem5ts ( small scale ph5om5a8 ,x seems to me t ! exp]im5tal w>rant = ?is conviction has n yet be5 giv54 ,! failure ( ! attempt$ electrical explanation ( ! univ]se is a case 9 po9t4 ,h[ev]1 ! failure to prove a proposition is no gu>antee t "s "t x may n be prov$1 & _m physici/s are conv9c$ ( ! ultimate feasibility ( ?is program4 ,p]sonally ,i feel t ! l>ge may n always be analyz$ into ! small]2 ! subject w be discuss$ aga94 ,a conviction ( ! significance ( microscopic analysis has _m features 9 common ) ! usual conviction ( ! ultimate simplicity ( nature4 ,! !sis ( simplicity involves 9 addition ! assumption t ! k9ds ( small scale elem5ts are few 9 numb]1 b actually ?is involves no important diff]5ce betwe5 ! two convictions1 because we h se5 t ! elem5ts ( :i* we build our /ructure become few] 9 numb] z we approa* ! limit ( ! exp]im5tally atta9able4 ,we may prop]ly grant to convictions ( ?is sort pragmatic value 9 sugge/+ new correlations & exp]im5ts1 b a recognition ( ! empirical basis ( all physics w n all[ u to g fur!r4 ,,models ,,& ,,con/ructs ,9 discuss+ ! concept ( l5g?1 we c\ld f9d no mean+ 9 que/ions su* z3 ,is space on a scale ( #aj-h cm4 ,euclidean8 ,nev]!less x w seem to _m t !y d atta* a p]fectly def9ite mean+ to a "q ( ?is k9d4 ,( c\rse x mu/ be agre$ t magnitudes ( #aj-h cm4 _c be ?\ght ( 9 t]ms ( imm$iate s5sation4 ,:5 "o ?9ks ( an atom z a ?+ ) any geometrical prop]ties at all1 ,i believe he w f9d t :at he ess5tially does is to imag9e a model1 multiply+ all ! hypo!tical dim5sions by a factor l>ge en\gh to br+ x to a magnitude ( ord9>y exp]i5ce4 ,?is l>ge scale model is giv5 prop]ties correspond+ to ^? ( ! physical ?+4 ,= example1 ! model ( ! atom :i* 0 accept$ 9 ! fall ( #aibe conta9s electrons rotat+ 9 orbits1 & e n[ & !n an electron jumps f "o orbit to ano!r1 & simultane\sly en]gy is radiat$ f ! atom4 ,su* a model is satisfactory if x (f]s ! c\nt]p>t ( all ! ph5om5a ( ! orig9al atom4 ,n[ ,i believe ! only mean+ t any "o c f9d 9 8 /atem5t t ! space ( ! atom is ,euclidean is t he believes t he c con/ruct 9 ,euclidean space a model ) all ! obs]v$ prop]ties ( ! atom4 ,?is possibility may or may n be suffici5t to give real physical significance to ! /atem5t t ! space ( ! atom is ,euclidean4 ,! situation "h is v mu* ! same z x 0 ) respect to me*anisms4 ,! model may h _m m prop]ties ?an correspond to measurable prop]ties ( ! atom1 & 9 p>ticul>1 ! op]ations by :i* ! space ( ! model is te/$ = its ,euclidean "* may & z a matt] ( fact ,i believe d n h any c\nt]p>t 9 op]ations :i* c be c>ri$ out on ! atom4 ,fur!r1 we _c atta* any real significance to ! /atem5t t ! space ( ! atom is ,euclidean unless we c %[ t no model con/ruct$ 9 non-,euclidean space c reproduce ! measurable prop]ties ( ! atom4 ,9 spite ( all ?is1 ,i believe t ! model is a useful & inde$ unescapable tool ( ?\ght1 9 t x enables u to ?9k ab\t ! unfamili> 9 t]ms ( ! famili>4 ,!re are1 h[ev]1 dang]s 9 its use3 x is ! function ( criticism to disclose ^! dang]s1 s t ! tool may be us$ ) confid5ce4 ,closely relat$ to ! m5tal model are m5tal con/ructs1 ( :i* physics is full4 ,!re are _m sorts ( con/ructs3 ^? 9 :i* we are int]e/$ are made by u to enable u to deal ) physical situations :i* we _c directly exp]i5ce ?r\gh our s5ses1 b ) :i* we h contact indirectly & by inf]5ce4 ,su* con/ructs usually involve ! elem5t ( inv5tion to a great] or less degree4 ,a con/ruct conta9+ v little ( inv5tion is t ( ! inside ( an opaque solid body4 ,we c nev] exp]i5ce directly ?r\gh our s5ses ! inside ( su* a solid body1 because ! in/ant we directly exp]i5ce x1 x ceases by def9ition to be ! inside4 ,we h "h a con/ruct1 b s natural a "o z to be practically unavoidable4 ,an example ( a con/ruct involv+ a great] am\nt ( inv5tion is ! /ress 9 an ela/ic body4 ,a /ress is by def9ition a prop]ty ( ! int]ior po9ts ( a body :i* is connect$ ma!matically 9 a simple way ) ! =ces act+ across ! free surface ( ! body4 ,a /ress is !n1 by its v nature1 =ev] beyond ! rea* ( direct exp]i5ce1 & x is !re=e a con/ruct4 ,! entire /ructure ( a /ress corresponds to no?+ 9 direct exp]i5ce2 x is relat$ to =ce1 b is itself a six-fold magnitude1 :]eas a =ce is only ?ree-fold4 ,we h next to ask :e!r ! /ress1 :i* we h inv5t$ to meet ! situation 9 a body expos$ to =ces1 is a good con/ruct4 ,9 ! fir/ place1 a /ress has ! same numb] ( degrees ( fre$om z ! obs]vable ph5om5on1 = x is "o ( ! propositions ( ! ma!matical !ory ( ela/icity t ! b\nd>y conditions1 :i* are ! exp]im5tal v>iables1 uniquely det]m9e ! /ress 9 a giv5 body i4e4 a body ( giv5 ela/ic con/ants2 & ( c\rse x is at once obvi\s1 by an inspection ( ! equations1 t conv]sely a possible /ress sy/em uniquely det]m9es ! b\nd>y conditions to ! significant am\nt4 ,!re is1 !re=e1 a unique "o-to-"o correspond5ce betwe5 a /ress & ! physical situation x 0 made to meet1 & s f> a /ress is a good con/ruct4 ,up to ?is po9t a /ress1 f ! po9t ( view ( ! op]ations 9 t]ms ( :i* x is def9$1 is a purely ma!matical inv5tion1 :i* is ju/ifi$ because x is conv5i5t 9 describ+ ! behavior ( bodies subject$ to ! action ( =ce4 ,b we wi% n[ to g f>!r & ascribe physical reality to a /ress1 mean+ by ?is t a /ress 9 a solid body %all correspond to "s real physical /ate ( ! int]ior po9ts4 ,let u exam9e1 f ! po9t ( view ( op]ations1 :at ! mean+ ( a /atem5t l ?is may be4 ,s9ce we n[ wi% to ascribe an additional physical mean+ to a /ress beyond t ( ! ma!matical op]ations 9 t]ms ( :i* ! /ress 0 det]m9$1 !re mu/ exi/ additional physical op]ations correspond+ to ?is mean+1 or else our /atem5t is mean+less4 ,n[ ( c\rse x is a matt] ( ! mo/ elem5t>y exp]i5ce t physical ph5om5a d exi/ :i* all[ ^! o!r indep5d5t op]ations4 ,a body "u /ress is also 9 a /ate ( /ra91 :i* may be det]m9$ f ! ext]nal de=mations1 or ! /ra9 at int]nal po9ts may be made m vividly real by ^? optical effects ( d\ble refraction 9 transp>5t bodies :i* are n[ s ext5sively us$ 9 model exp]im5ts1 or if ! /ress is pu%$ beyond a c]ta9 po9t1 we h su* new ph5om5a z p]man5t set or f9ally1 rupture4 ,we h1 !n1 e reason to be satisfi$ ) our con/ruct ( /ress4 ,9 ! fir/ place1 f ! =mal po9t ( view1 x is a good con/ruct because !re is a unique correspond5ce betwe5 x & ! physical data 9 t]ms ( :i* x is def9$2 & 9 ! second place we h a "r to ascribe physical reality to x because x is uniquely connect$ ) o!r physical ph5om5a1 indep5d5t ( ^? :i* ent]$ its def9ition4 ,?is la/ requirem5t1 9 fact1 f ! op]ational po9t ( view1 am\nts to no?+ m ?an a def9ition ( :at we mean by ! reality ( ?+s n giv5 directly by exp]i5ce4 ,s9ce n[ 9 addition to satisfy+ ! =mal requirem5ts1 exp]i5ce %[s t a /ress is mo/ useful 9 correlat+ ph5om5a1 we are ju/ifi$ 9 giv+ to ?is con/ruct ( /ress a prom95t place among our concepts4 ,consid] n[ ano!r con/ruct1 "o ( ! mo/ important ( physics1 t ( ! electric field4 ,9 ! fir/ place1 an exam9ation ( ! op]ations by :i* we det]m9e ! electric field at any po9t w %[ t x is a con/ruct1 9 t x is n a direct datum ( exp]i5ce4 ,to det]m9e ! electric field at a po9t1 we place an explor+ *>ge at ! po9t1 measure ! =ce on x1 & !n calculate ! ratio ( ! =ce to ! *>ge4 ,we !n all[ ! explor+ *>ge to become small] & small]1 repeat+ our measurem5t ( =ce on ea* small] *>ge1 & def9e ! limit ( ! ratio ( ! =ce to ! *>ge z ! electric field int5sity at ! po9t 9 "q1 & ! limit+ direction ( ! =ce on a small *>ge z ! direction ( ! field4 ,we may ext5d ?is process to e po9t ( space1 & s obta9 ! concept ( a field ( =ce1 by :i* e po9t ( ! space surr\nd+ electric *>ges is tagg$ ) ! appropriate numb] & direction1 ! explor+ *>ge hav+ completely disappe>$4 ,! field is1 !n1 cle>ly a con/ruct4 ,next1 f ! =mal po9t ( view ( ma!matics1 x is a good con/ruct1 because !re is a "o to "o correspond5ce betwe5 ! electric field & ! electric *>ges 9 t]ms ( :i* x is def9$1 ! field be+ uniquely det]m9$ by ! *>ges1 & conv]sely !re be+ only "o possible set ( *>ges correspond+ to a giv5 field4 ,n[ ne>ly e physici/ takes ! next /ep1 & ascribes physical reality to ! electric field1 9 t he ?9ks t at e po9t ( ! field !re is "s real physical ph5om5on tak+ place :i* is connect$ 9 a way n yet precisely det]m9$ ) ! numb] & direction :i* tag ! po9t4 ,at fir/ ?is view mo/ naturally involv$ z a coroll>y ! exi/5ce ( a m$ium1 b lately x has become ! fa%ion to say t ! m$ium does n exi/1 & t only ! field is real4 ,! reality ( ! field is self-consci\sly inculcat$ 9 our elem5t>y tea*+1 (t5 ) consid]able difficulty = ! /ud5t4 ,?is view is usually cr$it$ to ,f>aday1 & is consid]$ ! mo/ fundam5tal concept ( all mod]n electrical !ory4 ,yet 9 spite ( ?is1 ,i believe t a critical exam9ation w %[ t ! ascription ( physical reality to ! electric field is entirely )\t ju/ification4 ,i _c f9d a s+le physical ph5om5on or a s+le physical op]ation by :i* evid5ce ( ! exi/5ce ( ! field may be obta9$ indep5d5t ( ! op]ations :i* ent]$ ! def9ition4 ,! only physical evid5ce we ev] h ( ! exi/5ce ( a field is obta9$ by go+ !re ) an electric *>ge & obs]v+ ! action on ! *>ge :5 ! *>ges are inside atoms we may h optical ph5om5a1 :i* is precisely ! op]ation ( ! def9ition4 ,x is !n ei!r mean+less to say t a field has physical reality1 or we are guilty ( adopt+ a def9ition ( reality :i* is ! crasse/ tautology4 ,!re c be no "q :atev] ( ! trem5d\s importance ( ! concept ( ! electric field z a tool 9 ?9k+ ab\t1 describ+1 correlat+1 & pr$ict+ ! prop]ties ( electrical sy/ems2 electrical sci5ce is inconceivable )\t ?is or some?+ equival5t4 ,b 9 addition to ?is aspect ( ! field concept1 ! fur!r tacit implication ( physical reality is almo/ always pres5t1 & has _h ! greate/ influ5ce on ! "* ( physical ?\ght & exp]im5t4 ,yet ,i d n believe t ! additional implication ( physical reality has ju/ifi$ itself by br++ to light a s+le positive result1 or c (f] m ?an ! pragmatic plea ( hav+ /imulat$ a l>ge numb] ( exp]im5ts1 all ) p]si/5tly negative results4 ,x is suffici5t to m5tion ! fate ( ! attempt ( ,f>aday & ,maxwell to ascribe a /ress l t ( ord9>y matt] to ! e!r1 :i* fail$ because1 among o!r reasons1 no?+ c exi/ 9 ! e!r analog\s to ! /ra9 ( ord9>y matt]1 to indicate ! unfruitfulness ( ! idea ( physical reality4 ,x seems to me t any pragmatic ju/ification 9 po/ulat+ reality = ! electric field has n[ be5 exhau/$1 & t we h rea*$ a /age :]e we %\ld attempt to get clos] to ! actual facts by ridd+ ! field concept ( ! implications ( reality4 ,ano!r indisp5sable & mo/ int]e/+ con/ruct is t ( ! atom4 ,?is is evid5tly a con/ruct1 because no "o ev] directly exp]i5c$ an atom1 & its exi/5ce is entirely inf]5tial4 ,! atom 0 inv5t$ to expla9 con/ant comb9+ weights 9 *emi/ry4 ,= a long "t !re 0 no o!r exp]im5tal evid5ce ( its exi/5ce1 & x rema9$ a pure inv5tion1 )\t physical reality1 useful 9 discuss+ a c]ta9 gr\p ( ph5om5a4 ,x is "o ( ! mo/ fasc9at+ ?+s 9 physics to trace ! accumulation ( indep5d5t new physical in=mation all po9t+ to ! atom1 until n[ we are z conv9c$ ( its physical reality z ( our h&s & feet4 ,a con/ruct :i* _h to be ab&on$ because x did n turn out to h physical reality1 & :i* fur!rmore 0 n suffici5tly useful 9 ! light ( newly discov]$ ph5om5a1 0 t ( a caloric fluid4 ,! notion ( physical reality is n ( prime importance to ?is discussion ( ! "* ( our con/ructs2 our def9ition ( ! mean+ ( physical reality may n appeal to ev]yone4 ,! ess5tial po9t is t our con/ructs fall into two classes3 ^? to :i* no physical op]ations correspond o!r ?an ^? :i* ent] ! def9ition ( ! con/ruct1 & ^? :i* admit ( o!r op]ations1 or :i* c\ld be def9$ 9 sev]al alt]native ways 9 t]ms ( physically di/9ct op]ations4 ,?is diff]5ce 9 ! "* ( con/ructs may be expect$ to correspond to ess5tial physical diff]5ces1 & ^! physical diff]5ces are mu* too likely to be ov]look$ 9 ! ?9k+ ( physici/s4 ,we mu/ always be on our gu>d n to =get ! physical diff]5ces betwe5 a ?+ l a /ress 9 an ela/ic body & an electromagnetic field4 ,! moral ( all ?is is t con/ructs are mo/ useful & ev5 unavoidable ?+s1 b t !y may h great dang]s1 & t a c>eful critique may be necess>y to avoid read+ into !m implications = :i* !re is no w>rant 9 exp]i5ce1 & :i* may mo/ pr(\ndly affect our physical outlook & c\rse ( action4 ,,! ,r,,le ,,( ,,ma!matics ,,9 ,,physics ,practically all ! =mulations ( !oretical physics are made 9 ma!matical t]ms2 9 fact to obta9 su* =mulations is g5]ally felt to be ! goal ( !oretical physics4 ,x is !n evid5tly p]t95t to consid] :at ! nature ( ! ma!matics is to :i* we assign s prom95t a rle4 ,we h 9 ! fir/ place to und]/& :y x is possible to express physical relations 9 ma!matical language at all4 ,i am n sure t !re is mu* mean+ 9 ?is "q4 ,x is ! m]e/ truism1 evid5t at once to unsophi/icat$ obs]vation1 t ma!matics is a human inv5tion4 ,fur!rmore1 ! ma!matics 9 :i* ! physici/ is int]e/$ 0 develop$ = ! explicit purpose ( describ+ ! behavior ( ! ext]nal _w1 s t x is c]ta9ly no accid5t t !re is a correspond5ce betwe5 ma!matics & nature4 ,! correspond5ce is n by any means p]fect1 h[ev]1 b !re is always 9 ma!matics a precise quality to :i* none ( our in=mation ab\t nature ev] atta9s4 ,! !orems ( ,euclid's geometry illu/rate ?is 9 a preem95t degree4 ,! /atem5t t !re is j "o /raight l9e betwe5 two po9ts & t ?is is ! %orte/ possible pa? betwe5 ! po9ts is entirely diff]5t 9 "* f any in=mation ev] giv5 by physical measurem5t1 = all our measurem5ts are subject to error4 ,x is possible1 nev]!less1 to give a c]ta9 real physical mean+ to ! ideally precise /atem5ts ( geometry1 because x is a result ( ev]yday exp]i5ce t z we ref9e ! accuracy ( our physical measurem5ts ! quantitative /atem5ts ( geometry are v]ifi$ )9 an ev] decreas+ m>g9 ( error4 ,f ?is arises t view ( ! nature ( ma!matics :i* app>5tly is mo/ commonly held2 namely t if we c\ld elim9ate ! imp]fections ( our measurem5ts1 ! relations ( ma!matics w\ld be exactly v]ifi$4 ,ab/ract ma!matical pr9ciples are suppos$ to be active 9 nature1 controll+ natural ph5om5a1 z ,py?agoras long ago tri$ to express ) 8 h>mony ( ! sph]es & ! my/ic relations ( numb]s4 ,?is idealiz$ view ( ! connection ( ma!matics ) nature c\ld be ma9ta9$ only dur+ t hi/orical p]iod :5 ! accuracy ( physical measurem5t 0 l[1 & mu/ n[ be ab&on$4 ,= x is no long] true t ! precise relations ( ,euclid's geometry may be indef9itely approximat$ to by increas+ ! ref9em5ts ( ! measur+ process1 b !re are ess5tial physical limitations to ! v concepts ( l5g?1 etc41 :i* ent] ! geometrical =mulations1 set by ! discrete /ructure ( matt] & ( radiation4 ,?is is no academic matt]1 b t\*es ! ess5ce ( ! situation4 ,!re is no long] any basis = ! idealization ( ma!matics1 & = ! view t our imp]fect k ( nature is responsible = failure to f9d 9 nature ! precise relations ( ma!matics4 ,x is ! ma!matics made by u :i* is imp]fect & n our k ( nature4 ,f ! op]ational po9t ( view x is mean+less to attempt to sep>ate nature f k ( nature4 ,! concepts ( ma!matics are inv5tions made by u 9 ! attempt to describe nature4 ,n[ we %all repeat$ly see t x is ! mo/ difficult ?+ 9 ! _w to inv5t concepts :i* exactly correspond to :at we "k ab\t nature1 & we app>5tly nev] a*ieve success4 ,ma!matics is no exception2 we d\btless come clos] to ! ideal "h ?an any:]e else1 b we h se5 t ev5 ari?metic does n completely reproduce ! physical situation4 ,ma!matics appe>s to fail to correspond exactly to ! physical situation 9 at lea/ two respects4 ,9 ! fir/ place1 !re is ! matt] ( errors ( measurem5t 9 ! range ( ord9>y exp]i5ce4 ,n[ ma!matics c deal ) ?is situation1 al?\gh some:at clumsily1 & only approximately1 by specifically supplem5t+ its equations by /atem5ts ab\t ! limit ( error1 or replac+ equations by inequalities--9 %ort1 ! sort ( ?+ done 9 e discussion ( ! propagation ( error ( measurem5t4 ,9 ! second place1 & mu* m important1 ma!matics does n recognize t z ! physical range increases1 ! fundam5tal concepts become hazy1 & ev5tually cease entirely to h physical mean+1 & !re=e mu/ be replac$ by o!r concepts :i* are op]ationally q diff]5t4 ,= in/ance1 ! equations ( motion make no di/9ction betwe5 ! motion ( a /> into our galaxy f ext]nal space1 & ! motion ( an electron ab\t ! nucleus1 al?\gh physically ! mean+ 9 t]ms ( op]ations ( ! quantities 9 ! equations is entirely diff]5t 9 ! two cases4 ,! /ructure ( our ma!matics is su* t we are almo/ =c$1 :e!r we want to or n1 to talk ab\t ! inside ( an electron1 al?\gh physically we _c assign any mean+ to su* /atem5ts4 ,z at pres5t con/ruct$1 ma!matics rem9ds "o ( ! loquaci\s & n always coh]5t orator1 :o 0 said to be able to set 8 m\? go+ & g (f & leave x4 ,:at we w\ld l is "s developm5t ( ma!matics by :i* ! equations c\ld be made to cease to h mean+ outside ! range ( num]ical magnitude 9 :i* ! physical concepts !mselves h mean+4 ,9 o!r words1 ! problem is to make our equations correspond m closely to ! physical exp]i5ce back ( !m2 x evid5tly ne$s "s sort ( new inv5tion to accompli% ?is4 ,we return lat]1 9 discuss+ ,lor5tz's equations ( electrodynamics1 to ! disadvantages aris+ f ! pres5t undiscrim9at+ "* ( ma!matics4 ,9 ! meantime1 we mu/ recognize t !re are v important advantages "h1 z well z disadvantages4 ,all exp]i5ce ju/ifies ! expectation t ! laws ( nature ) :i* we are already famili> hold at lea/ approximately & )\t viol5t *ange 9 ! unexplor$ regions imm$iately beyond our pres5t rea*4 ,by assum+ an unlimit$ validity = ! laws z we n[ "k !m1 ma!matics enables u to p5etrate ! twilight zone1 & make pr$ictions :i* may be lat] v]ifi$4 ,x is only :5 we are c>ri$ too f> afield t we mu/ deprecate ?is *>act]i/ic ( our ma!matics4 ,!re is ano!r aspect ( ! use ( ma!matics 9 describ+ nature t is (t5 lo/ sight (2 namely1 t any sy/em ( equations c conta9 only a v small "p ( ! actual physical situation2 !re is beh9d ! equations an enorm\s descriptive backgr\nd ?r\gh :i* ! equations make connection ) nature4 ,?is backgr\nd includes a description ( all ! physical op]ations by :i* ! data are obta9$ :i* ent] ! equations4 ,= in/ance1 :5 ,e9/e9 =mulates ! behavior ( ! univ]se 9 t]ms ( ! _w l9es ( ev5ts1 ! ev5ts z !y ent] ! equations are entirely colorless ?+s1 m]ely #c space & #a "t cord9ate4 ,to make connection ) exp]i5ce !re mu/ be a descriptive backgr\nd giv+ ! physical cont5ts ( ! ev5ts2 = example1 !re may be ! /atem5t t "s ( ! ev5ts are light signals4 ,?is descriptive backgr\nd is suppos$ to rema9 fix$1 unaffect$ by any op]ations to :i* ! equations !mselves are subject4 ,if1 = example1 ! frame ( ref]5ce ( ! equations is alt]$ by *ang+ its velocity1 ! physical significance ( ! descriptive backgr\nd is suppos$ to rema9 unalt]$1 or r no m5tion is usually made ( ?is "q at all4 ,x w\ld seem1 h[ev]1 t ?is matt] ne$s "s discussion4 ,! descriptive backgr\nd gets its mean+ only 9 t]ms ( c]ta9 physical op]ations4 ,if ! descriptive backgr\nd rema9s unalt]$ :5 ! uni=m velocity ( ! frame ( ref]5ce is *ang$1 = in/ance1 ?is means t ! motion ( ! frame ( ref]5ce does n at all affect ! possibility ( c>ry+ out c]ta9 op]ations4 ,?is is pretty close to ! re/rict$ pr9ciple ( relativity itself1 :i* /ates t ! =m ( natural laws is n affect$ by uni=m velocity4 ,until a m c>eful analysis ( ! situation is made x w\ld seem !re=e t !re is "s gr\nd = ! suspicion t ! pr9ciple ( relativity is involv$ 9 ! possibility ( giv+ to physical ph5om5a a complete ma!matical =mulation1 und]/&+ complete to mean includ+ ! descriptive backgr\nd4 ,,*apt] ,,iii ,,detail$ ,,consid]ation ,,( ,,v>i\s ,,concepts ,,( ,,physics ,,we n[ beg9 our detail$ consid]ation ( ! mo/ important concepts ( physics4 ,x is entirely beyond ! scope ( ?is essay to attempt m ?an an indication ( "s ( ! mo/ important matt]s4 ,nei!r is x to be expect$ t ! p>ts ( ?is discussion w always h a v close connection ) ea* o!r2 ! purpose ( ! discussion is to aid 9 acquir+ ! greate/ possible self-consci\sness ( ! :ole /ructure ( physics4 ,,! ,,concept ,,( ,,space ,a logically satisfy+ def9ition ( :at we und]/& by ! concept ( space is d\btless difficult to give1 b we %all n be f> f ! m>k if we ?9k ( x z ! aggregate ( all ^? concepts :i* h to d ) position4 ,position means position ( some?+4 ,! position ( ?+s is det]m9$ by "s sy/em ( measurem5t2 p]haps ! simple/ is t impli$ 9 a ,c>tesian cord9ate sy/em ) its ?ree measurem5ts ( l5g?4 ,h5ce mu* ( ! ess5tial discussion ( space has already be5 giv5 9 connection ) ! concept ( l5g?4 ,we h se5 t measurem5ts ( l5g? are made ) physical measur+ rods appli$ to "s physical object4 ,we _c measure ! di/ance betwe5 two po9ts 9 empty space1 because if space 7 empty !re w\ld be no?+ to id5tify ! position ( ! ends ( ! measur+ rod :5 we move x f "o position to ! next4 ,we see1 !n1 f ! po9t ( view ( op]ations t ! framework ( ,c>tesian geometry1 (t5 imag9$ 9 an ideal ma!matical s5se1 is really a physical framework1 & t :at we mean by spatial prop]ties is no?+ b ! prop]ties ( ?is framework4 ,:5 we say t space is ,euclidean1 we mean t ! physical space ( met] /icks is ,euclidean3 x is mean+less to ask :e!r empty space is ,euclidean4 ,geometry1 !re=e1 9 s f> z its results are expect$ to apply to ! ext]nal physical _w1 & 9 z f> z x is n a logical sy/em built up f po/ulates1 is an exp]im5tal sci5ce4 ,?is view is n[ well und]/ood & accept$1 b !re 0 a "t :5 x 0 n accept$1 b vigor\sly attack$2 ! *ange ( attitude t[>d ?is "q is symptomatic ( a *ange ( attitude t[>d _m o!r simil> que/ions4 ,we h already emphasiz$ t ! space ( a/ronomy is n a physical space ( met] /icks1 b is a space ( light waves4 ,we may1 !re=e1 h diff]5t k9ds ( space1 dep5d+ on ! fundam5tal op]ations4 ,! space ( met] /icks we h call$ tactual space1 & ! space ( light beams optical space4 ,if we ask :e!r a/ronomical space is ,euclidean1 we mean m]ely to ask :e!r ^? features ( optical space :i* are )9 ! rea* ( a/ronomical measurem5t are ,euclidean4 ,! only possible attitude ) respect to ?is "q1 or su* relat$ que/ions z :e!r ! total volume ( space is f9ite1 or :e!r space has curvature1 is t x is entirely = exp]im5t to decide1 & t we h no "r to =m any preconceiv$ notion :atev]4 ,x is !re=e beyond ! scope ( ?is discussion4 ,x is int]e/+ to notice t ! re/rict$ !ory ( relativity virtually assumes1 al?\gh (t5 )\t mak+ ! explicit /atem5t1 t tactual & optical space are ! same4 ,?is equival5ce results f ! prop]ties assum$ = light beams4 ,! di/ance ( a mirror may be f\nd equally well by measur+ x ) met] /icks1 or by det]m9+ ! "t requir$ by a light signal to travel !re & back4 ,?is situation is1 h[ev]1 logically unsatisfy+1 because x mu/ be assum$ t ! op]ations = measur+ "t are indep5d5tly def9$1 & we %all see t !y are n4 ,x is a consequ5ce ( ! assum$ equival5ce ( tactual & optical space t ! pa? ( a beam ( light is a /raight l9e1 z a /raight l9e is det]m9$ by op]ations ) met] /icks4 ,:5 we come to a/ronomical ph5om5a1 ! physical op]ations ) met] /icks c no long] be c>ri$ out1 & x is mean+less to ascribe to beams ( light on an a/ronomical scale ! same geometrical prop]ties t we d on a small scale4 ,,! ,,concept ,,( ,,"t ,accord+ to our viewpo9t1 ! concept ( "t is det]m9$ by ! op]ations by :i* x is measur$4 ,we h to di/+ui% two sorts ( "t2 ! "t ( ev5ts tak+ place ne> ea* o!r 9 space1 or local "t1 & ! "t ( ev5ts tak+ place at consid]ably sep>at$ po9ts 9 space1 or ext5d$ "t4 ,z we n[ "k1 ! concept ( ext5d$ "t is inextricably mix$ up ) t ( space4 ,?is is n prim>ily a /atem5t ab\t nature at all1 & might h be5 made simply by ! obs]vation t ! op]ations by :i* ext5d$ "t is measur$ involve ^? = measur+ space4 ,( c\rse hi/orically ! doctr9e ( relativity 0 responsible = ! critical attitude :i* l$ to an exam9ation ( ! op]ations ( measur+ "t1 b relativity 0 n necess>y = a realization ( ! spatial implications ( "t1 any m ?an ! discov]y ( ,planck's quantum unit h 0 necess>y = ! inv5tion by ,planck ( 8 absolute units ( measurem5t1 al?\gh hi/orically he 0 inspir$ to make ?is inv5tion by discov]+ h1 & 9 8 own m9d seems to h ?\ght ( ! connection z a necess>y "o4#g ,footnote #g3 ,max ,planck1 ,! ,!ory ( ,heat ,radiation1 translat$ by ,masius1 ,p4 ,blaki/on's ,son ,co41 #aiad edition1 p4 #agd4 ,! physical op]ations at ! basis ( ! measurem5t ( "t h nev] be5 subject$ to ! critical exam9ation :i* seems to be requir$4 ,"o me?od ( measurem5t1 = in/ance1 involves ! prop]ties ( light4 ,a met] /ick is set up ) mirrors at ! two ends1 & a light beam travels back & =? betwe5 ! two mirrors )\t absorption4 ,! "t requir$ = a s+le passage back & =? is def9$ z ! unit ( "t1 & "t is measur$ simply by c\nt+ ^! int]vals4 ,b su* a proc$ure is unsatisfactory if we are to p]mit ourselves all ^? op]ations :i* are dem&$ by ev5 ! simple/ po/ulate ( relativity1 = we mu/ be able to move our clock f place to place1 transf] x f "o sy/em to ano!r 9 relative motion1 & ) x det]m9e ! prop]ties ( light beams 9 ! /ation>y or mov+ sy/em4 ,we recognize 9 pr9ciple t ! l5g? ( ! met] /ick may be diff]5t :5 x is 9 motion1 t x may *ange also dur+ ! accel]ation incid5t to mov+ x f "o place to ano!r1 & t until prov$ to ! contr>y ! velocity ( light may be a function ( velocity or accel]ation4 ,! complicat$ int]play ( all ^! possibilities leaves u 9 mu* d\bt z to ! physical significance ( su* po/ulates z1 = example1 t ! velocity ( light is ! same 9 ! mov+ sy/em & ! /ation>y sy/em4 ,9 ord] to ascribe any simple significance to po/ulates ab\t ! velocity ( light1 x w\ld seem t we mu/ h an in/rum5t = measur+ ?is velocity1 & !re=e = measur+ "t1 :i* does n itself involve ! prop]ties ( light4 ,to d ?is we might seek to specify ! measurem5t ( "t 9 purely me*anical t]ms1 z = in/ance 9 t]ms ( ! vibration ( a tun+ =k1 or ! rotation ( a fly:eel4 ,b "h aga9 we enc\nt] great difficulties1 because we recognize t ! dim5sions ( our me*anical clock may *ange :5 x is set 9 motion1 & t ! mass ( its p>ts may also *ange4 ,we want to use ! clock z a physical in/rum5t 9 det]m9+ ! laws ( me*anics1 :i* ( c\rse are n det]m9$ until we c measure "t1 & we f9d t ! laws ( me*anics ent] into ! op]ation ( ! clock4 ,! dilemma :i* confronts u "h is n an impossible "o1 & is 9 fact ( ! same nature z t :i* confront$ ! fir/ physici/ :o _h to discov] simultane\sly ! approximate laws ( me*anics & geometry ) a /r+ :i* /ret*$ :5 he pull$ x4 ,we mu/ fir/ guess at :at ! laws are approximately1 !n design an exp]im5t s t1 9 accordance ) ?is guess1 ! effect ( motion on "s ph5om5on is mu* great] ?an ! expect$ effect on ! clock1 !n f measurem5ts ) uncorrect$ clock "t f9d an approximate expression = ! effect ( motion on mass or l5g?1 ) :i* we correct ! clock1 & s on ad inf9itum4 ,h[ev]1 s f> z ,i "k1 ! possibility ( su* a proc$ure has n be5 analyz$1 & until ! analysis is giv51 our complac5cy is tr\bl$ by a real disquietude1 ! int5sity ( :i* dep5ds on ! natural skepticism ( our temp]am5t4 ,9 practice1 ! difficulties ( su* a logical treatm5t are s great t ! matt] has be5 entirely gloss$ ov]4 ,x is conv5i5t to po/ulate a clock1 ( unkn[n con/ruction1 b su* t ! velocity ( light1 :5 measur$ 9 t]ms ( x1 has c]ta9 prop]ties4 ,su*1 = example1 is ! po9t ( view 9 ,birkh(f's rec5t book4#h ,footnote #h3 ,g4 ,d4 ,birkh(f4 ,relativity & ,mod]n ,physics1 ,h>v>d ,univ]sity ,press1 #aibc4 ,! difficulty ) ?is me?od is t ! result+ edifice is z divorc$ f physical reality z is ! logical geometry ( po/ulates4 ,we _c be at all sure t ! prop]ties ( light z measur$ ) our physical clocks are ! same z ! !oretical prop]ties4 ,! difficulty is p>ticul>ly important & fundam5tal 9 ! g5]al !ory ( relativity2 ! basis ( ! :ole !ory is ! inf9itesimal int]val ds1 :i* is suppos$ to be giv54 ,once giv51 ! ma!matics foll[s4 ,b 9 a physical _w1 ds is n giv51 b mu/ be f\nd by physical op]ations1 & ^! op]ations involve measurem5ts ( l5g? & ( "t ) clocks ^: con/ruction is n specifi$4 ,9 any actual physical application ! "q mu/ be answ]$ :e!r ! physical in/rum5t us$ 9 measur+ ! temporal "p ( ds is really a clock or n4 ,!re is at pres5t no crit]ion by :i* ?is "q c be answ]$4 ,if ! vibrat+ atom is a clock1 !n ! light ( ! sun is %ift$ t[>d ! infra-r$1 b h[ d we "k t ! atom is a clock 7"s say yes1 o!rs no78 ,if we f9d ! displacem5t physically h we !reby prov$ t g5]al relativity is physically true1 or h we prov$ t ! atom is a clock1 or h we m]ely prov$ t !re is a p>ticul> k9d ( connection betwe5 ! atom & ! re/ ( nature1 leav+ ! possibility op5 t nei!r is ! atom a clock nor g5]al relativity true8 ,9 practice1 ( c\rse1 we %all adopt ! solution :i* is simple/ & mo/ satisfy+ ae/hetically1 & d\btless %all say t ! atom is a clock & relativity true4 ,b if we adopt ?is simple view1 we mu/ also cultivate ! abid+ consci\sness t at "s "t 9 ! future tr\bles may h _! orig9 "h4 ,x seems to me t ! logical position ( g5]al relativity !ory is m]ely ?is3 ,giv5 any physical sy/em1 !n x is possible to assign values to ds su* t relations ma!matically d$uc$ by ! pr9ciple ( relativity correspond to relations betwe5 measurable quantities 9 ! physical sy/em2 b t ! ?+s t we physically call ds are any?+ m ?an approximately connect$ ) ! ds's requir$ to give ! ma!matical relations1 is at pres5t no m ?an a pi\s fai?4 ,to return to ! concept ( "t1 we h already /at$ t !re are two ma9 problems1 t ( measur+ "t at a s+le po9t ( space1 & t ( spread+ a "t sy/em ov] all space4 ,! second aspect ( ! problem is t to :i* att5tion has be5 direct$ by relativity !ory2 ! foll[+ detail$ exam9ation %[s h[ ! op]ations ( relativity = sett+ & syn*roniz+ clocks at di/ant places involve ! measurem5t ( space4 ,x is a fundam5tal po/ulate t ! adju/m5t ( ! clocks is to be accompli%$ by light signals4 ,! syn*ronization ( ! clocks is n[ simple en\gh4 ,we m]ely dem& t light signals s5t f ! ma/] clock at int]vals ( "o second arrive at any di/ant clock at int]vals ( "o second z measur$ by x1 & we *ange ! rate ( ! di/ant clock until x measures ^! int]vals z "o second4 ,aft] its rate has be5 adju/$1 ! di/ant clock is to be s set t :5 a light signal is despat*$ f ! ma/] clock at its indicat$ z]o ( "t ! "t ( arrival record$ at ! di/ant clock %all be su* t ! di/ance ( ! clock f ! ma/] clock divid$ by ! "t ( arrival %all give ! velocity ( light1 assum$ already kn[n4 ,?is op]ation involves a measurem5t ( ! di/ance ( ! di/ant clock1 s t 9 spread+ ! "t coord9ates ov] space ! measurem5t ( space is involv$ by def9ition1 & ! measurem5t ( "t is1 !re=e1 n a self-conta9$ ?+4 ,?is is ! physical basis = ! treatm5t ( space & "t z a f\r-dim5sional manifold4 ,al?\gh ma!matically ! numb]s measur+ space & "t ent] ! =mulas symmetrically1 nev]!less ! physical op]ations by :i* ^! numb]s are obta9$ are entirely di/9ct & nev] fuse1 & ,i believe x c lead only to confusion to see 9 ! possibility ( a f\r dim5sional treatm5t any?+ m ?an a purely =mal matt]4 ,! notion ( ext5d$ "t1 !re=e1 involves ! measurem5t ( space4 ,x is an int]e/+ "q :e!r ! notion ( local "t also involves ! measurem5t ( space4 ,a rigor\s answ] to ?is "q involves giv+ ! specifications = ! con/ruction ( a clock1 :i* we h se5 has n yet be5 done4 ,x seems to me probable1 h[ev]1 t ! con/ruction ( ev5 a s+le local clock involves 9 "s way ! measurem5t ( space4 ,if1 = example1 we use a vibrat+ tun+ =k1 we mu/ f9d h[ ! "t ( vibration dep5ds on ! amplitude ( vibration1 & ?is involves space measurem5t1 or if we use a rotat+ fly:eel1 we h to correct = ! *ange ( mom5t ( in]tia due to ! *ange ( dim5sions :5 x is set into motion or br\ght into a gravitational field1 & all ?is involves space measurem5t4 ,h[ev]1 ^! consid]ations are n c]ta91 & p]haps ! "q is n important4 ,!re is n[ ! fur!r consid]ation t actually 9 practice ! concept ( local "t is n entirely divorc$ f t ( ext5d$ "t1 = two bodies _c occupy ! same space at ! same "t1 & ! "t ( any ev5t is actually measur$ on an in/rum5t at "s di/ance1 communication be+ ma9ta9$ by light or ela/ic signals4 ,b exp]i5ce conv9ces u t 9 ! limit1 z ! ph5om5on to be measur$ gets clos] to ! clock1 !re is no measurable diff]5ce1 :e!r communication ) ! clock is ma9ta9$ by light1 or ac\/ical or tactual signals1 s t we h come 9 physical practice to accept measurem5t ( ! "t ( ev5ts 9 ! imm$iate neighborhood ( ! clock 7local "t7 z "o ( ! ultimately simple ?+s beh9d :i* we d n attempt to g4 ,local "t is1 !re=e1 a concept treat$ by ! physici/ ev5 n[ z simple & unanalyzable4 ,?is concept is :at mo/ p h 9 m9d :5 !y ?9k ( "t4 ,"t1 accord+ to ?is concept1 is some?+ ) ! prop]ties ( local "t2 x 0 some?+ ( ?is k9d t ,newton mu/ h meant by 8 absolute "t1 & x is ! tacit ret5tion ( ?is sort ( concept t is responsible = ! difficulty s (t5 f\nd 9 grasp+ ! idea ( ! relativity ( simultaneity1 :i* is ( c\rse entirely =eign to our exp]i5ce ( simultaneity 9 local "t4 ,an exam9ation ( ! op]ations involv$ 9 ext5d+ "t has %[n h[ ! concept ( ext5d$ "t is diff]5t f t ( simple local "t2 ?is diff]5ce leads to appreciably diff]5t num]ical relations :5 we are deal+ ) high velocities or great di/ances4 ,local "t is prov$ by exp]i5ce n to be a satisfactory concept = deal+ ) ev5ts sep>at$ by great di/ances 9 space or ) ph5om5a involv+ high velocities4 ,= in/ance1 we mu/ n talk ab\t ! age ( a beam ( light1 al?\gh ! concept ( age is "o ( ! simple/ d]ivatives ( ! concept ( local "t4 ,nei!r mu/ we all[ ourselves to ?9k ( ev5ts tak+ place 9 ,arcturus n[ ) all ! connotations atta*$ to ev5ts tak+ place "h n[4 ,x is difficult to inhibit ?is habit ( ?\ght1 b we mu/ le>n to d x4 ,! nave feel+ is v /rong t x does mean some?+ to talk ab\t ! entire pres5t /ate ( ! univ]se indep5d5t ( ! process by :i* news ( ! condition ( di/ant p>ts is det]m9$ by u4 ,i believe t an exam9ation ( ?is feel+ w %[ t x is psy*ological 9 "*2 :at we mean by ! totality ( ! pres5t is m]ely ! entire pres5t cont5t ( our consci\sness4 ,?is is app>5tly a simple direct ?+2 we d n appreciate until we make fur!r analysis t our pres5t consci\sness ( ! exi/5ce ( ! moon or a /> is due to light signals1 & t !re=e ! app>5tly simple imm$iate consci\sness ( ev5ts di/ant 9 space involves complicat$ physical op]ations4 ,simil>ly1 if we cont9ue to use local "t1 we get into tr\ble1 :5 we g to high velocities1 ) our simple concept ( velocity1 :i* may be def9$ 9 t]ms ( a comb9ation ( space & "t concepts4 ,! concept ( local "t ?us loses its value & becomes m]ely a blunt$ tool :5 we try to c>ry x out ( its orig9al range4 ,b ! concept ( ext5d$ "t1 ) :i* we h to replace local "t1 is a complicat$ ?+1 to :i* we h n yet got ourselves accu/om$2 x may p]haps prove to be s complicat$ z nev] to be a v useful intuitive tool ( ?\ght4 ,all ^! consid]ations ab\t "t h be5 conc]n$ only ) int]vals ( su* an ord] ( magnitude t !y are readily exp]i5c$ by any individual4 ,if we h to deal ) int]vals ei!r v long or v %ort1 x is obvi\s t our entire proc$ure *anges1 & consequ5tly ! concept *anges4 ,9 ext5d+ ! "t concept to eras remote 9 ! pa/1 = example1 we try z always1 to *oose ! new op]ations s z to piece on cont9u\sly ) ^? ( ord9>y exp]i5ce4 ,a precise analysis ( ! *ange 9 ! concept ( "t :5 appli$ to ! remote pa/ does n seem to be ( great significance = our pres5t physical purpose1 & w n be attempt$ "h4 ,x is p]haps wor? :ile to po9t out1 h[ev]1 t all our o!r concepts1 z well z t ( "t1 mu/ be modifi$ :5 appli$ to ! remote pa/2 an example is ! concept ( tru?4 ,x is amus+ to try to discov] :at is ! precise mean+ 9 t]ms ( op]ations ( a /atem5t l ?is3 ,x is true t ,d>ius ! ,m$e arose at #f3cj on ! morn+ ( 8 ?irtie? bir?day4 ,( m conc]n = our physical purposes is ! modification :i* ! "t concept und]goes :5 appli$ to v %ort int]vals4 ,:at is ! mean+1 = example1 9 say+ t an electron :5 collid+ ) a c]ta9 atom is br\ght to re/ 9 #aj-ah seconds8 ,"h ,i believe ! situation is v simil> to t ) reg>d to %ort l5g?s4 ,! nature ( ! physical op]ations *anges entirely1 & z be=e1 comes to conta9 op]ations ( an electrical & optical "*4 ,! imm$iate significance ( #aj-ah is t ( a numb]1 :i* :5 sub/itut$ into ! equations ( optics1 produces agreem5t ) obs]v$ facts4 ,?us %ort int]vals ( "t acquire mean+ only 9 connection ) ! equations ( electrodynamics1 ^: validity is d\btful & :i* c be te/$ only 9 t]ms ( ! space & "t coord9ates :i* ent] !m4 ,"h is ! same vici\s circle t we f\nd be=e4 ,once aga9 we f9d t concepts fuse toge!r on ! limit ( ! exp]im5tally atta9able4 ,?is discussion ( ! concept ( "t w d\btless be felt by "s to be sup]ficial 9 t x makes no m5tion ( ! prop]ties ( ! physical "t to :i* ! concept is design$ to apply4 ,= in/ance1 we d n discuss ! "o dim5sional fl[ ( "t1 or ! irrevocability ( ! pa/4 ,su* a discussion1 h[ev]1 is beyond our pres5t purpose1 & w\ld take u deep] ?an ,i feel compet5t to g1 & p]haps beyond ! v]ge ( mean+ itself4 ,our discussion "h is f ! po9t ( view ( op]ations3 we assume ! op]ations to be giv51 & d n attempt to ask :y precisely ^! op]ations 7 *os51 or :e!r o!rs might n be m suitable4 ,su* prop]ties ( "t z its irrevocability are implicitly conta9$ 9 ! op]ations !mselves1 & ! physical ess5ce ( "t is buri$ 9 t long physical exp]i5ce t taught u :at op]ations are adapt$ to describ+ & correlat+ nature4 ,we may digress1 h[ev]1 to consid] "o "q4 ,x is q common to talk ab\t a rev]sal ( ! direction ( fl[ ( "t4 ,p>ticul>ly1 = example1 9 discuss+ ! equations ( me*anics1 x is %[n t if ! direction ( fl[ ( "t is rev]s$1 ! :ole hi/ory ( ! sy/em is retrac$4 ,! /atem5t is sometimes add$ t su* a rev]sal is actually impossible1 because x is "o ( ! prop]ties ( physical "t to fl[ always =w>d4 ,if ?is la/ /atem5t is subject$ to an op]ational analysis1 ,i believe t x w be f\nd n to be a /atem5t ab\t nature at all1 b m]ely a /atem5t ab\t op]ations4 ,x is mean+less to talk ab\t "t mov+ backw>d3 by def9ition1 =w>d is ! direction 9 :i* "t fl[s4 ,,! ,,causality ,,concept ,! causality concept is unque/ionably "o ( ! mo/ fundam5tal1 p]haps z fundam5tal z t ( space & "t1 & !re=e at lea/ equally entitl$ to a fir/ place 9 ! discussion4 ,b z ord9>ily und]/ood1 !re are c]ta9 spatial & temporal implications 9 ! causality concept1 s t x c be/ be discuss$ 9 ?is ord] aft] our exam9ation ( space & "t4 ,!re is an aspect ( ! causality concept t 9 _m respects is closely relat$ to ! "q ( explanation1 = to f9d ! causes ( an ev5t usually involves at ! same "t f9d+ its explanation4 ,b !re are nev]!less suffici5t diff]5ces to w>rant a sep>ate discussion4 ,x seems fairly evid5t t !re 0 orig9ally 9 ! causality concept an animi/ic elem5t mu* l t 9 ! concept ( =ce to be discuss$ lat]4 ,! physical ess5ce ( ! concept z we n[ h x1 fre$ z mu* z possible f ! animi/ic elem5t1 seems to be some:at z foll[s4 ,we assume 9 ! fir/ place an isolat$ sy/em on :i* we c p]=m unlimit$ id5tical exp]im5ts1 t is1 ! sy/em may be />t$ ov] aga9 f a def9ite initial condition z (t5 z desir$4#i ,footnote #i3 ,we mu/ include 9 g5]al 9 ! concept ( initial condition ! pa/ hi/ory ( ! sy/em4 ,9 ord] n to make ?is condition s broad z to defeat itself1 we h to add ! obs]vation t actually id5tity ( pa/ hi/ory is necess>y ov] only a comp>atively %ort int]val ( "t4 ,logical precision seems unatta9able "h--! physical concepts !mselves h n ! necess>y precision4 ,we assume fur!r t :5 s />t$1 ! sy/em always runs ?r\gh exactly ! same sequ5ce ( ev5ts 9 all its p>ts4 ,?is conta9s ! assumption t ! c\rse ( ev5ts runs indep5d5t ( ! absolute "t at :i* !y occur--!re is no *ange ) "t ( ! prop]ties ( ! univ]se4#aj ,x is a result ( exp]i5ce t sy/ems ) ^! prop]ties actually exi/4 ,an alt]native way ( /at+ our fundam5tal hypo!sis is t two or m isolat$ simil> sy/ems />t$ f ! same initial condition run ?r\gh ! same future c\rse ( ev5ts4 ,^u ! sy/em giv5 9 ?is way1 :i* by itself runs a def9ite c\rse ( ev5ts1 we assume t we c sup]pose f ! outside c]ta9 *anges1 :i* h no connection ) ! previ\s hi/ory ( ! sy/em1 & are completely arbitr>y4 ,n[ ( c\rse 9 nature1 z we obs]ve x1 !re is no su* ?+ z an arbitr>y *ange1 )\t connection ) pa/ hi/ory1 s t /rictly our assumption is a pure fiction4 ,x is "h t ! animi/ic elem5t /ill seems to p]si/1 al?\gh p]haps n necess>ily4 ,footnote #aj3 ,z s (t5 9 physics1 we appe> to be do+ two ?+s at once "h4 ,x is d\btful :e!r we c give a mean+ to def9ite initial condition ap>t f ! future behavior ( ! sy/em1 s t we h no real "r to inf] f uni=m future behavior bo? a con/ancy ( ! laws ( nature1 indep5d5t ( "t1 & a con/ancy ( initial condition4 ,i v mu* "q :e!r a ?or\ghgo+ op]ational analysis w\ld %[ t !re are really two indep5d5t concepts "h1 & :e!r ! use ( two =mally q diff]5t concepts is any?+ m ?an a conv5i5ce 9 expression4 ,x seems to me t x may be j z mean+less to ask :e!r ! laws ( nature are indep5d5t ( "t z x 0 to ask ) ,clif=d :e!r ! absolute scale ( magnitude may n be *ang+ z ! sol> sy/em travels ?r\gh space4 ,we reg>d our acts z n det]m9$ by ! ext]nal _w1 s t *anges produc$ 9 ! ext]nal _w by acts ( our wills are1 to a c]ta9 degree ( approximation1 arbitr>y4 ,! sy/em1 !n1 on :i* we are exp]im5t+1 is "o capable ( isolation f u 9 t we may reg>d ourselves z outside ! sy/em1 & hav+ no connection ) x4 ,! sy/em1 fur!rmore1 is capable ( isolation f ! re/ ( ! physical univ]se1 9 t ev5ts tak+ place outside ! sy/em h no connection ) ^? tak+ place inside4#aa ,exp]i5ce gives ! ju/ification = assum+ t physical isolation ( ?is sort is possible4 ,actually1 ( c\rse1 isolation is nev] complete1 b only p>tial1 up to presumably any desir$ degree ( approximation4 ,footnote #aa3 ,"h aga91 ! concept ( isolation or connection is def9$ only 9 t]ms ( ! behavior ( ! sy/em1 & x is n cle> :e!r ?is is really an op]ationally indep5d5t concept or n4 ,! /atem5t t two exactly simil> isolat$ sy/ems1 />t+ f ! same initial conditions 7includ+ pa/ hi/ory 9 ! g5]al idea ( initial condition7 w run ?r\gh ! same future c\rse ( ev5ts involves z a coroll>y t if diff]5ces develop 9 ! behavior ( two su* app>5tly simil> sy/ems ^! diff]5ces are evid5ce ( o!r previ\s diff]5ces4 ,! !sis t ?is corresponds to exp]i5ce may be call$ ! !sis ( ess5tial connectivity & is p]haps ! broade/ we h3 x is ! !sis t diff]5ces betwe5 ! behavior ( sy/ems d n occur isolat$ b are associat$ ) o!r diff]5ces4 ,x is ess5tially ! same !sis z t already m5tion$ 9 connection ) explanation1 namely t x is possible to correlate any ( ! ph5om5a ( nature ) o!r ph5om5a4 ,if n[ ! connectivity or correlation betwe5 ph5om5a is ( a special k9d1 we h a causal connection2 namely1 if :5ev] we arbitr>ily impress ev5t ,a on a sy/em we f9d t ev5t ,b1 always occurs1 :]eas if we _h n impress$ ,a1 ,b w\ld n h occurr$1 !n we say t ,a is ! cause ( ,b1 & ,b ! effect ( ,a4 ,by suitably *oos+ ! ev5t ,a1 we may f9d ! effect ( any ev5t ( :i* ! sy/em is susceptible4 ,! relation betwe5 ,a & ,b is an unsymmetrical "o1 by ! v nature ( ! def9ition1 ! cause be+ ! arbitr>y v>iable elem5t1 & ! effect t :i* accompanies x4 ,fur!rmore1 ,a may obvi\sly be ! cause ( m ?an "o ev5t ,b1 & may cause a :ole tra9 ( ev5ts4 ,! causal concept analyz$ 9 ?is way is n simple by any means4 ,we d n h a simple ev5t ,a causally connect$ ) a simple ev5t ,b1 b ! :ole backgr\nd ( ! sy/em 9 :i* ! ev5ts occur is includ$ 9 ! concept1 & is a vital "p ( x4 ,if ! sy/em1 includ+ its pa/ hi/ory1 7 diff]5t1 ! nature ( ! relation betwe5 ,a & ,b might *ange entirely4 ,! causality concept is !re=e a relative "o1 9 t x involves ! :ole sy/em 9 :i* ! ev5ts take place4 ,9 practice we n[ take an exce$+ly pregnant /ep & seek to ext5d ! concept1 & rid ourselves z mu* z possible ( its relativity4 ,x is a matt] ( exp]i5ce t !re are (t5 a great numb] ( sy/ems 9 :i* ,a is ! cause ( ,b4 ,9 _m cases ! causal relation p]si/s ?r\gh su* a v wide range ( sy/ems t we lose sight entirely ( ! sy/em1 & come to assume t we h an absolute causal connection betwe5 ,a & ,b4 ,= in/ance1 :5 ,i /rike a bell1 & he> ! s\nd1 ! causal connection p]si/s ?r\gh su* a great numb] ( diff]5t k9ds ( sy/em t ,i might ?9k t "h is an absolute causal connection4 ,su* an absolute causal connection w\ld mean t always "u all circum/ances1 ! /rik+ ( ! bell is accompani$ by a s\nd4 ,b all conditions means only all ^? conditions cov]$ by exp]im5t4 ,?us 9 ! case ( ! bell1 all our exp]im5ts 7 made 9 ! pres5ce ( ! atmosph]e4 ,! causal connection betwe5 ! /rik+ ( ! bell & ! s\nd %\ld h be5 always recogniz$ 9 pr9ciple z relative to ! pres5ce ( ! atmosph]e4 ,inde$1 lat] exp]im5ts 9 ! abs5ce ( ! atmosph]e %[ t ! atmosph]e does play an ess5tial "p4 ,n[ z a matt] ( fact1 ! atmosph]e is s comp>atively easy to remove t we v readily include ! atmosph]e 9 ! *a9 ( causal connection4 ,b if ! atmosph]e _h be5 impossible to remove1 l ! old e!r ( space1 our idea ( ! causal connections betwe5 ! /rik+ ( ! bell & its s\nd might h be5 q diff]5t4 ,9 actual physical applications ( ! causality concept1 ! con/ant backgr\nd :i* is ma9ta9$ dur+ all ! v>iations by :i* ! causal connection is e/abli%$ usually has to be inf]r$ f ! context4 ,x is a matt] ( p]haps univ]sal exp]i5ce t ! ev5t ,a is accompani$ by n only "o ev5t1 :i* is ! effect ( ,a by def9ition1 b ,a entails a :ole causal tra9 ( ev5ts4 ,x seems to be a g5]alization f exp]i5ce t ! causally connect$ tra9 ( ev5ts />t$ by ,a is a nev] end+ tra91 provid$ ! sy/em is l>ge en\gh4 ,?is is p]haps n necess>y 9 ! g5]al case1 b if ! ev5t ,a involves imp>t+ ext]nal en]gy to ! sy/em1 or ! action ( ext]nal =ce 7mom5tum *ange71 !re c be no "q4 ,t !re is a causal tra9 />t$ by ,a is p>ticul>ly evid5t if ,a & ,b are sep>at$ 9 space4 ,?us 9 ! case ( ! bell1 ! impulse giv5 to ! air by ! vibration ( ! bell is propagat$ ?r\gh ! air z an ela/ic wave1 :i* ?us con/itutes ! causal tra9 ( ev5ts4 ,! ph5om5on ( propagation is *>act]i/ic ( causal connections ( a me*anical "*1 & is ! ju/ification = ! introduction ( ! "t concept 9 connection ) ! causality concept1 :]e x n[ appe>s = ! fir/ "t4 ,x is evid5t t :5 a di/urbance is propagat$ to a di/ant po9t1 ! effect foll[s ! cause 9 "t1 z "t is usually measur$4 ,we ext5d ?is result1 & usually ?9k t ! effect necess>ily foll[s ! cause4 ,we n[ exam9e :e!r ?is is a necess>y result ( ! causality concept4 ,if we are to talk ab\t ! "t ( ev5ts at diff]5t places1 we mu/ h "s way ( sett+ clocks all ov] space4 ,if ?is is done arbitr>ily1 !re is no necess>y connection betwe5 ! local clock times ( a cause & its effect1 b nev]!less ! causality concept involves a c]ta9 temporal relation ev5 9 ?is mo/ g5]al case4 ,suppose t ev5t ,a takes place at po9t #a & its effect1 ev5t ,b1 at po9t #b4 ,we /ation a conf$]ate at #b :o s5ds a light signal 7or any o!r sort ( signal7 to #a1 z soon z ! ev5t ,b occurs at #b4 ,!n x is a consequ5ce ( ! nature ( ! causality concept t ! signal _c arrive at #a be=e ev5t ,a occurs4 ,= if x did arrive be=e ,a1 we %\ld m]ely omit to p]=m ,a1 :i* by hypo!sis is arbitr>y1 & entirely 9 our control1 & !n our assumption w\ld be violat$ t ! sy/em is su* t ! ev5t ,b occurs only :5 ,a also occurs4 ,! same argum5t %[s a =tiori t if ! effect ,b occurs at ! same place z its cause ,a1 x _c prec$e x 9 "t4 ,i _c see t ! nature ( ! causality concept imposes any fur!r re/riction on ! "t ( ,b4 ,! re/rict$ pr9ciple ( relativity1 h[ev]1 9 po/ulat+ t no signal c be propagat$ fa/] ?an a light signal1 virtually makes a fur!r assumption ab\t ! temporal connection ( causally connect$ ev5ts1 namely1 t ! ev5t ,b at #b _c occur be=e ! arrival at #b ( a light signal :i* />t$ f #a at ! in/ant t ,a occurr$ at #a4 ,= if ,b did occur e>li]1 we c\ld use ev5ts ,a & ,b z a signal+ code1 ?us violat+ our hypo!sis4 ,!re is ?us a close/ connection 9 "t1 :5 "t is ext5d$ ov] space z ! !ory ( relativity directs1 betwe5 cause & effect1 dep5d+ on _! sep>ation 9 space2 f ?is arises ! relativity concept ( ! causal cone1 :i* 9 ! f\r dim5sional manifold ( space-"t divides ! aggregate ( all ^? ev5ts :i* may be causally relat$ f ! aggregate ( ^? :i* are sep>at$ by su* a small int]val 9 "t & su* a l>ge int]val 9 space t communication by light signals & !re=e a causal connection is n possible4 ,giv5 n[ two ev5ts ,a & ,b :i* are relat$ z cause to effect 9 "o sy/em ( ref]5ce1 !n !y mu/ be causally relat$ also 9 e o!r sy/em ( ref]5ce4 ,= if !y 7 n1 we c\ld by def9ition ( causality suppress ! ev5t ,a 9 "o ( ! sy/ems 9 :i* ! causal relation does n hold1 & ?is1 because ( ! nature ( ! concept ( ev5t1 involves suppress+ ,a 9 all ! sy/ems1 ?us violat+ our hypo!sis ( a causal connection 9 ! orig9al sy/em4 ,! concept ( ev5t involv$ 9 ?is argum5t w be exam9$ lat]4 ,x appe>s !n1 t ! fundam5tal po/ulate ( relativity 7t ! =m ( natural laws is ! same 9 all ref]5ce sy/ems7 dem&s t ! temporal ord] ( ev5ts causally connect$ be ! same 9 all ref]5ce sy/ems4 ,! :ole univ]se at ?is pres5t mom5t is (t5 suppos$ to be causally connect$ ) all succe$+ /ates4 ,?is means t if we c\ld repeat exp]i5ce1 />t+ f ! same initial conditions1 ! future c\rse ( ev5ts w\ld always be f\nd to be ! same4 ,! tru? ( ?is conviction c nev] be te/$ by direct exp]im5t1 b x is some?+ at :i* we arrive by ! usual physical process ( successive approximation4 ,x is difficult to =mulate precisely :at we mean by pres5t /ate ( ! univ]se1 & !re is e reason to ?9k t su* a =mulation is n unique1 b ! concept conta9s ! necess>y implication t none ( ! ev5ts con/itut+ ! pres5t c be causally connect$4 ,! ev5ts 9 di/ant places :i* con/itute ! pres5t mu/ be sep>at$ by an int]val ( "t less ?an "t requir$ by light to travel betwe5 ! two places4 ,! conviction1 aris+ f exp]i5ce1 t ! future is det]m9$ by ! pres5t & correspond+ly ! pres5t by ! pa/1 is (t5 phras$ diff]5tly by say+ t ! pres5t causally det]m9es ! future4 ,?is is 9 a c]ta9 s5se a g5]alization ( ! causality concept4 ,x is "o ( ! pr9cipal jobs ( physics to analyze ?is complex causal connection into compon5ts1 repres5t+ z f> z possible ! future /ate ( ! sy/em z ! sum ( indep5d5t tra9s ( ev5ts />t$ by ea* individual ev5t ( ! pres5t4 ,h[ f> su* an analysis is possible mu/ be decid$ by exp]im5t4 ,x is c]ta9ly possible to a v l>ge ext5t 9 mo/ cases1 b !re seems to be no reason to expect t a complete analysis is possible4 ,s f> z ! sy/em is describable 9 t]ms ( l9e> diff]5tial equations1 ! causal tra9s />t$ by diff]5t ev5ts propagate !mselves 9 space & "t )\t int]f]5ce & ) simple addition ( effects1 & conv]sely ! pres5t may be analyz$ back into ! simple sum ( elem5t>y ev5ts 9 ! pa/1 b if ! equations gov]n+ ! motion ( ! sy/em are n l9e>1 effects are n additive1 & su* a causal analysis into elem5ts is n possible4 ,no emphasis is to be laid "h on ! diff]5tial aspect ( ! equations3 x is q possible t f9ite diff]5ce equations may h ! same prop]ty ( additivity4 ,al?\gh !re c be no "q t l9e> equations enorm\sly prepond]ate1 nei!r c !re be any d\bt t "s ph5om5a _c be describ$ 9 t]ms ( l9e> equations 7e4g41 f]ro-magnetism71 s t !re seems no reason to ?9k t a causal analysis is always possible4 ,i believe1 h[ev]1 t ! assumption t su* an analysis into small scale elem5ts is possible is tacitly made 9 ! ?\ght ( _m physici/s4 ,if ! analysis is n possible1 we may expect to f9d results foll[+ ! coop]ation ( sev]al ev5ts :i* _c be built up f ! results ( ! ev5ts occurr+ individually4 ,:5 a causal analysis is possible1 f9d+ ! simple/ ev5ts :i* act z ! orig9 ( indep5d5t causal tra9s is equival5t to f9d+ ! ultimate elem5ts 9 a s*eme ( explanation1 s t "h we m]ge ) ! concept ( explanation1 z already m5tion$4 ,z 0 true ( ! explanatory sequ5ce1 s "h !re c be no =mal end ( ! causal sequ5ce1 because we c always ask = ! cause ( ! la/ memb]4 ,b x may be physically mean+less to ext5d ! causal sequ5ce beyond a c]ta9 po9t4 ,we h se5 f ! po9t ( view ( op]ations t ! causal concept dem&s ! possibility ( v>iation 9 ! sy/em4 ,x is !re=e mean+less to say t ,a is ! cause ( ,b unless we c exp]i5ce sy/ems 9 :i* ,a does n occur4 ,n[ if 9 ext5d+ ! causal sequ5ce1 we ev5tually arrive at a condition s broad t physically no fur!r v>iation c be made1 our causal sequ5ce has to /op4 ,correspond+ to ?is prop]ty ( ! causality concept1 ! causal sequ5ce may be t]m9at$ ei!r =mally1 by po/ulate1 or naturally1 by ! intr9sic physical nature ( ! elem5ts ( ! sequ5ce4 ,?us if we say t light gets f po9t to po9t because x is propagat$ by a m$ium ( unalt]able prop]ties1 :i* fills all space1 :i* is always pres5t & c nev] be elim9at$ physically1 we h by ! po/ulat$ prop]ties ( ! m$ium br\ght ! possibility ( fur!r inquiry to a close1 because to take ! next /ep & ask ! cause ( ! prop]ties ( ! e!r1 dem&s t we be able to p]=m exp]im5ts ) ! e!r alt]$ or abs5t4 ,su* an end+ ( ! sequ5ce is evid5tly pure =malism1 )\t physical significance4 ,b o!r consid]ations may give physical significance4 ,?us if !re are o!r sorts ( exp]im5t t c be expla9$ by assum+ a univ]sal m$ium ( ! same prop]ties1 ! concept proves n only to be useful1 b to h a c]ta9 degree ( physical significance4 ,an example ( an inevitable t]m9ation ( ! causal sequ5ce is af=d$ by ! possibility1 already m5tion$1 t ! value ( ! gravitational con/ant may be det]m9$ by ! total quantity ( matt] 9 ! univ]se4 ,)\t fur!r qualification1 ?is is an entirely /]ile /atem5t1 b if x c be %[n t !re is a simple num]ical connection1 ! matt] takes on int]e/1 & we may seek fur!r = a correlation betwe5 ! num]ical relation & o!r ?+s4 ,?is analysis ( ! causality concept does n pret5d to be complete & leaves _m int]e/+ que/ions unt\*$4 ,p]haps "o ( ! mo/ int]e/+ ( ^! que/ions is :e!r we c sep>ate into cause & effect two ph5om5a :i* always accompany ea* o!r1 & :e!r !re=e ! classification ( ph5om5a into causally connect$ gr\ps is an exhau/ive classification4 ,b ! discussion is broad en\gh = our purpose "h2 ! mo/ important po9ts ( view to acquire are t ! causality concept is relative to ! :ole backgr\nd ( ! sy/em :i* conta9s ! causally connect$ ev5ts1 & t we mu/ assume ! possibility ( an unlimit$ numb] ( id5tical exp]im5ts1 s t ! causality concept applies only to sub-gr\ps ( ev5ts sep>at$ out f ! aggregate ( all ev5ts4 ,,! ,,concept ,,( ,,id5tity ,"o ( ! mo/ fundam5tal ( all ! concepts ) :i* we describe ! ext]nal _w is t ( id5tity2 9 fact1 ?9k+ w\ld be almo/ inconceivable )\t su* a concept4 ,by ?is concept we bridge ! passage ( "t2 x enables u to say t a p>ticul> object 9 our pres5t exp]i5ce is ! same z an object ( our pa/ exp]i5ce4 ,f ! po9t ( view ( op]ations1 ! mean+ ( id5tity is det]m9$ by ! op]ations by :i* we make ! judgm5t t ?is object is ! same z t "o ( my pa/ exp]i5ce4 ,9 practice !re are _m indirect ways ( mak+ ?is judgm5t1 b ,i believe ! ess5ce ( ! situation lies 9 ! possibility ( cont9u\s connection betwe5 ! object ( ! pres5t & ! pa/ by cont9u\s obs]vation 7ei!r direct or indirect7 ?r\gh all int]m$iate "t4 ,we mu/1 = example1 be able to look cont9u\sly at ! object1 & /ate t :ile we look at x1 x rema9s ! same4 ,?is involves ! possession by ! object ( c]ta9 *>act]i/ics--x mu/ be a discrete ?+1 sep>at$ f its surr\nd+s by physical discont9uities :i* p]si/4 ,! concept ( id5tifiability applies1 !re=e1 only to c]ta9 classes ( physical objects2 no "o ?9ks ( try+ to id5tify ! w9d ( to-day ) ! w9d ( ye/]day4 ,x is some:at easi] to id5tify a liquid su* z wat] 9 its fl[ 9 a /ream1 because we c make ! motion ( ! wat] visible by solid p>ticles susp5d$ 9 x1 b ev5 "h x is n easy to prove to a capti\s critic t x is really ! wat] & n ! susp5d$ p>ticles ( solid t we are id5tify+4 ,ev5 solids1 :5 our measurem5ts are suffici5tly ref9$1 seem to lose _! discont9u\s edges1 z has be5 sugge/$ 9 ! discussion ( ! approximate "* ( exp]im5tal ari?metic1 & ! id5tity concept becomes hazy4 ,!re c be no "q t ! concept ( id5tity is a tool p]fectly well adapt$ to deal approximately ) nature 9 ! region ( our ord9>y exp]i5ce1 b we h to ask a m s]i\s "q4 ,does n ! app>5t dem& ( our ?9k+ app>atus to be furni%$ ) discrete & id5tifiable ?+s to ?9k ab\t impose a v ess5tial re/riction on any picture ( ! physical univ]se :i* we are able to =m8 ,we are cont9ually surpris+ ourselves 9 ! inv5tion ( discrete /ructure fur!r & fur!r d[n 9 ! scale ( ?+s1 :ole sole raison d'tre is to be f\nd entirely )9 ourselves4 ,?us ,osborne ,reynolds#ab has speculat$ s]i\sly & mo/ elaborately ab\t an atomic /ructure 9 ! e!r1 & we f9d ,edd+ton#ac h9t+ at ! exi/5ce ( /ructure ( an ord] ( magnitude ( #aj-dj cm4 ,on a mu* l>g] scale ( magnitude we also ?9k 9 ! same t]ms1 & conceive positive & negative elem5t>y *>ges ) h>d & imp5etrable cores1 :i* involves a complete *ange 9 ! law ( =ce at po9ts suffici5tly close4 ,:at physical assurance h we t an electron 9 jump+ ab\t 9 an atom pres]ves its id5tifiability 9 any?+ l ! way t we suppose1 or t ! id5tity concept applies "h at all8 ,footnote #ab3 ,osborne ,reynolds1 ,! ,sub-,me*anics ( ! ,univ]se1 #bed pp41 ,cambridge ,univ]sity ,press1 #aijc4 ,footnote #ac3 ,a4 ,s4 ,edd+ton1 ,report on ,gravitation1 ,lon4 ,phys4 ,soc41 #aiah1 p4 #ia4 ,9 fact1 ! id5tity concept seems to lose all mean+ 9 t]ms ( actual op]ations on ?is level ( exp]i5ce4 ,! m9d seems ess5tially incapable ( deal+ ) cont9uity z a prop]ty ( physical ?+s2 x is n ev5 able to talk ab\t cont9uity except 9 negative t]ms4 ,to ea* attempt$ description ( ! prop]ties ( a truly cont9u\s sub/ance1 x c say ,no1 x is n t1 b _c imag9e exp]i5ce :i* corresponds to :at x conceives a really cont9u\s ?+ ought to feel l4 ,9 t]ms ( op]ations1 cont9uity has only a sort ( negative mean+4 ,n[ c]ta9 implications ( ?is inability ( ! m9d c be remov$ by appropriate po/ulates1 z1 = example1 we c po/ulate ! complete annihilation ( a negative by a positive *>ge1 z is n[ be+ done 9 c]ta9 speculations4#ad ,!re is po9t 9 do+ ?is1 because ! annihilation ( two *>ges has physical mean+4 ,b x is a "q :e!r all implications ( ?is habit ( ?\ght c be remov$1 & :e!r any picture t we c =m ( nature w n be t+$--sickb$ o'er ) ! pale ca/ ( ?\ght4 ,footnote #ad3 ,= example1 ,j4 ,h4 ,jeans1 ,nat4 #aad1 #hbh-hbi1 #aibd4 ,! op]ational view sugge/s t 9 ?is la/ we are com+ p]il\sly close to a mean+less "q1 al?\gh !re is a c]ta9 s5se 9 :i* !re is mean+ "h4 ,x may turn out z a matt] ( fact t we %all n be able to c>ry our delv+ into small-scale ph5om5a deep] ?an a c]ta9 po9t1 & t nature w appe> to be f9ite d[nw>d1 s t we %all br+ up aga9/ a wall ( "s k9d4 ,b to ask 9 su* a situation :e!r we h come to ! end because nature is really f9ite1 or :e!r we only appe> to be at an end because ( "s prop]ty ( our m9ds1 su* z inability to deal ) cont9uity1 is1 ,i believe1 a mean+less "q4 ,9 actual use ! id5tity concept is ext5d$1 & id5tity is us$ 9 o!r s5ses ?an ! fundam5tal "o exam9$ above4 ,= in/ance1 we speak ( two obs]v]s see+ ! same object1 or if ! object moves or does some?+1 we may speak ( two obs]v]s p]ceiv+ ! same happ5+4 ,a happ5+ ab\t :i* ! judgm5t ( sam5ess is possible :5 p]ceiv$ by diff]5t obs]v]s 7or ma!matically express$ :5 obs]v$ 9 two ref]5ce frames7 is :at we mean by an ev5t1 :i* is "o ( ! fundam5tal concepts ( relativity !ory4 ,:at n[ is involv$ 9 ?is concept ( ev5t1 or :at d we mean :5 we say t two obs]v]s exp]i5ce ! same ev5t8 ,a fir/ crude attempt might say t ! ev5t is ! same if x is describ$ 9 ! same way by ! two obs]v]s4 ,b ?is leads u into all ! complicat$ que/ions ( ! mean+ ( language1 :i* we w\ld gladly avoid1 & is fur!rmore n true1 because ! :i/le ( a locomotive1 = example1 does n h ! same pit* = two obs]v]s mov+ ) diff]5t velocities4 ,a satisfactory analysis ( ! situation is difficult to give1 b ,i believe ! ess5ce lies 9 ! discrete "* ( ! ev5t1 j z ! id5tity concept :5 appli$ only to objects involv$ discret5ess4 ,! ev5t is b\nd$ on all sides by discont9uities1 bo? 9 space & "t4 ,n[ x seems to be a result ( exp]i5ce t discont9uities h a c]ta9 absolute significance1 9 t !re is a "o-to-"o correspond5ce betwe5 ! discont9uities obs]v$ 9 any "o ref]5ce sy/em & ^? obs]v$ 9 any o!r4 ,correspond+ discont9uities 9 two ref]5ce sy/ems are by def9ition ! same4 ,an ev5t is by def9ition ! aggregate ( all ph5om5a b\nd$ by c]ta9 discont9uities1 & two ref]5ce sy/ems are by def9ition describ+ ! same ev5t if ! discont9u\s b\nd>ies ( ! ev5t are ! same1 irrespective ( ! appe>ance ( ! ev5t 9 ! two sy/ems4 ,! emission ( a light signal1 = example1 is an ev5t accord+ to ?is def9ition1 al?\gh x may appe> z r$ light 9 "o ref]5ce sy/em & gre5 9 ano!r4 ,we n[ see t ! concept ( ev5t is only an approximate concept1 z 0 also t ( id5tity1 & = ! same reason1 namely1 !re are no su* ?+s 9 exp]i5ce z %>p discont9uities1 b z our measurem5ts become m ref9$1 ! edges ( suppos$ discont9uities become blurr$4 ,z we g to small] scales ( magnitude ?is blurr+ becomes m important1 until ! physical possibility ( p]=m+ ^? op]ations by :i* ! discont9uities are detect$ entirely disappe>s1 & ! concept ( ev5t acquires1 9 t]ms ( op]ations1 an entirely diff]5t mean+4 ,we cont9ue to ?9k ( ! ev5t 9 ! same way z be=e 9 t]ms ( a m5tal model1 b ! true op]ational significance n[ dep5ds on ! p>ticul> ph5om5on "u consid]ation4 ,! concept ( ev5t is really n ! same sort ( ?+ :5 appli$ to ! emission ( a quantum ( radiation f an atom1 or ! emission ( gamma radiation f a radioactive dis9tegration1 or ! fla%+ ( a signal f a d>k lant]n by op5+ & clos+ a %utt]4 ,"h z always1 :5 our range ( exp]i5ce is ext5d$1 we mu/ be prep>$ at "s future "t to f9d t1 by ext5d+ ! ord9>y concept ( ev5t to small-scale ph5om5a by ! device ( ! m5tal model1 we h by implication smuggl$ into our picture ph5om5a :i* d n exi/1 s t x w be necess>y to revise our ?9k+1 ca/+ x into t]ms correspond+ to direct exp]i5ce4 ,,! ,,concept ,,( ,,velocity ,! concept ( velocity1 z ord9>ily def9$1 involves ! two concepts ( space & "t4 ,! op]ations by :i* we measure ! velocity ( an object are ^!3 we fir/ obs]ve ! "t at :i* ! object is at "o position1 & !n lat] obs]ve ! "t at :i* x is at a second position1 divide ! di/ance betwe5 ! two positions by ! "t int]val1 & if necess>y1 :5 ! velocity is v>iable1 take ! limit4 ,z long z we deal ) fairly l[ velocities we d n h to inquire c>efully z to ! k9d ( "t we use 9 ^! op]ations1 b :5 ! velocities become high1 we d h to take c>e to use ! local times at ! two positions ( ! body1 :i* means t we mu/ h a "t sy/em spread ov] space1 or1 9 o!r words1 ! ext5d$ "t sy/em4 ,?is velocity concept1 def9$ 9 ?is way1 may be us$ z a tool 9 describ+ nature1 & x w be f\nd t nature has c]ta9 prop]ties2 = example1 ! velocity ( light is #c x #ajaj cm4_/sec4 ,fur!r1 no mat]ial ?+ c be giv5 a velocity z high z ?is1 b z its velocity is made to approa* ?is value1 increm5ts ( en]gy increas+ )\t limit are requir$4 ,b n[ x is v mu* a "q = exam9ation :e!r ! velocity concept def9$ 9 ?is p>ticul> way has be5 *os5 wisely z a tool = describ+ natural ph5om5a4 ,x is q possible to modify ! velocity concept1 t is1 to set up o!r op]ations :i* correspond to our in/9ctive feel+ ( :at velocity is 9 t]ms ( imm$iate s5sation & su* t all num]ical measures are unmodifi$ at l[ velocities4#ae ,= example1 a travell] 9 an automobile measures 8 velocity by obs]v+ ! clock on 8 in/rum5t bo>d & ! mile /ones :i* he passes on ! road4 ,?is op]ation diff]s f t ( ! def9ition above 9 t ! "t is no long] ext5d$ "t1 b is ! local "t ( ! mov+ object4 ,! space coord9ates us$ 9 ?is alt]native op]ation at fir/ seem a hybrid sort ( ?+1 b !y are :at ! obs]v] w\ld actually mo/ naturally use3 !y are :at he w\ld measure ) a tape measure fix$ to a po9t ( ! road & all[$ to unw9d z he proce$s1 or :at is measur$ by a vessel at sea ) a log l9e let out beh9d4 ,footnote #ae3 ,x is an int]e/+ "q = ! psy*ologi/ :e!r ! velocity concept is n a m primitive ?+ 9 ord] ( appreh5sion ?an t ( "t1 & :e!r ! concept ( "t is n d]iv$ f obs]v+ ?+s 9 motion1 or :e!r inde$ !re is any necess>y connection at all betwe5 velocity & "t 9 t]ms ( untutor$ exp]i5ce4 ,or !re is /ill ano!r mo/ int]e/+ way ( def9+ velocity1 9 :i* ! analysis into space & "t is n made at all1 b velocity is directly measur$ by build+ up ! giv5 velocity by physical addition ( a unit velocity select$ arbitr>ily4 ,?is matt] is discuss$ at "s l5g? 9 my book ,dim5sional ,analysis1#af b is ( suffici5t p]t95ce "h to describe briefly4 ,we may 9 ! fir/ place con/ruct a concrete /&>d = velocity1 z1 = example1 by /ret*+ a /r+ betwe5 two pegs on a bo>d ) a fix$ weight4 ,if we /rike ! /r+1 a di/urbance travels along ! /r+ :i* we c foll[ ) ! eye1 & we def9e unit velocity z ! velocity ( ?is di/urbance4 ,an object has great] ?an unit velocity if x outruns ! di/urbance1 & less if x lags beh9d4 ,we may n[ duplicate our /&>d1 mak+ ano!r bo>d ) pegs & /ret*$ /r+1 & *eck ! equality ( ! two velocities by obs]v+ t ! two di/urbances run toge!r4 ,we n[ def9e two units ( velocity z ! velocity ( any?+ :i* runs ) ! di/urbance ( ! /r+ ( ! second bo>d1 :5 ! second bo>d is made to move bodily ) su* a velocity t x runs ) ! di/urbance ( ! fir/ /r+4 ,! process may be ext5d$ indef9itely1 & any velocity measur$4 ,footnote #af3 ,yale ,univ]sity ,press1 #aibb4 ,if ei!r ( ^! two alt]native def9itions ( velocity 7 adopt$1 x w\ld be f\nd t ! velocity ( light is inf9ite4 ,fur!r1 !re w\ld be no limit to ! velocity :i* c be imp>t$ to mat]ial bodies on giv+ !m unlimit$ en]gy1 :i* is :at we are prep>$ to reg>d f ord9>y exp]i5ce is natural & simple4 ,! inf9ite velocity = light1 on ! o!r h&1 is mo/ unnatural1 p>ticul>ly if we favor a m$ium po9t ( view4 ,we are "h fac$ ) a dilemma--all sorts ( ph5om5a _c at ! same "t be treat$ simply4 ,if we atta* ! mo/ fundam5tal significance to ! behavior ( mat]ial bodies1 we %all d well to adopt "o ( ! alt]native def9itions ( velocity4 ,if1 on ! o!r h&1 we reg>d ! ph5om5a ( light z ! mo/ fundam5tal1 we %all endeavor to =m our def9ition s t ! prop]ties ( light are simple4 ,?is 0 precisely ! po9t ( view ( ,e9/e92 x is *>act]i/ic ( 8 entire s*eme ( re/rict$ relativity t light is ! fundam5tal ?+1 & ?is influ5c$ him 9 adopt+ ! fir/ def9ition ( velocity4 ,n[ "o c h no qu>rel ) ?is desire to make light fundam5tal 7! wisdom ( do+ ?is is to be ju/ifi$ by ! results71 & if ! prop]ties ( light are to be treat$ ma!matically1 "o c easily see ! desirability ( gett+ rid ( inf9ite attributes1 & s admit ! desirability ( mak+ ! velocity ( light f9ite4 ,b all ?is involves ano!r v insidi\s assumption :i* we ourselves h tacitly us$ 9 all our prec$+ discussion1 namely1 t ! notion ( velocity prop]ly p]ta9s to light at all4 ,e9/e9 has v def9itely adopt$ ?is po9t ( view1 & s det]m9$ ! "* ( ! entire /ructure ( relativity4 ,i believe1 on ! contr>y1 t x is v gravely to be que/ion$ :e!r ! id5tification ( light ) a ?+ travell+1 :i* is involv$ 9 apply+ ! velocity concept1 %\ld be made4 ,?is discussion mu/ be po/pon$1 h[ev]1 until we deal ) ! prop]ties ( light4 ,! important po9ts = u to notice at pres5t are t ! def9ition ( velocity actually us$ involves ! concept ( ext5d$ "t1 & t x w\ld be possible to def9e velocity 9 diff]5t ways1 :i* w\ld give q a diff]5t complexion to ph5om5a at high velocities1 b :i* w\ld leave unt\*$ our ord9>y exp]i5ce4 ,! velocities at :i* ! precise =m ( def9ition becomes important are high] ?an c be rea*$ 9 ord9>y me*anical exp]im5ts4 ,su* velocities c be atta9$ 9 t]re/rial laboratories only ) electrifi$ p>ticles1 z 9 exp]im5ts 9 high vacua or ) radioactive dis9tegrations4 ,x is int]e/+ to notice t we v seldom attempt a direct measurem5t ( velocity 9 su* exp]im5ts by foll[+ a discrete p>ticle 9 its flight & f9d+ ! "t requir$ to pass ov] a measur$ di/ance1 b ! velocities are measur$ indirectly1 by calculation f ! equations ( electrodynamics & 9 t]ms ( su* imm$iately obs]v$ ?+s z curvature ( pa?4 ,x is true t "o or two exp]im5ts h attempt$ a m direct measure ( velocity1 b x seems !re is room = m "w "h4 ,,! ,,concepts ,,( ,,=ce ,,& ,,mass ,ano!r concept ( great importance is t ( =ce4 ,s9ce ! usual analysis f9ds a connection betwe5 =ce & accel]ation1 & accel]ation involves velocity1 ?is is a natural place = ! discussion ( =ce4 ,?is concept has be5 subject$ to mu* analysis by v>i\s writ]s4 ,9 orig9 ! concept d\btless arises f ! muscul> s5sations ( resi/ance exp]i5c$ f ext]nal bodies4 ,?is crude concept may at once be put on a quantitative basis by sub/itut+ a spr+ balance = our muscles1 or in/ead ( ! spr+ balance we may use any ela/ic body1 & measure ! =ce ex]t$ by x 9 t]ms ( its de=mation4 ,( c\rse1 ! v>i\s precautions :i* mu/ be tak5 9 c>ry+ out ?is idea physically are complex2 ! matt] ( precautions aga9/ temp]ature *anges1 = example1 is "o ( ! mo/ easily und]/ood4 ,! concept ( =ce s def9$ is limit$ to /atic sy/ems2 x is ! task ( /atics to f9d ! relation betwe5 ! =ces 9 sy/ems at re/4 ,we next ext5d ! =ce concept to sy/ems n 9 equilibrium1 9 :i* !re are accel]ations1 & we mu/ conceive t at fir/ all our exp]im5ts are made 9 an isolat$ laboratory f> out 9 empty space1 :]e !re is no gravitational field4 ,we "h enc\nt] a new concept1 t ( mass1 :i* z x is orig9ally met is entangl$ ) ! =ce concept1 b may lat] be dis5tangl$ by a process ( successive approximations4 ,! details ( ! v>i\s /eps 9 ! process ( approximation are v in/ructive z typical ( all me?ods 9 physics1 b ne$ n be elaborat$ "h4 ,suffice x to say t we are ev5tually able to give to ea* rigid mat]ial body a num]ical tag *>act]i/ic ( ! body1 su* t ! product ( ?is numb] & ! accel]ation x receives "u ! action ( any giv5 =ce appli$ to x by a spr+ balance is num]ically equal to ! =ce1 ! =ce be+ def9$1 except = a correction1 9 t]ms ( ! de=mation ( ! balance1 exactly z x 0 9 ! /atic case4 ,9 p>ticul>ly1 ! relation f\nd betwe5 mass1 =ce1 & accel]ation applies to ! spr+ balance itself by :i* ! =ce is appli$1 s t a correction has to be appli$ = a dim9ution ( ! =ce ex]t$ by ! balance aris+ f its own accel]ation4 ,we n[ ext5d ! scope ( our measurem5ts by br++ our laboratory into ! gravitational field ( ! e>?1 & imm$iately our exp]i5ce is ext5d$1 9 t we cont9ually see bodies accel]at$ ) no spr+ balance 7t is1 no =ce7 act+ on !m4 ,we ext5d ! concept ( =ce1 & say t any body accel]at$ is act$ on by a =ce1 & ! magnitude ( ?is =ce is def9$ z t :i* w\ld h be5 necess>y to produce 9 ! same body ! same accel]ation ) a spr+ balance 9 empty space4 ,!re is physical ju/ification = ?is ext5sion 9 t we f9d we c remove ! accel]ation :i* a body acquires 9 a gravitational field by ex]t+ on x ) a spr+ balance a =ce ( exactly ! specifi$ am\nt 9 ! opposite direction4 ,?is ext5d$ idea ( =ce may also be appli$ to sy/ems 9 :i* !re are electrical actions4 ,we ?us see t 9 ext5d+ ! notion ( =ce f bodies 9 re/ to bodies 9 motion1 ! "* ( ! concept has *ang$1 because ! op]ations by :i* =ce is measur$ *ange--! =ce act+ on a body is n[ measur$ 9 t]ms ( its accel]ation4 ,b 9 det]m9+ ! =ce f ! accel]ation1 we h to "k ! mass4 ,?is mass has to be indep5d5tly measur$ ) ! orig9al concept ( =ce2 o!rwise we h no basis = su* simple /atem5ts z t ! =ce ( gravity on a body is proportional to its mass4 ,all ?is applies to ! ord9>y range ( exp]im5ts ) l[ velocities4 ,if n[ we ext5d ! range ( measurem5ts1 we f9d ph5om5a :i* we _h n expect$2 = example1 !re seem to be difficulties 9 ! way ( indef9itely increas+ ! velocity ( a mat]ial body1 z ( a *>g$ atom4 ,we beg9 to ask se>*+ que/ions3 is ! =ce ( gravity indep5d5t ( velocity at high velocities1 or is ! mass indep5d5t ( velocity "u ! same conditions or indep5d5t ( ! gravitational field1 etc48 ,9 attempt+ to answ] ^! new que/ions1 we f9d difficulty ) ! concepts 9 t]ms ( :i* !y are =mulat$4 ,!re are no op]ations by :i* we c f9d :e!r =ce is indep5d5t ( velocity unless we fir/ "k ! mass1 or any op]ations by :i* a mass c be measur$ unless we "k a =ce4 ,! purely me*anical sy/ems ) ! highe/ velocities ( :i* we h any exp]im5tal k are ! heav5ly bodies4 ,! motion ( ^! is1 ) ! important exception ( ,m]cury1 t pr$ict$ by ! ord9>y laws ( me*anics1 s t at fir/ x might appe> t we h "h confirmation ( ! laws ( me*anics = bodies ) comp>atively high velocities4 ,b x mu/ be rememb]$ t all we c obs]ve ( ! heav5ly bodies is _! positions1 & t we _c p]=m on ^! bodies all ! op]ations by :i* we c *eck ! laws ( me*anics = t]re/rial ph5om5a4 ,if1 = example1 mass & ! =ce ) :i* gravity acts on mass 7 bo? equally affect$ by velocity1 ! motion ( ! heav5ly bodies w\ld be exactly ! same z t obs]v$ n[4 ,h5ce z we increase ! range ( velocity1 ! concepts ( =ce & mass simultane\sly lose _! def9it5ess1 & become p>tially fus$4 ,?is is typical ( :at we h n[ come always to expect ne> ! limit ( ! exp]im5tally atta9able2 exp]i5ce becomes less ri*1 ! *oice ( physical op]ations m re/rict$1 concepts *ange & become few] 9 numb]4 ,if we are to reta9 ! same =mal numb] ( concepts1 we mu/ introduce arbitr>y conv5tions or def9itions4 ,^! def9itions are to be det]m9$ l>gely by conv5i5ce4 ,9 ! case ( me*anical sy/ems1 ?is motive ( conv5i5ce is suppli$ by consid]ations f outside ! doma9 ( me*anical ph5om5a4 ,! highe/ velocities ( practice are n rea*$ 9 me*anical1 b 9 electrical sy/ems1 9 exp]im5ts ) vacuum tubes1 etc4 ,consid]ations ( conv5i5ce are !re=e dictat$ f ! electrical po9t ( view4 ,^! consid]ations w be gone into 9 mu* m detail lat]2 ! conclusion is all t we ne$ "h1 :i* is t x is conv5i5t to assume = ! *>ge ( ! electron a con/ant numb]1 indep5d5t ( ! velocity1 & ?is involves mak+ its mass v>iable 9 a def9ite way ) velocity4 ,n[ if ! pr9ciple ( relativity is accept$1 ! mass ( me*anical objects mu/ v>y ) velocity 9 ! same way z ! mass ( electrical *>ges4 ,s9ce ! v>iability ( ?is latt] is fix$1 me*anical mass becomes a def9ite function ( velocity1 & ! =ce is !re=e also fix$ 9 any specific physical case4 ,! fundam5tal def9ition ( =ce giv5 above is highly academic1 involv+ z x does hypo!tical exp]im5ts 9 laboratories situat$ f> out 9 empty space4 ,"s sort ( proc$ure l ?is seems to correspond to m or less explicit /atem5ts to be f\nd 9 ! lit]ature ( me*anics4 ,! mean+ 9 t]ms ( actual op]ations to be giv5 to su* def9itions involves complicat$ inf]5tial reason+4 ,we w\ld make mu* clos] connection ) ! conditions ( actual exp]im5t if 9 ! def9ition we sub/itut$ = ! hypo!tical op]ations 9 empty space m or less approximately realizable op]ations on bodies slid+ on level table tops )\t friction4 ,i suppose our in/9ctive feel+ = ! laws ( me*anics is su* t we are conv9c$ t def9itions 9 t]ms ( an int]/ell> space laboratory or a level table top are actually ! same4 ,b 9 pr9ciple we mu/ recognize t :5 ! op]ations are diff]5t1 ! concepts are diff]5t1 & if we adopt some?+ equival5t to ! table top def9ition1 z x seems we are physically =c$ to d1 we mu/ leave op5 9 our ?9k+ ! possibility ( f9d+ 9 ! pres5t p5umbra1 :5 our accuracy is suffici5tly increas$1 su* ph5om5a p]haps z directional attributes ( mass 9 a gravitational field4 ,we h j consid]$ ! sort ( problem t we enc\nt] on ord9>y scales ( magnitude on go+ f l[ to high velocities2 :at becomes ( ! concepts ( =ce & mass :5 we g to a v small scale8 ,d[n to ! atomic scale we may at lea/ slur ov] ! new physical difficulties1 = al?\gh we _c ( c\rse exp]im5t ) actual atoms1 we c nev]!less make measurem5ts ( ! ,br[nian#ag movem5t ( susp5sions 9 liquids settl+ 9 a gravitational field1 = example1 & ! extrapolation to ! atom is n a v great "o4 ,! mass ( ea* individual atom is obta9$ by :at is equival5t to a process ( c\nt+1 assum+ ! law ( cons]vation ( mass on an atomic scale4 ,?is is ju/ifi$ by all *emical exp]i5ce4 ,! mass ( ! compon5t p>ts ( ! atoms1 ! electrons1 may also p]haps be giv5 a unique significance aft] we h decid$ on ! laws ( ! electrical field1 by exp]im5ts on accel]ation 9 electrical fields4 ,! "q :i* int]e/s 9 pr9ciple "h is :at mean+1 if any1 %all be atta*$ to ! mass ( ! elem5ts ( ! electron4 ,footnote #ag3 ,?is ph5om5on is discuss$ at l5g? 9 ! book by ,j4 ,p]r91 ,br[nian ,movem5t & ,molecul> ,reality1 translat$ by ,f4 ,soddy1 ,taylor & ,francis1 ,london1 #aiji4 ,x is evid5t t we "h g beyond any possible exp]i5ce1 at lea/ = ! pres5t1 & t exp]i5ce has aga9 become poor] & our concepts few] 9 numb]4 ,all t we c n[ dem& is t c]ta9 comb9ations ( numb]s1 "s ( :i* repres5t me*anical mass & o!rs electrical *>ge1 h prop] relations to ea* o!r :5 integrat$ ?r\gh\t ! entire body ( ! electron4 ,simil> que/ions confront u :5 we ask :at are ! =ces :i* ! p>ts ( ! electron ex]t on ea* o!r4 ,we return to ?is "q 9 consid]+ ! nature ( ! electrical concepts4 ,9 any ev5t1 ! concepts ( bo? =ce & mass are entirely alt]$ 9 ?is doma94 ,x is int]e/+ to note1 9 pass+1 t pres5t electrical !ory gives no mean+ to ! mass ( ! elem5ts ( ! electron1 s9ce ! total electromagnetic mass ( ! electron is built up f ! mutual t]ms 9 ! action ( ! elem5ts--! total mass is n a l9e> resultant ( ! action ( ! elem5ts4 ,,! ,,concept ,,( ,,en]gy ,9 exam9+ ! concept ( en]gy1 we />t ) purely me*anical en]gy4 ,9 isolat$ me*anical sy/ems1 9 :i* !re are only cons]vative =ces1 ! sum ( k9etic & pot5tial en]gy is con/ant4 ,! k9etic en]gy may be def9$ z mv#b1 =m$ = all p>ts ( ! body4 ,! pot5tial en]gy is det]m9$ by ! position ( ! p>ts ( ! sy/em1 & has physical significance only ) ref]5ce to a datum position1 t is1 only *anges ( pot5tial en]gy h mean+ 9 t]ms ( op]ations4 ,! total en]gy ascrib$ to ! sy/em has !re=e an elem5t ( arbitr>9ess 9 t ! datum position may be *os5 at r&om1 & en]gy acquires mean+ only on trac+ ! hi/ory back to ! epo* ( ! datum position4 ,! concept ( en]gy may be ext5d$ f me*anical sy/ems to all sy/ems ) :i* we are acqua9t$2 ! op]ations by :i* mean+ is giv5 to ! ext5d$ en]gy concept involve ! g5]aliz$ cons]vation pr9ciple1 or ! fir/ law ( !rmodynamics4 ,! ext5sion to !rmal sy/ems is imm$iate2 ! inclusion ( optical & electrical sy/ems 9 ! s*eme 0 a mo/ important physical /ep1 :i* ( c\rse requir$ c>eful exp]im5tal ju/ification4 ,because ( its wide range ( application1 ! en]gy concept has n[ come to be reg>d$ z "o ( ! mo/ important 9 physics2 ?is idea 0 held by ,o/wald#ah tw5ty & m ye>s ago1 & is n[ mu* to ! front because ( ! connection betwe5 mass & en]gy indicat$ by ! !ory ( relativity1 & ! important rle assign$ to en]gy levels 9 spectrum analysis4 ,footnote #ah3 ,w4 ,o/wald1 ,die ,en]gie1 ,b>?1 ,leipzig1 #aijh4 ,:at n[ is ! precise nature & significance ( ! g5]al en]gy concept8 ,9 ! fir/ place ! cons]vation prop]ty ( en]gy is "o ( ! simple/ & mo/ obvi\s ( ! prop]ties ( matt]1 s t 9 ?is prop]ty ( en]gy is se5 a reason = ascrib+ to x c]ta9 ( ! prop]ties ( matt]1 9 p>ticul> & mo/ important1 t ( localization 9 space4 ,we mu/ recognize1 h[ev]1 t ?is idea ( a location 9 space is inject$ into ! situation entirely by ourselves1 & corresponds to no?+ directly giv5 by ! op]ations ( exp]im5t4 ,! idea has _h a mo/ important effect1 h[ev]4 ,witness1 = in/ance1 ! importance ascrib$ to ! discov]y by ,kelv9 ( a function by :i* ! total en]gy ( an electric field c be repres5t$ z di/ribut$ ?r\gh space2#ai ?is 0 "o ( ! mo/ important props ( ! m$ium po9t ( view4 ,footnote #ai3 ,?is function is times ! scal> product ( electric =ce & displacem5t4 ,if ,maxwell's def9ition ( displacem5t is adopt$1 ! factor is replac$ by 1 & an accurate analogy results betwe5 ! en]gy /or$ 9 ! e!r & ! ela/ic en]gy /or$ 9 a b5t spr+4 ,a m critical exam9ation is likely to dim9i% consid]ably our satisfaction ) ?is naive analogy drawn betwe5 matt] & en]gy4 ,) reg>d to matt]1 we may /ill be tol]ably satisfi$ ) our ascription to matt] ( location 9 space1 b x is q diff]5t ) reg>d to cons]vation ( matt]4 ,9 j :at s5se is matt] cons]v$8 ,c]ta9ly n 9 t]ms ( mass1 z we at "o "t ?\ght4 ,nev]!less we und5iably h a feel+ t !re is "s sort ( cons]vation prop]ty "h1 & are driv5 to =mulate x badly 9 t]ms ( a hypo!tically con/ant numb] ( protons & electrons4 ,i h long ?\ght t ,newton 0 grop+ aft] "s v simil> idea :5 he s f> =got himself z to def9e mass z quantity ( matt]1 a def9ition p]fectly mean+less to a rigor\s & unsympa!tic int]pretation4 ,on ! o!r h&1 :atev] mean+ may reside 9 our idea ( cons]vation ( matt]1 x c]ta9ly is n1 9 at lea/ "o important respect1 l ! cons]vation ( en]gy4 ,= ! en]gy ( an isolat$ me*anical sy/em is a function ( ! frame ( ref]5ce 9 :i* x is describ$2 m]ely by giv+ velocity to ! ref]5ce frame & alt]+ 9 no way ! me*anical sy/em we may *ange its k9etic1 & s its total1 en]gy by any direct am\nt4 ,?is does n ev5 remotely resemble ord9>y matt]4 ,i _c see t ! op]ations :i* are equival5t to ! en]gy concept ju/ify u 9 say+ m ?an t en]gy is a prop]ty ( a mat]ial sy/em2 ! op]ations d n seem to give any unique mean+ to a location associat$ ) en]gy4 ,we n[ ask :at significance is to be ascrib$ to ! sort ( cons]vation t en]gy does h4 ,we re/rict ourselves fir/ to me*anical sy/ems4 ,! motions ( a me*anical sy/em satisfy c]ta9 diff]5tial equations ( ! second ord]1 & ! actual motion is to be f\nd by an integration ( ! equations4 ,9 ! integral ( a diff]5tial equation c]ta9 con/ants appe> :i* are det]m9$ by ! initial conditions1 & are !re=e ! same dur+ all ! future motion ( ! sy/em2 obvi\sly ^! con/ants ( motion correspond to cons]vative prop]ties4 ,?is reason+ c ( c\rse be at once ext5d$4 ,any sy/em1 me*anical or n1 ^: motion is det]m9$ by diff]5tial equations1 w h c]ta9 cons]vative prop]ties4 ,= ! sy/ems ( me*anics en]gy is "o ( ! cons]vative functions2 o!rs are mom5tum & mom5t ( mom5tum4 ,en]gy is p>ticul>ly simple1 9 t x is connect$ ) measurable prop]ties ( ! sy/em by a simple =mula 7 mv#b71 & is fur!rmore scal>1 :i* is also a prop]ty ( quantity ( matt]4 ,b to g fur!r & ascribe to en]gy o!r prop]ties ( matt]1 su* z localization 9 space1 is entirely ov]look+ ! ess5tial diff]5ce 9 ! "* ( ! op]ation by :i* matt] & quantity ( en]gy are measur$1 t is1 ov]look+ ! ess5tial diff]5ce 9 _! physical "*4 ,! possible ext5sion ( ! en]gy concept f me*anics to !rmodynamics receives a suffici5t physical explanation 9 t]ms ( our views ( ! ess5tially me*anical "* ( !rmal ph5om5a4 ,t ! idea c be ext5d$ also to simple electrical or magnetic sy/ems1 9 :i* ! effect ( velocity ( propagation is neglect$1 is a consequ5ce ( ! fact t 9 ^! sy/ems ! equations ( motion rema9 ( ! same g5]al me*anical type1 x hav+ be5 %[n by ,maxwell t ! equations ( su* sy/ems may be writt5 9 ! g5]aliz$ ,lagrangean =m4 ,:51 h[ev]1 we ext5d our =mulas to sy/ems 9 :i* ! velocity ( propagation is important 7t is1 :5 we consid] ! field equations 9 _! g5]al =m7 we f9d t ! ,lagrangean equations no long] apply to matt] tak5 by itself1 & en]gy is no long] cons]v$ 9 ! orig9al s5se4 ,a new function appe>s1 h[ev]1 :i* behaves ma!matically 9 ! same way t ! en]gy did be=e4 ,! equations ( motion ( ! sy/em rema9 ,lagrangean 9 =m if ! me*anical p>ts ( ! sy/em are supplem5t$ by ! electric & magnetic fields 9 space4 ,9 ?is ext5d$ =m we h1 !re=e1 a cons]vative function z be=e1 & ! en]gy concept may be reta9$ 9 ?is enl>g$ aspect4 ,! physical op]ations by :i* en]gy is det]m9$ are entirely alt]$1 h[ev]1 & ! physical "* ( ! concept is *ang$4 ,no m ?an be=e is !re ju/ification = localiz+ en]gy 9 space1 or ascrib+ to x o!r prop]ties ( matt]4 ,yet ! mat]ialization ( ! en]gy concept1 & ! consequ5t desire t en]gy be localiz$ 9 space1 is "o ( ! /ronge/ argum5ts 9 _m m9ds = ! exi/5ce ( a m$ium4 ,z f> z ,i c see1 !re=e1 ! exi/5ce ( cons]vative functions is involv$ 9 ! possibility ( describ+ natural ph5om5a ) diff]5tial equations4 ,t fur!r !re is a cons]vative function ( ! precise =m f\nd 9 me*anics is a consequ5ce ( ! p>ticul> =m ( ! equations & ! nature ( ! =ces4 ,! "q ( ! significance ( ! fact t ! =ces ( nature appe> to be cons]vative1 ) respect to ?is p>ticul> function ( me*anics1 is ( mu* int]e/1 b x is n our imm$iate conc]n n[4 ,we are int]e/$ r to ask "u :at g5]al conditions we %all h cons]vative functions4 ,quantum !ory /rongly sugge/s t :5 we pass to ph5om5a on a small en\gh scale1 we may no long] be able to employ diff]5tial equations 9 our descriptions1 & h5ce ! previ\s reason = ! exi/5ce ( con/ants connect$ ) ! motion disappe>s4 ,n[ !re is "o obvi\s rem>k to be made ab\t ?is m g5]al situation4 ,:5ev] ! future hi/ory ( a sy/em is s connect$ ) its pres5t condition t we c retrace our way to ! pres5t f any future configuration1 we %all always h cons]vative functions4 ,= any future configuration conta9s c]ta9 fix$ 7or cons]vative7 features1 9 t we c recon/ruct ! unique pres5t f any future /ate4 ,!re is no reason to expect t ! op]ations by :i* we f9d ! fix$ features w always be simple1 z 9 ! me*anical case4 ,n[ ! det]m9ation ( ! future by ! pres5t1 & conv]sely ! possibility ( recon/ruct+ ! pres5t f ! future 7or ! pa/ f ! pres5t71 is1 we are conv9c$1 a prop]ty :i* is at lea/ approximately true ( ph5om5a d[n to a small] scale ( magnitude ?an we h yet rea*$1 & s we expect to f9d ^! cons]vative functions 9 sy/ems ^: ultimate laws ( motion are mu* m g5]al ?an any ) :i* we are yet famili>4 ,! p>ticul> =m ( ! cons]vative function dep5ds on ! "* ( ! sy/em4 ,t !re is a scal> cons]vative function = ord9>y sy/ems dep5ds ( c\rse on p>ticul> prop]ties ( ! sy/em1 b we are at lea/ prep>$ to f9d t a scal> cons]vative function does n necess>ily mean a diff]5tial equation ( ! second ord]4 ,! pot5tial en]gy ( a sy/em has a p>ticul> significance ) respect to ?is po9t ( view4 ,9 an ord9>y me*anical sy/em1 ! pot5tial en]gy simply measures ! "w done by ! appli$ =ces 9 be+ displac$ f ! initial to ! f9al positions2 t is1 ! pot5tial en]gy is a measure ( ! deviation f ! initial position1 & s measures a c]ta9 feature ( ! hi/ory ( ! sy/em4 ,9 ! m g5]al sy/em1 9 :i* we may n h diff]5tial equations1 we may look = some?+ analog\s to ! pot5tial en]gy :i* %all measure ! displacem5t ( ! sy/em f its initial configuration4 ,su* a measure is always possible z long z ! pa/ c be recon/ruct$ f ! pres5t 7or ! pres5t f ! future74 ,we recall a rem>k ( ,po9c>'s#bj to ! effect t we ( necessity mu/ always h cons]vation1 because if we h a sy/em 9 :i* cons]vation app>5tly fails1 we m]ely h to inv5t a new =m ( pot5tial en]gy4 ,?is rem>k is obvi\sly n ( entire g5]ality1 b applies only to su* sy/ems z ^? consid]$ "h1 9 :i* ! pa/ may be recon/ruct$ f ! pres5t4 ,footnote #bj3 ,h5ri ,po9c>1 ,wiss5s*aft und ,hypo!se1 translat$ into ,g]man by ,f4 & ,l4 ,l9demann1 ,teubn]1 ,leipzig1 #aijf1 ,*ap4 ,,viii4 ,( late !re has be5 mu* discussion ( ! advisability1 on ! basis ( c]ta9 quantum ph5om5a1 ( giv+ up cons]vation z a pr9ciple appli$ to ! details ( ! emission & absorption ( light1 reta9+ x only 9 a /ati/ical s5se4 ,x seems to me t ! "q "h 9 ! m9ds ( physici/s 0 always m]ely "o ( conv5i5ce1 & t few1 if any1 d\bt$ ! ultimate applicability ( ! pr9ciple ( ,po9c>1 or ?\ght t we 7 "h conc]n$ ) a sy/em ( su* great g5]ality t ! pa/ c\ld n be recon/ruct$ f ! pres5t4 ,! "q 0 m]ely :e!r ^? v>iables 9 t]ms ( :i* ! pot5tial en]gy is def9$ make close en\gh connection ) o!r ?+s ( imm$iate exp]im5tal significance1 or :e!r on ! :ole ! ret5tion ( a pot5tial en]gy is n m tr\ble ?an is ju/ifi$ by its conv5i5ce1 mak+ a treatm5t f ! /ati/ical po9t ( view pref]able4 ,h[ev]1 ?is is all n[ a matt] ( m or less pa/ hi/ory1 because ) ! rec5t ext5sion ( ! exp]im5ts ( ,compton1#ba we seem to h exp]im5tal evid5ce = ! validity ( ! cons]vation law 9 detail = elem5t>y quantum processes1 ) a correspond+ simple pot5tial en]gy4 ,footnote #ba3 ,w4 ,bo! & ,h4 ,geig]1 #b,s4 f4 ,phys4 #cb1 #fci-ffc1 #aibe4 ,a4 ,h4 ,compton1 ,proc4 ,nat4 ,acad4 ,soc41 ,,ii1 #cjc-cjf1 #aibe4 ,go+ /ill deep]1 h[ev]1 !re are quantum ph5om5a :i* /ill may h to be treat$ by /ati/ical me?ods1 & ?is may mean giv+ up cons]vation 9 detail4 ,we h no exp]im5tal evid5ce1 = example1 ( :at ! electron is do+ :ile jump+ f "o quantum orbit to ano!r4 ,a situation l ?is m]ely means t ^? details :i* det]m9e ! future 9 t]ms ( ! pa/ may lie s deep 9 ! /ructure t at pres5t we h no imm$iate exp]im5tal k ( !m1 & we may = ! pres5t be compell$ to give a treatm5t f a /ati/ical po9t ( view bas$ on consid]ations ( probability4 ,b ,i suppose t no "o1 except p]haps ,norman ,campbell1#bb w ma9ta9 t su* a situation is m ?an tempor>y1 or w cease to se>* = consequ5ces ( ^! details ( /ructure :i* may be op5 to exp]im5tal v]ification4 ,footnote #bb3 ,norman ,campbell1 ,"t & ,*ance1 ,phil4 ,mag4 ,i1 #aajf-aaag1 #aibf4 ,simil>ly1 we _c p]man5tly be satisfi$ ) a picture ( radioactive ph5om5a :i* repres5ts radioactive dis9tegration z a matt] ( *ance4 ,! g5]al conclusion to :i* all ?is discussion leads is t en]gy is probably n entitl$ to ! fundam5tal position t physical ?\ght is incl9$ to give x1 b t x is a m or less incid5tal consequ5ce ( m deep-seat$ prop]ties1 & t ! "* ( ^! deep-seat$ prop]ties is subject to only ! mo/ g5]al re/rictions1 s t v little ab\t ! nature ( ! details c be inf]r$ f ! exi/5ce ( any en]gy function4 ,,! ,,concepts ,,( ,,!rmodynamics ,we %all n be conc]n$ "h ) ! _m te*nical que/ions :i* are ! prop] subject ( treatises on !rmodynamics1 b %all attempt an exam9ation only ( "s fundam5tal concepts4 ,! mo/ fundam5tal ( ^!1 :i* sets !rmodynamics (f ap>t f ! simpl] subjects1 is probably t ( temp]ature4 ,9 orig9 ?is concept 0 )\t "q physiological1 9 mu* ! same way z ! me*anical concept ( =ce 0 physiological4 ,b j z ! =ce concept 0 made m precise1 s ! temp]ature concept may be m or less divorc$ f its crude significance 9 t]ms ( imm$iate s5sation & be giv5 a m precise mean+4 ,?is precision may be obta9$ ?r\gh ! notion ( equilibrium /ates4 ,we h 9 ! fir/ place ! fundam5tal exp]im5tal fact t :5 a small body is plac$ inside a l>ge sy/em1 :i* we recognize by crude means z comp>atively inv>iable 9 temp]ature z "t goes on1 ! small body v soon acquires a /eady condition1 t is1 x comes to equilibrium ) its surr\nd+s4 ,we n[ h ! fur!r exp]im5tal fact t if ! small body ,a is 9 equilibrium ) its environm5t1 & body ,b is also 9 equilibrium ) ! same environm5t1 !re w be no *ange ( condition ( ,a & ,b :5 !y are br\ght into contact ) ea* o!r--t is1 ,a & ,b are ea* 9 equilibrium ) ! o!r & also ) ! environm5t & !re=e1 by def9ition1 at ! same temp]ature z ! environm5t4 ,! temp]ature ( ! environm5t is n[ measur$ 9 t]ms ( "s ( ! prop]ties ( ,a & ,b :i* crude exp]i5ce has %[n *ange ) ! physiological temp]ature ( ,a & ,b4 ,! physiological notion ( temp]ature is ?us made m precise by be+ connect$ ) ! physical ph5om5on ( equilibrium4 ,n[ x is at once evid5t t /at$ 9 ?is way )\t qualification we h said ?+s t are n true4 ,x is n true 9 g5]al t1 :5 ,a is 9 equilibrium ) an environm5t & ,b is 9 equilibrium ) ! same environm5t1 ,a w be 9 equilibrium ) ,b4 ,suppose1 = example1 t ! environm5t is a /ream ( wat] & ,a is a t9y wat] :eel mov+ freely 9 its be>+s1 & t ,b is a simil> :eel ) mu* friction4 ,!n we "k t ,b w become w>m1 & w n be 9 equilibrium ) ,a :5 br\ght into contact ) x4 ,or we may *oose = ,a a m]cury !rmomet] ) bulb cov]$ ) putty1 & = ,b a simil> !rmomet] ) bulb %ea!d 9 plat9um1 & we "k t ! two !rmomet]s w n regi/] ! same temp]ature 9 ! wat] /ream4 ,or /ill m simply1 we may try to read ! temp]ature ( ! air 9 our g>d5 on any bright day ) a silv]$ & ) a black5$ bulb !rmomet]2 we "k t ! two !rmomet]s w read diff]5t temp]atures4 ,x is evid5t1 !re=e1 t we %all h to specify mu* m c>efully ! conditions "u :i* equilibrium holds if we are to give precise significance to ! temp]ature concept4 ,x seems fairly evid5t 9 ! fir/ place t we %all h to rule out sy/ems 9 :i* !re is l>ge scale me*anical motion2 ! simple notion ( temp]ature does n apply to a sy/em mov+ ) respect to u4 ,only :5 ! two !rmomet]s ,a & ,b move ) ! same velocity z ! /ream d we h ?ree-fold equilibrium betwe5 ! /ream1 ,a & ,b4 ,we may /ate ?is 9 ano!r way by say+ t ! temp]ature ( a mov+ body mu/ be measur$ on a !rmomet] /ation>y ) respect to ! body1 b ?is is only a matt] ( words1 & prop]ly speak+ ! temp]ature concept applies only to a c]ta9 aspect ( ! relation betwe5 two bodies mutually at re/4 ,we "h entirely neglect relativity que/ions su*1 = example1 z ! prop] way ( correct+ = ! *ange ( dim5sions ( mov+ !rmomet]s4 ,if n[ ! body ^: temp]ature we are measur+ does n move ) ! same velocity 9 all its p>ts1 we may /ill give a mean+ to local temp]ature by divid+ ! body into p>ts s small t ! velocity ( ea* "p is ess5tially uni=m1 & measur+ ! temp]ature ( ea* "p ) a !rmomet] /ation>y ) respect to x4 ,we are n[ confront$ ) ! "q ( h[ f> to c>ry ! process ( subdivision4 ,suppose we h a fluid ^: motion is completely turbul5t :5 measur$ ) in/rum5ts ( ! ord9>y scale ( magnitude4 ,= su* a fluid ! fundam5tal equilibrium proportions hold betwe5 two measur+ bodies ,a & ,b & ! fluid1 provid$ t ! bodies ,a & ,b are s l>ge t ! motion is completely turbul5t on _! scale ( magnitude4 ,we may !n def9e ! temp]ature ( ! turbul5t fluid f ! /&po9t ( ^! l>ge scale bodies4 ,b we may also def9e ! temp]ature f ! small scale po9t ( view z ! av]age ( ! temp]atures record$ by suffici5tly small !rmomet]s1 ea* mov+ ) ! velocity ( a local bit ( ! fluid4 ,^! two temp]atures w 9 g5]al be diff]5t1 & we mu/ m or less arbitr>ily select "o :i* we def9e z ! true temp]ature4 ,x w\ld seem t ! small scale temp]ature is ! bett] "o to *oose1 because !re is a c]ta9 degree ( arbitr>9ess 9 specify+ ! scale f :i* ! motion %all be judg$ completely turbul5t ,b on ! o!r h&1 !re are difficulties 9 ! small scale def9ition1 because ! turbul5ce may become m & m f9e gra9$1 until we end ) ! motion ( ! molecules !mselves1 :5 ! op]ations c]ta9ly fail :i* give mean+ to ! temp]ature concept4 ,9 ?is case ( molecul> turbul5ce1 we are driv5 back to ! l>ge scale def9ition1 :i* obvi\sly corresponds to ord9>y physical practice4 ,x appe>s !n t ! temp]ature concept is n a clean cut ?+1 :i* c be made to apply to all exp]i5ce1 b t x is m or less arbitr>y1 involv+ ! scale ( our measur+ in/rum5ts4 ,9 any special case1 ! mean+ ( ! temp]ature concept mu/ be set by special conv5tion4 ,9 practice ?is does n (t5 make difficulty1 because 9 ! majority ( cases !re is no l>ge scale motion ) respect to ! !rmomet]s4 ,consid] n[ ! o!r aspect ( ! equilibrium problem sugge/$ by ! !rmomet]s ) black5$ & silv]$ bulbs 9 ! sun%9e4 ,our common exp]i5ce tells u h[ to deal ) ?is situation effectively en\gh = ord9>y purposes4 ,we recognize t ! possibility ( temp]ature equilibrium is di/urb$ by ! radiation1 & we protect ! bulbs ( ! !rmomet]s f ! sun's radiation by appropriate %ields4 ,b ?is only m9imizes ! difficulty4 ,= ! %ield is w>m$ by ! sun1 & 9 turn w>ms to a less degree by its radiation ! bulb ( ! !rmomet] )94 ,we mu/ recognize t e body1 no matt] :at its temp]ature1 is always emitt+ radiation1 s t ! bulb ( our !rmomet] is always 9 a radiation field4 ,at fir/ ?is puts u 9 a s]i\s qu&>y z to ! :ole "q ( equilibrium & ! mean+ ( temp]ature4 ,! situation is sav$ by ! exp]im5tal obs]vation t !re is a p>ticul> radiation field :i* affects all !rmomet]s equally1 namely1 ! field inside an inf9ite body all at ! same temp]ature4 ,logically ?is looks l ! vici\s circle aga91 = we h n yet def9$ :at we mean by ! same temp]ature4 ,b actually we avoid ! circle "h1 z 9 s _m o!r physical cases1 by a process ( asymptotic approximation4 ,! proc$ure is p]haps some?+ l ?is3 we f9d t if we exp]im5t ) l>g] & l>g] bodies1 isolat$ & at great di/ances f o!r bodies at approximately ! same temp]ature z judg$ by crude physiological s5sations1 two !rmomet]s1 id5tical except t ! bulb ( "o is black5$ & t ( ! o!r is silv]$1 record m ne>ly ! same temp]ature z "t goes on & z ! !rmomet]s are sunk to great] dep?s 9 ! body4 ,9 actual practice1 ( c\rse1 ! radiational opacity ( mo/ bodies is s high t ^! precautions aga9/ ! effects ( ext]nal radiation c usually be entirely ignor$4 ,at high temp]atures1 on ! o!r h&1 radiation has to be explicitly dealt )4 ,! conclusion = u f ^! consid]ations is t op]ationally ! concept ( temp]ature is ti$ up ) t ( radiation--! equilibrium concept ( temp]ature is /rictly nev] exactly applicable2 x is only a limit+ sort ( concept applicable :5 ! radiation field is ( a special sort1 namely1 t ( a black body4 ,9 spite ( ! explicit recognition :i* we h to give radiation 9 def9+ temp]ature1 we usually entirely lose sight ( x 9 ?9k+ ab\t ! me*anism ( ord9>y physical processes1 z = in/ance :5 we picture ! temp]ature ( a gas z det]m9$ by ! k9etic en]gy ( its molecules4 ,n[ ,i h no d\bt t neglig5ce ( ?is sort c be ju/ifi$1 b ! necess>y logical analysis is app>5tly complicat$1 & involves a great _m diff]5t sorts ( exp]im5t by me?ods ( asymptotic approximation1 by :i* we e/abli% ! exi/5ce ( v>i\s sorts ( physical con/ants1 su* z con/ants ( emission & absorption & reflection & scatt]+ & fluoresc5ce & !rmal conductivity4 ,we d n ne$ to make ! analysis "h1 b ,i believe t "s "t x w\ld be wor? :ile to attempt x4 ,su* an analysis w ju/ify ! pr9ciple s (t5 us$3 t if a body is 9 !rmal equilibrium ! v>i\s processes involv$1 su* z radiation or !rmal conductivity1 mu/ :5 tak5 sep>ately also be 9 equilibrium4 ,d\btless1 if our exp]i5ce _h be5 conf9$ to high] temp]atures1 l t ( ! sun1 ?is notion ( diff]5t me*anisms act+ indep5d5tly w\ld h be5 m difficult to acquire4 ,we next consid] ano!r fundam5tal concept ( !rmodynamics1 t ( quantity ( heat4 ,we are at fir/ p]haps incl9$ to ?9k ( ?is z a comp>atively /raight=w>d concept1 giv5 imm$iately 9 t]ms ( exp]i5ce1 b an analysis ( ! op]ations by :i* we measure quantity ( heat w %[ t ! situation is really mo/ complicat$4 ,consid]1 = example1 ,j\le's exp]im5t 9 :i* ! me*anical equival5t ( heat 0 measur$ by det]m9+ ! rise ( temp]ature ( ! wat] 9 a conta9] :5 /irr$ by paddles driv5 by a fall+ weight4 ,we d n "q t ! rise ( temp]ature ( ! wat] has its orig9 9 ! me*anical "w done on x by ! paddles4 ,b :at ab\t ! rise ( temp]ature ( ! conta9]8 ,we %all d\btless say t "p ( ?is rise comes f heat communicat$ to x by ! w>m] wat] 9 contact ) x1 & "p f me*anical "w done on x by turbul5t impact ( ! wat]4 ,b by :at op]ations %all we measure :at "p ( ! en]gy communicat$ to ! conta9] is heat & :at "p me*anical "w8 ,we try to give an idealiz$ answ] to ?is "q 9 t]ms ( ,maxwell demons /ation$ at all p>ts ( ! b\nd>y ( ! conta9+ vessel ) small scale measur+ in/rum5ts4 ,to measure ! heat ent]+ at any po9t ,i c see no?+ else = ! ,lilliputian obs]v]s to d b to det]m9e ! temp]ature gradi5t at e po9t ( ! b\nd>y f temp]ature obs]vations at two diff]5t levels1 & calculate ! heat infl[ f ! gradi5t & ! !rmal conductivity ( ! mat]ial ( ! walls--!re seems no way ( measur+ a fl[ ( heat z su*4 ,! infl[ ( me*anical en]gy mu/ be calculat$ f a detail$ k ( ! ela/ic waves & o!r l>ge scale de=mations ( ! walls4 ,"h aga9 !re is an arbitr>y elem5t 9 our proc$ure2 if our me*anical measur+ in/rum5ts are on too gross a scale1 we may miss me*anical en]gy :i* we w\ld cat* ) f9] in/rum5ts4 ,?is situation :i* we h j submitt$ to detail$ analysis is1 ,i believe1 typical ( ! g5]al situation2 x is n possible 9 ! g5]al case to f9d any?+ :i* we c call heat z su*4 ,)\t fur!r explicit exam9ation1 we c unambigu\sly speak ( a body los+ or ga9+ heat only :5 !re has be5 no en]gy int]*ange ( any o!r sort ) o!r bodies4 ,9 su* a case ! heat is measur$ 9 t]ms ( ! temp]ature *ange ( ! body4 ,! heat concept is 9 ! g5]al case a sort ( wa/ebasket concept1 def9$ negatively 9 t]ms ( ! en]gy left ov] :5 all o!r =ms ( en]gy h be5 all[$ =4 ,! ess5tial fact t a quantity ( heat c by itself be def9$ only 9 t]ms ( a drop ( temp]ature is some:at obscur$ by ! usual me?od ( !rmodynamic analysis4 ,9 describ+ a ,c>not eng9e1 = example1 x is specifi$ t ! eng9e %all "w betwe5 a s\rce & a s9k s l>ge t _! temp]ature is n *ang$ by ! heat giv5 out or absorb$ by !m1 s t ! impression is natural t heat may 9 "s way be measur$ ap>t f temp]ature *anges4 ,?is ( c\rse is n ! case2 we m]ely require t ! s\rce & s9k be s l>ge t _! temp]ature *anges are ( a diff]5t ord] ( magnitude f ^? 9 ! work+ sub/ance itself1 s t ) respect to ! work+ sub/ance1 s\rce & s9k may be consid]$ to be at con/ant temp]ature4 ,assum+ n[ t we are able to measure quantity ( heat 9 ^? cases 9 :i* ! concept has mean+1 let u exam9e ! fir/ law ( !rmodynamics1 :i* we write 9 ! =m3 d,q d,w d,e ,"h d,q is ! heat imp>t$ to a giv5 body by o!r bodies1 d,w is ! "w ( all k9ds done on x f outside1 & d,e is ! increase ( int]nal en]gy4 ,n[ if ?is equation says :at appe>s at a nave fir/ glance1 x %\ld say t we f9d exp]im5tally t ! relation writt5 always holds betwe5 ! measur$ quantities d,q1 d,w1 & d,e4 ,we h se5 t 9 ! g5]al case x is n possible to assign a unique op]ational significance to d,q & d,w1 & presumably n to _! sum4 ,we ignore = ! pres5t difficulties ( ?is k9d & conf9e att5tion on d,e2 h[ %all we measure x8 ,i believe x does n take mu* exam9ation to conv9ce u t !re are no physical op]ations = measur+ d,e z su*1 & t !re=e ! equation express+ ! fir/ law mu/ h a diff]5t significance f t :i* appe>s on ! surface4 ,?is is (t5 recogniz$ 9 ! /atem5t t ! ess5ce ( ! fir/ law is t d,e is an exact diff]5tial det]m9$ only by ! v>iables :i* fix ! int]nal condition ( ! body1 & n a function ( ! pa? by :i* ! body is c>ri$ f "o condition to ano!r4 ,b :at %all we mean by int]nal condition1 & h[ %all we be sure t we h f\nd all ! v>iables requir$ to specify x completely8 ,int]nal condition may be a mo/ complicat$ ?+ & require _m v>iables1 z %[n by a piece ( iron ) a complicat$ magnetic hi/ory or by a piece ( alum9um ab\t to und]go recry/allization aft] ov]/ra94 ,"h aga9 ,i believe !re is no physical proc$ure by :i* g5]al mean+ c be giv5 to ?is concept ( int]nal condition4 ,9 specific cases we c /ate :at ! v>iables are :i* det]m9e int]nal condition1 & ! crit]ion t we h f\nd ! correct int]nal v>iables is t d,e %all be a complete diff]5tial 9 t]ms ( !m4 ,! fir/ law ( !rmodynamics prop]ly und]/ood is n at all a /atem5t t en]gy is cons]v$1 = ! en]gy concept )\t cons]vation is mean+less4 ,! ess5ce ( ! fir/ law is conta9$ 9 ! /atem5t t ! en]gy concept exi/s 7or has mean+ 9 t]ms ( op]ations74 ,! fir/ law is (t5 ?\ght to be "o ( ! mo/ g5]al ( physics1 b 9 a p>adoxical s5se x is ! mo/ special ( all laws1 because no g5]al mean+ c be giv5 to ! en]gy concept1 b only specific mean+ 9 special cases4 ,! fir/ law owes its complete g5]ality to ! fact t no specific case has yet be5 f\nd ( s broad a "* t x _c be includ$ "u "o or ano!r special case4 ,exam9ation w at once ju/ify ?is view4 ,?us we f9d a great _m sy/ems :i* are adequately describ$ 9 t]ms ( two v>iables1 pressure & temp]ature1 9 t a function ( p & t c be f\nd su* t its diff]5tial equals d,q d,w4 ,!re are o!r sy/ems 9 :i* ! six compon5ts ( /ress & t completely fix ! int]nal condition 9 ! s5se t !y det]m9e a d,e4 ,9 o!r sy/ems ! specification ( a magnetic field may be necess>y1 or an electric1 or a gravitational field4 ,no case is kn[n :i* _c be h&l$ 9 t]ms ( ! action ( ext]nal =ces ( ! prop] k9d1 b !re is no g5]al proc$ure1 & ! fir/ law owes its g5]ality to ! exhau/ive catalog+ ( special cases4 ,we may n[ return to ! "q left 9 abeyance above ( ! ambiguity 9 d,q d,w4 ,9 all ! cases 9 :i* ! specific v>iables c be f\nd :i* def9e d,e1 d,q & d,w also h mean+4 ,consid]1 = example1 a gas1 ! int]nal condition ( :i* may be *>act]iz$ 9 t]ms ( t & p4 ,! m]e fact t ! int]nal condition c be specifi$ 9 t]ms ( two v>iables1 "o a me*anical v>iable1 %[s t ! sub/ance is me*anically homog5e\s4 ,be+ me*anically homog5e\s1 we d n h ! possibility ( ambigu\s values ( d,w v>y+ ) ! scale ( ! measur+ in/rum5ts1 & 9 fact we "k t d,w p dv4 ,simil>ly ! gas be+ homog5e\s & at re/ z a :ole all[s unique values = d,q4 ,( c\rse ?is _c obscure ! physical fact t ev5 9 su* a gas1 :5 we g to a small en\gh scale1 we f9d inhomog5eities aris+ f ! ,br[nian movem5t1 etc4 ,practically our /atem5t means t ! inhomog5eities are s f9e gra9$ t ov] a v wide range ( scale ( ! measur+ in/rum5ts we f9d ! same def9ite results4 ,! same sort ( consid]ations apply to m complicat$ sy/ems4 ,if d,e is a complete diff]5tial 9 t]ms ( t & six /ress compon5ts1 ?is means aga9 t ! body is homog5e\s1 its condition is det]m9$ by temp]ature & /ress1 :i* are ! same ?r\gh\t ! body1 & aga9 !re is no possible ambiguity f ! scale ( ! in/rum5ts :i* measure d,w & d,q4 ,x seems 9 g5]al1 !n1 t if ! body all[s op]ations by :i* d,e acquires mean+1 at ! same "t d,q & d,w are provid$ =4 ,9 work+ out ?is idea 9 full detail1 "s c>e mu/ be giv5 to ! "q ( ord] ( diff]5tials4 d,q1 = unit "t & unit volume1 is /rictly equal to k#b t1 :]e k is !rmal conductivity1 s t 9 det]m9+ d,q ! second d]ivatives ( temp]ature are involv$4 ,if ! body is obvi\sly n homog5e\s1 x is /ill a matt] ( exp]i5ce t x c be divid$ into small pieces1 ea* ( :i* are by !mselves suffici5tly homog5e\s1 & ! fir/ law 9 its usual =m may be appli$ to ea* ( ! pieces4 ,f9ally1 we emphasize a fact already implicitly m5tion$1 namely1 t no physical significance c be directly giv5 to fl[ ( heat1 & !re are no op]ations = measur+ x4 ,all we c measure are temp]ature di/ributions & rates ( rise ( temp]ature4 ,z at pres5t def9$1 a heat curr5t is a pure inv5tion1 )\t physical reality1 = any det]m9$ heat fl[ may always be modifi$ by ! addition ( a sol5oidal vector1 ) *ange 9 no measurable quantity4 ,if someone /ates t ?r\gh\t all space !re is a uni=m heat curr5t ( #ajf cal4_/cm4#b sec4 9 ! direction ( ,pol>is1 no dispro( c be giv51 = su* a /ream is sol5oidal1 & z mu* heat fl[s out ( e clos$ surface 9 unit "t z fl[s 94 ,su* a sol5oidal fl[ is mean+less 9 t]ms ( op]ations2 we c\ld give mean+ to su* a fl[ only 9 t]ms ( "s slight modification ( ! sol5oidal condition introduc$ by ! measur+ in/rum5t4 ,9 all ord9>y conditions ! fl[ ( heat giv5 by ! simple relation q k ,grad t corresponds exactly to :at our atomic pictures lead to expect 9 ^? cases :]e ! details ( ! picture c be work$ out4 ,b !re may be cases :]e x is advantage\s to supplem5t ! ord9>y heat fl[ 7 k ,grad t7 by ! pure fiction ( a sol5oidal fl[1 because 9 ?is way x may be possible to acc\nt = new ph5om5a :i* appe> :5 ! sol5oidal conditions are slightly dep>t$ f4 ,?us if 9 a conductor at uni=m temp]ature c>ry+ a /eady electric curr5t we say t a heat curr5t is also fl[+ proportional to ! electric curr5t & !re=e sol5oidal1 we may provide ! possibility = a simple correlation ( ph5om5a f\nd "u ^? m complicat$ conditions :5 an electric curr5t fl[s 9 a conductor ( non-uni=m temp]ature 9 a magnetic field4 ,if x %\ld turn out t ! heat curr5t is uniquely det]m9$ by consid]ations ( ?is "*1 !n we h tak5 ! fir/ /ep away f ! pure =malism :i* ?is sort ( ?+ o!rwise is 9 ! direction ( giv+ physical reality to ! inv5tion ( heat curr5t4 ,!re are o!r int]e/+ que/ions ( a fundam5tal !rmodynamic "*1 su* = example1 z :e!r ! entropy concept has any g5]al significance ap>t f ! scale ( our measur+ in/rum5ts1 & :at is ! op]ational significance ( apply+ !rmodynamic concepts to radiation1 b we %all n consid] ^! que/ions "h4 ,,electrical ,,concepts ,we n[ set ourselves ! problem ( f9d+ ! mean+ ( ! v>i\s concepts 9 t]ms ( :i* we describe ! behavior ( electrical sy/ems1 assum+ t we und]/& :at we mean by electrical4 ,we />t ) ! simple/ electrical sy/ems1 namely1 ^? 9 :i* we deal ) /atic ph5om5a on a l>ge scale4 ,9 su* sy/ems !re are indep5d5t physical op]ations by :i* we may f9d ! magnitude ( any *>ge1 provid$ t x is effectively conc5trat$ 9 a geometrical po9t4 ,! measurem5ts involv$ 9 ^! op]ations are measurem5ts ( ord9>y me*anical =ces2 we assume t our k ( me*anics has already taught u h[ to make su* measurem5ts4 ,an electrically *>g$ body exp]i5ces =ces1 :i* may be measur$ by ty+ a /r+ to x & pull+ on ! /r+ ) a spr+ balance h>d en\gh to keep ! body 9 equilibrium4 ,?ree *>ges are num]ically equal if :5 ea* is plac$ at unit di/ance f ano!r1 9 ! abs5ce ( ! ?ird 7or o!r *>ge71 ! =ces are always ! same4 ,if fur!rmore ! =ces are ( unit magnitude1 ! *>ges are def9$ z unit *>ge4 ,hav+ obta9$ unit *>ge1 we def9e ! magnitude ( any o!r *>ge z equal to ! =ce :i* x exp]i5ces :5 plac$ at unit di/ance f unit *>ge4 ,?is ( c\rse is all v trite2 ! important ?+ = u is m]ely t magnitude ( *>ge1 or quantity ( electricity1 is an indep5d5t physical concept1 & t unique op]ations exi/ = det]m9+ x4 ,^! op]ations presuppose ! ability to p]=m c]ta9 op]ations ( me*anics4 ,hav+ n[ le>n$ h[ to measure electrical quantities1 we discov] exp]im5tally ! inv]se squ>e law ( =ce1 & lat] arrive at ! concept ( ! electric field4 ,z we h se51 ! field is an inv5tion2 "h we %all use ?is concept only = ! purpose = :i* ! inv5tion 0 made1 & %all n involve ourselves 9 any ( ! implications ( ascrib+ physical reality to ! field4 ,notice t z long z we deal only ) po9t *>ges we d n h to def9e field /r5g? 9 t]ms ( ! limit+ proc$ure ( mak+ ! explor+ *>ge small]1 = ! limit+ small *>ge is necess>y only to avoid ! reaction ( ! explor+ *>ge on ! positions ( ! *>ges :i* g5]ate ! field4 ,all ?is aga9 is trite2 ! important po9t is t ! op]ations by :i* ! inv]se squ>e law & ! concept ( ! field are e/abli%$ presuppose t ! *>ge is giv5 z an indep5d5t concept1 s9ce ! op]ations involve a k ( *>ges4 ,! op]ations also involve ! measurem5t ( =ces by ! ord9>y /atic proc$ure ( me*anics ) spr+ balances4 ,) ! means n[ at our comm& we e/abli% "o v important prop]ty ( electric *>ges1 namely t ! total am\nt ( *>ge on an isolat$ body ( f9ite size is cons]v$1 no matt] h[ ! *>ge is =c$ to re>range itself by ! motion ( *>ges on adjac5t bodies4 ,by proc$ures exactly l ^? outl9$ above1 we may treat all ! correspond+ magnetic quantities2 !re is =mal p>allelism betwe5 ! two sets ( ph5om5a1 b !re is ! physical diff]5ce t we h to realize a s+le magnetic pole by ! device ( us+ a v long sl5d] magnet4 ,we n[ give our electrical sy/em m fre$om1 9 t we all[ ! *>ges to be 9 motion ) respect to ea* o!r4 ,p]haps ! mo/ imm$iate "q :i* we n[ h to ask is :e!r *>ge cont9ues to be cons]v$ :5 set 9 motion1 or :e!r ! total *>ge on an isolat$ body is a function ( its velocity8 ,to answ] ?is "q we mu/ g5]alize ! proc$ure by :i* we assign$ a num]ical value to a /ation>y *>ge4 ,p]haps ! simple/ way is to all[ two unit *>ges ea* to move ) con/ant velocity1 rema9+ at unit di/ance ap>t1 & measure ) a spr+ balance ! =ce requir$ to keep !m at con/ant di/ance ap>t4 ,n[ we imm$iately f9d t ! =ce is alt]$ "u ^! conditions1 s t our fir/ impulse is to say t ! *>ge is a function ( ! velocity4 ,b z we exp]im5t fur!r1 we f9d t ! /ate ( affairs is v complicat$2 ! =ce betwe5 ! two *>ges at any mom5t ( _! motion dep5ds n only on ! *>ges1 _! di/ance ap>t1 & _! velocities1 b also on ! angle betwe5 ! l9e jo9+ !m & ! direction ( motion 9 ! l9es4 ,fur!r exp]im5t ( o!r k9ds yields o!r in=mation2 x requires a =ce to ma9ta9 a *>ge 9 uni=m motion 9 a magnetic field1 or to ma9ta9 a magnetic pole 9 motion 9 an electric field4 ,a mov+ electric *>ge ex]ts a =ce on a /ation>y magnetic pole1 s t by def9ition ! mov+ *>ge is surr\nd$ by a magnetic field1 & simil>ly a mov+ magnetic pole is surr\nd$ by an electric field4 ,return+ to our two mov+ electric *>ges1 we are impell$ to ask :e!r1 if all ^! complications are possible1 ! num]ical con/ant 7unity = /atic *>ges7 9 ! inv]se squ>e law ( =ce is a function ( velocity z well z ! magnitude ( ! *>ges !mselves8 ,if we broad5 ! "q 9 ?is way1 z we app>5tly mu/1 our problem becomes indet]m9ate1 = we are try+ to answ] two diff]5t que/ions ) a s+le k9d ( measurem5t1 namely ( ! =ce betwe5 mov+ *>ges4 ,i h _h no bett] luck on try+ o!r me?ods ( measurem5t4 ,app>5tly ! op]ations d n exi/ by :i* unique mean+ c be giv5 to ! "q ( :e!r ! magnitude ( a *>ge is a function ( its velocity4 ,on realiz+ ?is situation1 we are at fir/ emb>rass$ to "k h[ to proce$1 b we reflect t ! emb>rassm5t is n ( our own mak+1 b corresponds to a physical fact4 ,! concept ( *>ge z a unique & indep5d5t ?+ ess5tially p]ta9s only to /atic sy/ems4 ,we may ext5d ! concept to mov+ sy/ems if we wi%1 z a matt] ( conv5i5ce to ourselves1 b mu/ recognize t su* an ext5sion is an inv5tion ( ours & n a reality ( nature4 ,n[ we d make su* an ext5sion1 & we make x 9 ! simple/ possible way1 t is1 we def9e ! *>ge on an isolat$ body 9 motion z t :i* we %\ld f9d on x if we r$uc$ x to re/ & made measurem5ts accord+ to ! regul> /atic proc$ure4 ,t ?is is a conv5i5t ?+ to d dep5ds on ! exp]im5tal result t ! *>ge s f\nd is indep5d5t ( ! way 9 :i* velocity is imp>t$ to or remov$ f ! body2 9 o!r words1 :5ev] ! body is r$uc$ to re/1 ! same *>ge is always f\nd on x4 ,al?\gh ?is is pure def9ition on our "p1 x turns out to h a mo/ simple & conv5i5t connection ) exp]im5tal facts :i* 7 discov]$ aft] ! decision to treat a mov+ *>ge 9 ?is way 0 made2 ! discov]y is ( ! atomic /ructure ( electricity4 ,if !n we agree to call ea* elem5t>y *>ge a con/ant indep5d5t ( ! velocity1 ! total *>ge on a body becomes m]ely proportional to ! c\nt ( ! total numb] ( atomic *>ges on ! body1 :i* is c]ta9ly highly conv5i5t & sugge/ive4 ,hav+ n[ fix$ :at we mean by ! magnitude ( a mov+ *>ge1 we are ready to turn to ! g5]al problem ( ! behavior ( any sy/em ( *>g$ bodies 9 motion4 ,= ! pres5t we consid] only ph5om5a ( ! scale ( ev]yday exp]i5ce4 ,! mo/ g5]al problem t has mean+ "h is to det]m9e all measurable prop]ties ( ! sy/em 9 t]ms ( ^? data :i* exp]im5t %[s c be arbitr>ily specifi$4 ,n[ we h already emphasiz$ t ! electromagnetic field itself is an inv5tion1 & is nev] subject to direct obs]vation4 ,:at we obs]ve are mat]ial bodies1 ) or )\t *>ges 7includ+ ev5tually 9 ?is category electrons71 _! positions1 motions1 & ! =ces to :i* !y are subject4 ,! =ces are to be measur$ accord+ to def9ition 9 me*anical t]ms1 ei!r by ! /ra9s 9 memb]s ( a framework if ! sy/em is 9 equilibrium1 or 9 t]ms ( accel]ations & masses if x is n 9 equilibrium4 ,! electromagnetic field z su* is n ! f9al object ( our calculations1 b ! calculation ( x is only an int]m$iate auxili>y /ep1 conv5i5t to make because our ma!matical =mulation gives s simple a connection betwe5 electromagnetic field1 *>ges1 & me*anical action t ! latt] c be calculat$ at once 9 t]ms ( ! =m]4 ,9 fact ! connection is s simple t 9 _m cases we h come to reg>d our problem z solv$ if we c compute ! electromagnetic field1 ov]look+ ! fact t ! field has no imm$iate mean+ 9 t]ms ( exp]i5ce4 ,electromagnetic !ory n[ pres5ts u ) a solution ( ! g5]al problem2 ?is solution is conta9$ 9 ! f\r-field equations ( ,maxwell1 ! con/itutive equations1 & ^? additional equations 7q (t5 lo/ sight (7 :i* give ! =ces ex]t$ by ! field on electric *>ges1 or curr5ts1 or dielectrics4 ,let u inquire h[ we may set ab\t te/+ ! physical correctness ( ^! equations4 ,we may beg9 ) "o ( ! simple/ possible te/s1 & inquire :e!r ! equations are correct 9 /at+ t ! =ce act+ on a *>ge mov+ 9 an electric field is simply ! product ( ! *>ge & ! field /r5g?4 ,?is1 on ! face ( x1 is a surpris+ /atem5t4 ,! field itself is affect$ by ! motion ( ! *>ges :i* g5]ate x1 & x is natural to expect a conv]se effect4 ,if1 fur!rmore1 we h sympa?y ) ! m$ium po9t ( view1 x is easy to ?9k t :atev] x is 9 ! m$ium t gets hold ( a *>ge & ex]ts a =ce on x w f9d x h>d] to take hold :5 ! *>ge is 9 motion4 ,9 attempt+ to *eck our /atem5t exp]im5tally1 ! only additional complication1 z comp>$ ) ! /atic case :i* we h already *eck$1 is af=d$ by ! motion ( ! *>ge1 = we h def9$ ! magnitude ( a *>ge 9 motion1 s !re is no difficulty "h1 & we may fur!rmore suppose t ! field is g5]at$ by /ation>y *>ges1 s t we ne$ n tr\ble to inquire :e!r ! proc$ure by :i* ! field 0 orig9ally def9$ is "h applicable4 ,! task ( *eck+ ! equation !n r$uces to ! simple physical task ( measur+ ! =ce on ! mov+ *>ge4 ,h[ %all we d ?is8 ,if ! velocity is l[1 we may tie a /r+ to ! *>ge & measure ! =ce ) a spr+ balance 7or its equival5t74 ,b n[ an exam9ation ( ! equations %[s t 9 m complicat$ ph5om5a p]ceptible deviations f ! /atic behavior are to be expect$ only at mu* high] velocities ?an c be atta9$ by t[+ *>ges ) a /r+ & a spr+ balance1 s t x is evid5tly necess>y to *eck ! simple equation = ! =ce on a mov+ *>ge also at high velocity4 ,s9ce at high velocity ! spr+ balance me?od = measur+ =ces fails1 we are driv5 to ! only proc$ure t we h1 namely a measurem5t 9 t]ms ( ! resultant accel]ation1 calculat+ ! =ce by ,newton's fir/ law ( me*anics4 ,b ?is involves a k ( ! mass ( ! mov+ body1 :i* we recognize 9 g5]al may be a function ( ! velocity4 ,n[ we h already se51 9 discuss+ ! concepts ( me*anics1 t ! op]ations by :i* me*anical mass is def9$ _c be c>ri$ out at high velocities1 s t ei!r ! concept ( me*anical mass becomes mean+less at high velocities1 or we mu/ adopt ano!r def9ition4 ,9 attempt+ to give ?is new def9ition ( mass at high velocities1 we are driv5 to a result ( special relativity !ory1 namely t all mass1 me*anical or electrical1 mu/ be ! same function ( velocity4 ,if n[ electrical mass c be f\nd 9 t]ms ( velocity1 our imm$iate problem is solv$ & we %all be 9 a position to complete ! exp]im5tal *eck ( ! equation4 ,b z a matt] ( fact1 9 ord] to det]m9e electrical mass1 we h to use t equation :i* we are n[ engag$ 9 try+ to e/abli%4 ,logically we h aga9 ! vici\s circle1 ! physical significance ( :i* is t indep5d5t op]ations d n exi/ = giv+ unique mean+ to ! concept ( =ce on a *>ge at high velocity4 ,we seem$ s close to our goal a m9ute ago2 t we may all[ ourselves to jump ! logical *asm1 & assume t ! equation is correct4 ,electrical mass n[ becomes a def9ite function ( velocity1 me*anical mass ! same function1 & we are 9 a position to comp>e ! actual accel]ation receiv$ by a *>ge 9 a field ) t calculat$ by ! equation4 ,our conviction1 on ! basis ( all exp]i5ce up to ! pres5t1 is t ! two accel]ations w be f\nd to agree4 ,! equation !n does someh[ make correct connection ) exp]i5ce 9 t a consequ5ce ( ! equation c be v]ifi$ exp]im5tally1 9 spite ( ! fact t z ! equation /&s x is mean+less1 because ! op]ations d n exi/ by :i* mean+ c be giv5 to ! individual t]ms4 ,at l[ velocities ! equation really says :at x seems to say1 because ! individual t]ms h mean+ 9 t]ms ( op]ations2 &1 :at is m1 :at ! equation says agrees ) exp]im5t4 ,at high velocities ! equation does n mean at all :at appe>s on ! surface2 by itself x has no mean+2 x has mean+ only :5 consid]$ z a memb] ( a sy/em ( equations1 & only 9 s f> z ! sy/em ( equations makes by implication /atem5ts ab\t nature t h mean+ 9 t]ms ( op]ations t c be c>ri$ out physically4 ,! individual t]ms ( ! equation ( ! sy/em d n h mean+ at high velocities1 & 9 fact !re are m t]ms ?an !re are indep5d5t physical op]ations4 ,an exact analysis f ! op]ational po9t ( view ( ! significance ( ! equations at high velocities has p]haps nev] be5 made1 & is n necess>y = our imm$iate purpose4 ,! discussion has br\ght out1 h[ev]1 t ! numb] ( physically indep5d5t concepts has be5 cut d[n by two at lea/1 9 t we h made purely =mal def9itions ( ! mean+ ( quantity ( electricity1 & ( ! =ce ex]t$ by a field on a *>ge at high velocity4 ,!re is no reason to ?9k t !re is any?+ unique ab\t ?is analysis1 or t =mal def9itions might n h be5 giv5 to o!r concepts ?an *>ge & =ce4 ,we c only /ate t z f> z physical cont5t goes ! equations h at lea/ two degrees ( fre$om4 ,x %\ld !n be possible to f9d q diff]5t sorts ( equations :i* agree equally well ) exp]i5ce4 ,9 p>ticul>1 s9ce we h se5 t ! =ce on a mov+ *>ge has no mean+ 9 t]ms ( indep5d5t op]ations1 x %\ld be possible by arbitr>y def9ition to make ?is =ce any function ( velocity t we please 7( c\rse r$uc+ to ! prop] value at l[ velocities71 & !n to det]m9e ! o!r equations s t ! entire gr\p ( equations is consi/5t ) exp]im5t4 ,s f> z ,i "k1 no "o has tri$ to give su* a modifi$ set ( equations1 & inde$ !re is no p>ticul> reason :y anyone %\ld bo!r to d ?is1 because ! pres5t equations are simple en\gh1 & ! modifi$ equations1 al?\gh p]haps diff]+ greatly 9 appe>ance f ! pres5t ones1 w\ld h no advantage 9 any great] or diff]5t physical cont5t4 ,b !re is no reason to ?9k t ! pres5t /ate ( affairs w always cont9ue4 ,we h se5 t ! decrease 9 ! numb] ( concepts corresponds to our inability to measure z _m sorts ( physical ?+s at high velocities z at l[4 ,n[ x is ! task ( ! future exp]im5t] s to ref9e ! possibilities ( measurem5t at high velocities z to re/ore ^! two degrees ( fre$om4 ,9 p>ticul>1 mass %\ld be made measurable 9 me*anical t]ms at high velocities4 ,:5 ?is re/oration has be5 made1 & all ! quantities 9 our equations receive indep5d5t physical mean+1 ! significance ( ! equations 9 t]ms ( op]ations w be q alt]$1 al?\gh ! =mal appe>ance w be un*ang$4 ,we mu/ !n be prep>$ to f9d1 z always :5 we *ange ! range ( ph5om5a1 t ! equations 9 _! pres5t =m d n correspond to ! facts at all1 & t "o ( ! alt]native =ms all[$ by our pres5t two degrees ( fre$om is ! correct =m4 ,b until ! new exp]im5tal facts h be5 obta9$1 x seems h>dly wor? :ile to attempt to specify ! d\bly inf9ite v>iety ( =ms :i* ! equations might h consi/5tly ) pres5t exp]im5t4#bc ,footnote #bc3 ,s9ce ?is 0 writt51 a pap] has appe>$ by ,v4 ,bu%1 ,j\r4 ( ,ma?4 & ,phys41 vol4 ,v41 ,no4 #c1 #aibf1 9 :i* x is %[n t !re are advantages 9 suppos+ ! *>ge ( an electron to *ange :5 x is set 9 motion4 ,s f> we h discuss$ ! ext5sion ( ord9>y electric ph5om5a 9 only "o direction1 to high velocities4 ,!re is ano!r ext5sion :i* is mu* m important physically1 namely to v small scales ( magnitude4 ,?is ext5sion is necess>y to an und]/&+ ( ! prop]ties ( matt] 9 bulk1 ! electrical nature ( ! atom hav+ be5 once e/abli%$4 ,our problem is to %[ h[ ! /ati/ical av]age ( ! behavior ( a l>ge numb] ( electrons gives ! l>ge scale effects :i* are )9 ! rea* ( obs]vation1 & :i* are describ$ by ! equations we h j discuss$4 ,to get ?is /ati/ical av]age we mu/ be able to calculate at lea/ c]ta9 features ( ! behavior ( ! individual electrons1 :i* means t we mu/ "k ! =m ( ! equations d[n to dim5sions ( ! ord] ( ^? ( an electron1 or small]4 ,n[ if "o contra/s ! scale ( ! suppos$ dim5sions ( ! electron ) ! smalle/ dim5sions on :i* we c make indep5d5t exp]im5tal v]ification ( ^? equations1 he mu/ admit t !re is an enorm\s *ance = *ange 9 ! type ( equation beyond ! limit t we c rea* by direct exp]im5t1 & ! *ances ( guess+ ! correct ext5sion ( ! equation to small dim5sions are correspond+ly almo/ vani%+ly small4 7,we may p]haps say t exp]im5ts on ! ,br[nian motion on a scale a good _m atoms 9 diamet] br+ u ! close/ possible directly1 :i* means t we are #ajf or #ajg fold away f electronic dim5sions47 ,9 spite1 h[ev]1 ( ! app>5tly enorm\s *ances aga9/ x1 ?is program ( ext5d+ ! field equations to small dim5sions & foll[+ out ! consequ5ces 0 exactly ! program :i* ,lor5tz set himself4#bd ,t ,lor5tz saw t su* a program might be c>ri$ ?r\gh mu/ be recogniz$ z a vision ( extraord9>y g5ius1 & t he 0 will+ to devote to x ! ye>s ( ardu\s & detail$ calculation t he did is evid5ce ( a p]t9acity ( purpose ( ! highe/ moral ord]4 ,footnote #bd3 ,see = example1 ,h4 ,a4 ,lor5tz1 ,! ,!ory ( ,electrons1 ,b4 ,g4 ,teubn]1 #aiaf4 ,we n[ h to exam9e critically ?is program & to inquire :at is ! significance ( ! measure ( success t ,lor5tz atta9$4 ,! precise ext5sion ( ! equations t he made 0 v simple1 = ! l>ge scale equations ( ,maxwell 7 tak5 ov] ) z little *ange z possible4 ,! equations are s famili> t x is n necess>y = u to write !m 9 detail2 !y express relations betwe5 ! electric & magnetic =ce vectors 7=ce & induction n[ becom+ ! same ?+1 ! diff]5ce betwe5 !m 9 pond]able bodies be+ "o ( ! ?+s t is to be expla9$ 9 t]ms ( ! electrons71 ! space d5sity ( electric *>ge1 its velocity1 & ! =ce act+ on elem5t>y *>ge4 ,we h to notice t al?\gh =mally ! equations h *ang$ little 9 appe>ance1 nev]!less ! physical cont5t1 z judg$ by ! op]ations1 has *ang$ a great deal4 ,consid]1 = in/ance1 ! mean+ ( *>ge d5sity4 ,9 ! ,maxwell equations1 0 m]ely ! numb] ( discrete elem5t>y *>ges p] unit volume1 ! di/ances betwe5 ^! *>ges be+ suppos$ s small comp>$ ) ! scale ( ! ph5om5a involv$ t _! av]age effect c\ld be fairly repres5t$ 9 t]ms ( _! numb]s4 ,9 ! ,lor5tz equations1 on ! o!r h&1 has a value diff]5t f #j only inside ! electron2 ev]y:]e else #j4 ,n[ an exam9ation ( ! previ\s discussion1 9 :i* we que/ion$ :e!r ! magnitude ( ! *>ge might be a function ( its velocity1 w %[ t !re are no physical op]ations :atev] by :i* mean+ c be giv5 to at individual po9ts inside an electron4 ,!re is a s+le condition on ?is 1 namely1 t its integral ?r\gh\t ! total volume assign$ to ! electron %all equal ! total /atic *>ge ( ! electron4 ,obvi\sly a s+le scal> condition is a pretty blunt tool ) :i* to attempt to det]m9e a po9t function ?r\gh\t a volume4 ,aga91 ! equations talk ab\t ! velocity ( ! *>ge at int]ior po9ts ( ! electron2 :at possible physical op]ations are !re by :i* mean+ c be assign$ to ! velocity ( an amorph\s /ructureless sub/ance 9 regions inaccessible to exp]im5t8 ,"h aga91 ! concept z a detail$ description ( ! behavior at a po9t has become mean+less1 & aga9 !re is a s+le integral condition1 namely1 t ! v associat$ ) e mu/ be su* t :5 integrat$ ov] ! volume ( ! electron x w give a total transport ( *>ge equal to t c>ri$ by ! electron 9 its motion4 ,?is aga9 is a s+le condition on a function di/ribut$ ?r\gh space4 ,/ill aga91 ! equations conta9 ! electric & magnetic vectors at po9ts inside ! electron4 ,:at is ! possible mean+ ( ^! field vectors 9 t]ms ( op]ations8 ,our proc$ure = f9d+ ! field at a po9t involves by def9ition f9d+ ! =ce on an electric *>ge plac$ at t po9t4 ,b !re is no *>ge small] ?an an electron1 & ! proc$ure deg5]ates into a fiction4 ,aga9 !re is a s+le integral condition on ! field vectors2 ! integral ( ! =ce on ! assum$ *>ge d5sity :5 tak5 ov] ! total volume ( ! electron mu/ give a value correspond+ to exp]im5t4 ,except = ?is s+le condition1 ! concept ( ! field at po9ts inside ! electron is an inv5tion )\t physical reality4 ,n only is ! field concept mean+less at po9ts inside ! electron1 b x is mean+less at po9ts outside )9 a c]ta9 di/ance1 because ! explor+ *>ge c nev] be made small] ?an ! electron itself1 & s c nev] come clos] ?an a c]ta9 di/ance4 ,! actual /ate ( affairs is mu* worse ?an has already appe>$4 ,x 0 %[n 9 ! discussion ( space & "t t no indep5d5t physical mean+ c be atta*$ to l5g?s & times z small z h to be assum$ 9 describ+ ! behavior ( ! individual electrons4 ,! op]ations ,div1 ,curl1 d_/dt :i* ent] ! field equations are1 !re=e1 physically mean+less z !y /&2 !y h only a ma!matical mean+ :i* beg9s to acquire physical complexion 9 a mo/ complicat$ way :5 ! equations are integrat$ ov] l>ge en\gh volumes4 ,x is evid5t1 !re=e1 t ! concepts :i* ent] ! field equations h entirely lo/ _! l>ge scale significance2 !y h become blurr$1 fus$ toge!r1 & few] 9 numb]4 ,a precise analysis ( ?is situation has probably nev] be5 attempt$ & w\ld obvi\sly be difficult3 x w\ld be int]e/+ to "k at lea/ h[ _m really indep5d5t concepts !re are at ?is ord] ( ph5om5a4 ,an attempt at an analysis w\ld probably be wor? :ile f a physical po9t ( view 9 sugge/+ possible exp]im5ts by :i* ! numb] ( physically indep5d5t concepts c\ld be ext5d$4 ,s9ce ! quantities 9 ! field equations are mean+less 9 ! nak$ =m 9 :i* !y ent] ! equations1 x is mean+less to inquire :e!r ! equations z !y /& are true or n4 ,9 our pres5t /ate ( exp]im5tal k x is also mean+less to ask :e!r1 = example1 ! inv]se squ>e law betwe5 electric *>ges cont9ues to hold1 or :e!r an accel]at$ *>ge radiates4 ,^! que/ions h mean+ only :5 appli$ to ph5om5a on a scale l>ge en\gh to correspond to possible exp]im5t4 ,!re is a r int]e/+ obv]se to ! /atem5t t x is mean+less to ask :e!r ! field equations are true1 namely1 t x may n be mean+less to /ate t !y are false4 ,a /atem5t is n true unless x is true 9 e p>ticul>1 b x is false if x is false 9 a s+le p>ticul>4 ,if we c %[ t a s+le consequ5ce ( ! field equations ( ,lor5tz1 :5 integrat$ or av]ag$ 9 su* a way z to correspond to exp]im5tal possibilities1 is false1 !n ! equations mu/ be false4 ,x seems t1 reg>d$ z a complete description ( physical behavior on a small scale1 ! equations mu/ be judg$ false1 because !y conta9 no sugge/ion ( quantum ph5om5a4 ,ev5 if we h to recognize t ! equations are false1 !re c be no "q t !y correspond to an important "p ( reality1 & t !y h be5 ( ! greate/ s]vice to physics4 ,:at is ! significance ( ! success t !y h atta9$8 ,x is to be notic$ t all ! ph5om5a to :i* ! ,lor5tz equations h be5 successfully appli$1 al?\gh n l>ge scale ph5om5a 9 ! ord9>y s5se ( ! ^w1 are nev]!less ph5om5a involv+ ! cop]ation ( a numb] ( atoms1 & t ! equations unque/ionably fail :5 appli$ to ph5om5a involv+ s+le electrons4 ,x appe>s f our be/ pres5t evid5ce t on a small scale ! behavior ( nature is gov]n$ by quantum pr9ciples & is !re=e q diff]5t f l>ge scale behavior1 ,:i* we h se5 is gov]n$ by ! ,maxwell equations4 ,!re mu/ ( c\rse be a transition zone 9 :i* ! "* ( ph5om5a *anges f quantum to ,maxwell4 ,n[ any program l t ( ,lor5tz is almo/ inevitably b\nd to beg9 to give correct results :5 we get up z f> z ! transition zone1 = ! simple reason t ! relations ( ,maxwell h be5 put into ! equations & are always !re ready to appe> z soon z ! quantum relations beg9 to give way4 ,! physical significance ( ! success ( ! ,lor5tz program seems to be t ! transition f ,maxwell to quantum takes place at a /age pretty f> d[n t[>d ! individual atoms4 ,to f9d ! precise details ( ! transition f ,maxwell to quantum ph5om5a con/itutes a l>ge "p ( ! program ( ! imm$iate future4 ,all ?is skepticism ab\t ! classical "w ( ,lor5tz is likely to be r irritat+ or depress+1 p>ticul>ly if "o attempts to imag9e :at o!r c\rse c\ld h be5 adopt$4 ,inde$ x does seem t we f9d ourselves 9 a real qu&>y2 ,lor5tz 0 practically =c$1 because ( ! "* ( ! ma!matical tools at 8 comm&1 to take ! c\rse t he did1 9 spite ( any recognition ( ! physical mean+lessness ( ! ma!matical op]ations4 ,we h already se5 t conv5tional ma!matics does n correspond to ! physical reality2 x _c easily make a qualifi$ /atem5t subject to limitations1 & x recognizes no diff]5ce betwe5 ! physically big & ! physically little & ! correspond+ *ange 9 ! op]ational mean+ ( its symbols4 ,x beg9s by be+ a mo/ useful s]vant :5 deal+ ) ph5om5a ( ! ord9>y scale ( magnitude1 b ends by dragg+ u by ! scruff ( ! neck willy nilly into ! inside ( ! electron :]e x =ces u to repeat mean+less gibb]i%4 ,l>mor recogniz$ ?is1 & 9 8 electron !ory1 develop$ practically contemporane\sly ) t ( ,lor5tz1 endeavor$ to treat electrons z :oles1 & n to make mean+less /atem5ts ab\t _! insides4#be ,b he 0 mu* less successful ?an ,lor5tz 9 mak+ 8 analysis give physical results1 & "o may suspect t x 0 at lea/ 9 "p due to difficulty ) 8 tools4 ,footnote #be3 ,joseph ,l>mor1 !r & ,matt]1 ,cambridge ,univ]sity1 ,press1 #aijj4 ,9 ?is book ! electron is treat$ z a po9t s+ul>ity 9 ! e!r4 ,:at we %\ld l to be able to d is easy to see4 ,! ?+s t g into our equations mu/ h indep5d5t physical mean+1 & ! "* ( our ma!matical =mulation %\ld *ange to keep pace ) ! *ange 9 ! physical op]ations :i* give mean+ to ! t]ms4 ,= example1 electrical d5sity has a mean+ = l>ge scale ph5om5a1 b means no?+ on a small scale4 ,our ultimate electric unit is ! electron2 :5 we get d[n to ?is scale ( magnitude1 our ma!matics ought to be mak+ /atem5ts ab\t ! relative behavior ( discrete electrons1 & n m5tion s mu* z by implication ! d5sity at po9ts inside an electron4 ,b ?is sort ( ?+ we app>5tly _c yet d2 ! prop] ma!matical language has n be5 develop$4 ,su* a language1 :5 develop$1 mu/ n only be able to resi/ ! temptation to burr[ inside ! electron1 b mu/ also try to get along )\t ! field concept1 :i* we h se5 is liable to s mu* physical abuse1 & mu/ r$uce effects 9 complicat$ electrical sy/ems to ! ultimate elem5ts t h physical mean+1 namely1 a dual action betwe5 pairs ( electrical *>ges1 ) no implications ab\t physical action :]e ! *>ges are n4 ,,! ,,nature ,,( ,,light ,,& ,,! ,,concepts ,,( ,,relativity ,we h already discuss$ sev]al aspects ( ! !ory ( relativity 9 connection ) ! relation to x ( "s ( our fundam5tal concepts4 ,!re are /ill o!r topics connect$ ) relativity :i* dem& att5tion2 mo/ ( ^! involve ! prop]ties ( light4 ,x w n[ be conv5i5t to discuss toge!r ! prop]ties ( light & ^! concepts ( relativity4 ,we re/rict our discussion ( light to ^? simple prop]ties :i* be> on ! !ory ( relativity4 ,practically all our ?9k+ ab\t optical ph5om5a is done 9 t]ms ( an inv5tion1 by means ( :i* ^! ph5om5a are assimilat$ to ^? ( ord9>y me*anical exp]i5ce1 & s made easi] to ?9k ab\t4 ,to realize t inv5tion has be5 active "h1 we mu/ ?9k ourselves back into t naive frame ( m9d 9 :i* exp]i5ce is giv5 directly 9 t]ms ( s5sation4 ,! mo/ elem5t>y exam9ation ( :at light means 9 t]ms ( direct exp]i5ce %[s t we nev] exp]i5ce light itself1 b our exp]i5ce deals only ) ?+s light$4 ,?is fundam5tal fact is nev] modifi$ by ! mo/ complicat$ or ref9$ physical exp]im5ts t h ev] be5 devis$2 f ! po9t ( view ( op]ations1 light means no?+ m ?an ?+s light$4 ,n[ exp]i5ce %[s t ^! ?+s light$ may /& to ea* o!r 9 v>i$ relations2 9 attempt+ to r$uce ^! relations to ord] & und]/&ability we make a c]ta9 inv5tion4 ,?is is prompt$ by sev]al c>d9al exp]im5tal facts3 9 ! fir/ place1 ?+s light$ h a simple geometrical relation to ea* o!r1 9 t scre5s plac$ on /raight l9es betwe5 ! light$ objects may suppress ! illum9ation ( "o or ! o!r & !mselves become illum9at$4 ,?is leads to ! concept ( rectil9e> beams ( light1 :i* is no m ?an a description ( ! geometrical relation betwe5 light$ objects4 ,!n we h ! exp]im5tal fact ( ! asymmetrical relation ( ! light$ objects1 describ$ 9 t]ms ( s\rces & s9ks4 ,f9ally1 we h ! discov]y made at a mu* lat] /age1 & n possible until physical measurem5ts _h rea*$ a high ref9em5t1 t light has prop]ties analog\s to ! velocity ( mat]ial ?+s4 ,?is 0 fir/ discov]$ 9 connection ) a/ronomical ph5om5a 9 ! %ift ( ! "t ( eclipse ( ,jupit]'s satellites & 9 ab]ration1 b 0 lat] f\nd to hold = purely t]re/rial ph5om5a1 9 t a beam ( light reflect$ f a di/ant mirror does n return to ! s\rce until aft] ! lapse ( a "t int]val t c be measur$ ) means suffici5tly ref9$4 ,?is prop]ty ( return aft] ! lapse ( "t is precisely l t ( mat]ial ?+s1 su* z a mess5g] despat*$ = an answ]1 or a ball or a wat] wave b\nc+ f a wall4 ,^! v>i\s prop]ties ( light lead q naturally & almo/ inevitably to ! inv5tion ( light z a ?+ t travels1 ?+ n necess>ily connot+ mat]ial ?+4 ,! "q n[ = u is :e!r we %all reg>d ?is z a m]e inv5tion1 made = conv5i5ce 9 ?9k+1 or %all g fur!r & ascribe physical reality to x1 t is1 %all we ?9k ( light z capable ( indep5d5t physical exi/5ce 9 ! space betwe5 ! matt] t con/itutes ! s\rce & ! mirror8 ,n[ 9 spite ( ! resemblances po9t$ out above1 !re is at lea/ "o univ]sal & fundam5tal diff]5ce betwe5 a ?+ t travels & light4 ,we h indep5d5t physical evid5ce ( ! cont9u$ exi/5ce ( ! ball1 = example1 at all int]m$iate po9ts ( space2 we c see x1 or he> x1 or feel ! w9d 9 ! air z x passes1 or ev5 t\* x4 ,all ^! ph5om5a are indep5d5t ( ! initial & t]m9al ph5om5a1 & h5ce by our crit]ion = ! physical reality ( an inv5tion1 we are ju/ifi$ 9 ascrib+ physical reality to ! ball 9 transit4 ,b ) ! beam ( light x is entirely diff]5t2 ! only way by :i* we c obta9 physical evid5ce ( ! int]m$iate exi/5ce ( ! beam is by int]pos+ "s sort ( a scre51 & ?is act de/roys j t "p ( ! beam ^: exi/5ce we h !reby detect$4 ,!re is no physical ph5om5on1 :atev] by :i* light may be detect$ ap>t f ! ph5om5a ( ! s\rce & ! s9k 7und]/&+ t a mirror is includ$ 9 ! idea (1 s9k72 t is1 no ph5om5on exi/s indep5d5t ( ! ph5om5on :i* l$ u to ! inv5tion ( a ?+ travell+4 ,h5ce f ! po9t ( view ( op]ations x is mean+less or trivial to ascribe physical reality to light 9 int]m$iate space1 & light z a ?+ travell+ mu/ be recogniz$ to be a pure inv5tion4 ,! /atus ( light is exactly ! same z t ( an electric field2 !re is n ! slighte/ w>rant = ascrib+ physical reality to ei!r at po9ts ( empty space--light & field-at-a-po9t h no mean+ until we g !re & make exp]im5ts ) "s mat]ial ?+4 ,( c\rse ! electromagnetic !ory ( light makes ?is resemblance inevitable1 provid$ ! !ory & our views ( ! nature ( light & ! field are correct4 ,x _c be d5i$ t !re are "s ph5om5a :i* uncritically consid]$ appe> to ju/ify ?9k+ ( light z a ?+ t travels2 ^! w n[ be discuss$4 ,probably ! argum5t to :i* mo/ significance is usually ascrib$ is d]iv$ f ! ph5om5a ( en]gy4 ,! pass+ ( light f s\rce to s9k is accompani$ by ! transf] ( en]gy4 ,b en]gy is cons]v$1 s t we h to ask :]e ! en]gy is 9 ! "t int]val betwe5 ! emission ( light f ! s\rce & its absorption by ! s9k4 ,!re is an obvi\s answ]3 ! en]gy is 9 transit1 ( c\rse1 some:]e 9 ! int]m$iate space betwe5 s\rce & s9k4 ,if we ?9k ( light z propagat$ ?r\gh a m$ium1 !n ! m$ium is su* t en]gy may reside 9 x1 z 9 ! electromagnetic !ory ( light1 or if light is m mat]ial & balli/ic 9 "*1 ! ?+ t travels has itself en]gy4 ,we notice 9 ! fir/ place t ! cons]vation pr9ciple involves ! "t concept1 because :at we mean by cons]vation is t ! total en]gy ( ! univ]se1 at a fix$ in/ant ( "t1 is con/ant4 ,t is1 we h to integrate ov] all space ! local en]gy at a def9ite in/ant ( "t1 & ?is involves spread+ ! "t concept ov] all space4 ,x is fur!r evid5t t unless we spread ! "t concept ov] space 9 ! "r way we %all n get cons]vation4 ,! pro( t x is possible to spread ! "t concept ov] space 9 su* a way z to give cons]vation involves a k ( ! prop]ties ( light4 ,x w\ld seem1 !n1 t we ought n to assume cons]vation 9 d$uc+ ! prop]ties ( light1 :5 a k ( ! prop]ties ( light is necess>y to e/abli% cons]vation4 ,^! consid]ations _c be accept$ z f9al1 h[ev]1 until a detail$ analysis has be5 made1 & ?is w\ld be mo/ complicat$4 ,b !re is a m important consid]ation d]iv$ f our previ\s critique ( ! en]gy concept1 namely1 t !re is no basis = ass]t+ t en]gy is localiz$ 9 space at all2 en]gy is n a physical ?+1 b r :at we w\ld call a prop]ty ( a sy/em z a :ole4 ,if ?is view ( en]gy be grant$1 ! :ole en]gy argum5t = light z a ?+ travell+1 & also = ! exi/5ce ( a m$ium1 falls4 ,i believe t simil> consid]ations apply to any argum5ts f ! cons]vation ( mom5tum4 ,! possibility ( detect+ light 9 app>5tly empty space by a scre5 con/itutes p]haps ! mo/ imm$iate reason = consid]+ light z a ?+ t travels4 ,?is po9t ( view ,i believe is *>act]i/ic ( ! entire attitude ( ,e9/e9 9 d$uc+ ! !orems ( ! special !ory ( relativity4 ,e9/e9's light signal is = ! purposes ( ! d$uction ?\ght ( z a simple sph]ical wave spread+ f ! s\rce & capable ( be+ wat*$ z x spreads by an obs]v] outside ! sy/em1 9 mu* ! same way t a wat] wave c be wat*$4 ,( c\rse ! light signal _c actually be wat*$ 9 transit1 b we c come fairly close to ?is ideal by plac+ scre5s at any po9t we please to make ! wave visible4 ,x is true t ! m]e act ( %[+ ! exi/5ce ( ! light de/roys t "p ( ! beam ^: exi/5ce is detect$1 b ! scre5 ne$s only an inf9itesimal am\nt ( light to make x visible1 & s by ! usual physical argum5t we may suppose t ! detect+ scre5 produces only an inf9itesimal modification ( ! total orig9al light4 ,our satisfaction ) ?is picture evaporates if our pres5t quantum views ( ! nature ( light are correct4 ,we c no long] ?9k ( ! sph]ical light pulse z ( irr$ucible simplicity1 b x is an exce$+ly complicat$ ?+1 p]haps m complicat$ ?an a gas f ! po9t ( view ( k9etic !ory1 & simulates simplicity by "s sort ( av]ag+ ( ! effects ( ! elem5t>y quantum processes ( :i* x is compos$4 ,if ! pr9ciples ( relativity are to cont9ue to be reg>d$ z fundam5tal1 or ev5 if !y are to rema9 intelligible1 we mu/ apply our reason+1 n to sph]ical wavelets1 b to ! elem5t>y process ( :i* ^! wavelets are compos$4 ,n[ ! elem5t>y quantum act is ess5tially a tw(old ?+3 !re is a discrete act ( emission at "s discrete mat]ial p>ticle1 & ! act is consummat$ by ano!r discrete act 7absorption or scatt]+7 at "s o!r discrete p>ticle4 ,we _c yet fully *>act]ize ! details ( ?is tw(old process1 b h to connect ! place at :i* absorption takes place ) ! place ( emission by /ati/ical consid]ations4 ,x is evid5t1 h[ev]1 t to ?9k ( emission z />t+ "s process l a sph]ical wavelet travell+ l a ?+ ?r\gh space pres5ts an entirely incorrect view1 because 9 ! wave !re is no h9t ( ! discrete place :i* is to t]m9ate x4 ,we may say crudely t !re is no way by :i* ! wave c "k :at discrete mat]ial p>ticle is to complete ! emission process4 ,we may p]haps try to save ! situation by rememb]+ t a sph]ical wave is pol>iz$ & s has a unique direction associat$ ) x2 b fur!r exam9ation %[s t ?is does n help1 because ! unique direction is t ( no en]gy fl[1 & absorption c take place 9 any direction except ?is4 ,x appe>s !n t in/ead ( be+ a help1 ! ?+ travell+ po9t ( view is a positive emb>rassm5t :5 we try to picture by means ( x ! ess5tially tw(old nature ( ! elem5t>y quantum act4 ,ano!r plausible argum5t = light z a ?+ travell+ may be d$uc$ f our pr9ciple ( connectivity4 ,imag9e a d>k lant]n ) a %utt] t c be op5$ or clos$ s z to emit a mom5t>y fla% ( light1 a di/ant mirror1 & a receiv+ in/rum5t ne> ! s\rce4 ,"o ( ! prop]ties ( light t we always assume is t no p]man5t trace ( ! act ( emission is left beh9d 9 ! s\rce4 ,! mo/ m9ute exam9ation ( all ! details ( ! lant]n & its surr\nd+s at "s "t aft] ! emission ( ! fla% has n yet %[n any ph5om5on t betrays a remembrance ( ! emission ( ! fla%1 unless p]haps we measure ! total en]gy or mom5tum & h "s way ( kn[+ :at ! en]gy or mom5tum w\ld h be5 if ! fla% _h n be5 emitt$1 & 9 any ev5t we _c specify ! mom5t 9 pa/ "t :5 ! signal 0 emitt$4 ,9 ! same way we _c tell f an exam9ation ( a mirror :e!r x has at any "t 9 ! pa/ reflect$ a beam ( light4 ,consid] n[ two sy/ems1 ea* consi/+ ( a s\rce & a mirror di/ant #c x #ajaj cm41 id5tical 9 all respects1 except t 9 "o a light signal 0 fla%$ f ! s\rce #a4e seconds ago1 & 9 ! o!r only #j4e seconds ago4 ,accord+ to our hypo!sis1 ! mo/ complete exam9ation ( s\rce & mirror 9 ei!r sy/em fails to %[ ! slighte/ diff]5ce1 b nev]!less !re is some?+ ess5tially diff]5t ab\t ! two sy/ems1 = 9 "o a light signal arrives at ! scre5 9 #j4e seconds1 & 9 ! o!r n until #a4e seconds4 ,?is violates :at we h sugge/$ might be reg>d$ z ! c>d9al & mo/ g5]al pr9ciple ( all physics1 ! pr9ciple ( ess5tial connectivity1 :i* /ates t diff]5ces betwe5 two sy/ems mu/ be associat$ ) o!r diff]5ces4 ,a mo/ obvi\s & simple way ( ma9ta9+ our pr9ciple is m]ely to po9t out t ! sy/em really includ$ m ?an we inve/igat$3 ! sy/em prop]ly consi/s ( s\rce1 mirror1 scre51 & all int]m$iate space1 s t if we _h exam9$ int]m$iate space we %\ld h f\nd light !re 9 transit 9 diff]5t positions 9 ! two sy/ems1 ?us correlat+ ) ! diff]5ces 9 subsequ5t hi/ory4 ,?is argum5t appeals to me z p]haps ! /ronge/ t c be advanc$ = ! view ( light z a ?+ travell+4 ,b x seems 9 no way conclusive4 ,our pr9ciple ( ess5tial connectivity made no m5tion ( ! "t concept1 b we h someh[ smuggl$ x 9 mak+ ! application above4 ,we s\ght to give a complete description ( our sy/em at "s "o in/ant ( "t1 & ?is involv$ spread+ ! "t concept ov] space4 ,?is itself is a que/ionable op]ation & may be done 9 diff]5t ways4 ,b1 m important1 :at is ! ju/ification = suppos+ t ! sy/em c be completely describ$ by giv+ a complete description ( all ! measurable p>ts ( x at "s "o epo*8 ,we h se5 t 9 ! mo/ g5]al case ! pr9ciple ( ess5tial connectivity mu/ recognize t ! concept ( initial condition ( a sy/em involves all ! pa/ hi/ory1 & we may h "h a case 9 po9t4 ,! answ] c be giv5 only by exp]im5t4 ,9 deal+ ) ord9>y exp]i5ce1 :5 we d n h to di/+ui% betwe5 local & ext5d$ "t1 & are n deal+ ) optical ph5om5a1 !re c be little "q t exp]i5ce at lea/ approximately ju/ifies ! expectation t future behavior is det]m9$ 9 t]ms ( ! pres5t condition & t pres5t condition may be specifi$ 9 t]ms ( ! results ( pres5t op]ations p]=m$ 9 ! sy/em4 ,b be=e ext5d+ ?is pr9ciple to ph5om5a 9 :i* we h to di/+ui% betwe5 local & ext5d$ "t1 we h to answ] j t "q :i* we are n[ consid]+2 namely1 :e!r !re are physical ph5om5a tak+ place 9 app>5tly empty space1 & :e!r !re=e empty space has to be includ$ 9 ! sy/em4 ,we f9d ourselves aga9 tread+ ! vici\s circle4 ,p]haps exp]i5ce w %[ t ! ext5sion ( ! pr9ciple ( connectivity to optical ph5om5a involves some?+ l ?is3 namely1 ! future at any po9t 9 a mat]ial sy/em is det]m9$ by a complete description ( ! pres5t /ate ( ! sy/em 9 ! imm$iate vic9ity1 & by a hi/ory ( ! behavior at m di/ant po9ts1 ?is hi/ory ext5d+ ov] long] & long] int]vals ( "t z ! po9t becomes m remote4 ,i believe1 h[ev]1 t ^! possibilities w n seem v satisfactory1 & t mo/ physici/s w discov] 9 !mselves a v /rong disposition to feel t ! future is det]m9$ 9 t]ms ( a complete description ( "s sort ( in/antane\s configuration1 "t be+ ext5d$ 9 "s suitable way ov] space4 ,?is in/9ctive dem& t ! future be det]m9$ 9 t]ms ( ! pres5t may easily be consi/5t ) ! optical ph5om5a 9 our two sy/ems consi/+ ( s\rce1 mirror1 & scre51 )\t involv+ ! mat]ial exi/5ce ( light 9 empty space1 provid$ t our assumption t ! emission ( light leaves beh9d x no p]man5t record 9 ! s\rce 0 incorrect4 ,x may be t detail$ exam9ation ( a s\rce aft] emission w disclose p]man5t traces1 f :i* ! in/ant ( emission may be f\nd by extrapolation4 ,if ! conviction ( det]m9ism ( ! future is /rong1 ! physici/ may well be impell$ to se>* "h = new ph5om5a indicat+ su* a memory ( emission4 ,let u n[ inquire h[ our physical /ructure might be affect$ if we %\ld give up ! id5tification ( light ) a ?+ travell+4 ,"o consequ5ce is t light ne$ no long] be ?\ght ( z hav+ ! prop]ty ( velocity1 s9ce velocity1 9 t]ms ( imm$iate exp]i5ce1 is a prop]ty ( ?+s mov+ f place to place4 ,giv+ up ! concept ( light z a ?+ travell+ w\ld enable u1 !n1 to adopt an alt]native me?od ( describ+ nature ) a diff]5t concept ( velocity2 we h se5 t x is possible to def9e velocity 9 t]ms ( op]ations diff]5t f ! usual ones1 9 su* a way z to give ! usual num]ical results at small velocities1 b diff]5t results at high velocities1 & 9 p>ticul> to give an inf9ite velocity = light4#bf ,footnote #bf3 ,no difficulty arises f ! asymmetric "* ( light 9 assign+ an inf9ite velocity to light because ^? physical op]ations by :i* we discov] :i* is ! s\rce & :i* ! s9k are entirely di/9ct f ! op]ations by :i* a velocity is measur$2 or 9 o!r words1 ev5 9 ! limit1 x /ill has mean+ to say t an inf9ite velocity has a direction associat$ ) x4 ,!re is n[ no objection to an inf9ite numb] associat$ ) light1 if we no long] ?9k ( light z hav+ physical velocity4 ,we may1 if we l1 cont9ue = ! sake ( conv5i5ce to talk ( ! velocity ( light1 cle>ly und]/&+ t ! inf9ite value :i* mu/ be ascrib$ to ?is velocity corresponds to ! fact t ! physical concept ( velocity does n apply 9 all respects to light4 ,we %\ld n[ h to revise our process = ext5d+ ! "t concept ov] space1 because ?is 0 =m]ly s done z to give light a f9ite velocity4 ,we are n[ to make ?is velocity inf9ite1 :i* is obvi\sly to be done simply by sett+ a di/ant clock on z]o at ! in/ant x receives a light signal fla%$ f our clock at its z]o4 ,! behavior ( mat]ial ?+s n[ takes on a simple aspect--!re is no long] a f9ite upp] limit to ! velocity t c be giv5 a mat]ial ?+1 & light has no long] ! p>adoxical prop]ty ( be>+ ! same f9ite relation to ea* ( two mat]ial sy/ems :i* diff] f ea* o!r by a f9ite am\nt 7t is1 ! fir/ po/ulate ( relativity t ! velocity ( light is #c x #ajaj 9 all ref]5ce sy/ems74 ,light in/ead n[ be>s ! relation ( inf9itude to ea* ( two sy/ems :i* diff] f ea* o!r by only a f9ite am\nt1 & ?is is natural f ! ma!matical po9t ( view4 ,h[ev]1 all is n simplifi$ by ?is *ange 9 ! me?od ( sett+ clocks1 b a price has to be paid4 ,! price is t we h to give up ! simple connection betwe5 ! velocity ( a ?+ & its g & come "t4 ,our *anges h n affect$ local "t2 ! "t ( passage ( light to a di/ant mirror & return to ! s\rce is n *ang$1 & is !re=e /ill f9ite1 al?\gh we describe ! velocity ( light z inf9ite4 ,n[ exam9ation %[s at once t !re is no imm$iate connection betwe5 ! concepts ( velocity & ( g & come "t1 because ! op]ations involv$ are diff]5t4 ,a measurem5t ( a l9e> velocity accord+ to our def9ition involves two clocks at two diff]5t places or else a clock travell+ ) ! object1 :ile g & come "t dem&s only a s+le clock at a s+le place1 & also involves necess>ily a rev]sal ( direction ( motion 9 ! object "u measurem5t4 ,we see !n t1 accord+ to ! def9ition adopt$ = velocity1 we h ! *oice ei!r ( do+ z ,e9/e9 did 9 ! re/rict$ !ory ( relativity & mak+ g & come "t v simply relat$ to velocity2 or we may say t ref9$ physical measurem5ts %[ t some?+ ( significance happ5s :5 ! direction ( motion is rev]s$1 & t ph5om5a are n symmetrical ) respect to a rev]sal ( direction4 ,! asymmetry :i* results f rev]s+ ! direction ( motion we may visualize z a sort ( curvature 9 space & "t1 z ( a small piece ( an arc ( a circle b5t back on itself1 ) ! two ends div]g+4 ,?is alt]native way ( treat+ velocity w\ld mean t velocity c be measur$ simply only by a specially situat$ obs]v]2 ?is ne$ n be consid]$ di/urb+1 because 9 fact ! op]ations h be5 def9$ only ) respect to su* an obs]v]4 ,:i* ( ^! two possible treatm5ts ( velocity %all be adopt$ is to a c]ta9 ext5t a matt] ( conv5i5ce1 det]m9$ by ! sort ( ph5om5a 9 :i* we are mo/ int]e/$ & wi% mo/ to simplify4 ,e9/e9's *ief conc]n 0 ) optical ph5om5a1 s t ! motive = 8 *oice is evid5t4 ,9 ?is *oice ( ,e9/e9 x is n v evid5t t ! desire to make g & come "t simply connect$ ) velocity play$ a v prom95t "p1 b x seems r t ! desire to ?9k ( light z a ?+ travell+1 ) a f9ite velocity1 0 mu* m influ5tial4 ,?is way ( ?9k+ ( light is fundam5tal to all ! treatm5t ( re/rict$ relativity2 )\t ?is sort ( picture all ! ma!matical d$uctions w\ld lose _! simplicity & conv9c+ness1 = 9 all ! d$uctions we inevitably ?9k ( ourselves z an obs]v] f outside1 wat*+ a ?+ t we call light travell+ back & =? l any physical ?+4 ,n[ !re c be no d\bt t1 :5 *oice is possible1 conv5i5ce & simplicity are important consid]ations2 b ,i believe t !re is ano!r mu* m important consid]ation1 namely1 ! mo/ p]fect reproduction possible ( ! physical situation4 ,x seems to me t x is v que/ionable :e!r ,e9/e91 & all ! re/ ( mod]n physics1 = t matt]1 h n paid too high a price = simplicity & ma!matical tractability 9 *oos+ to treat light z a ?+ t travels4 ,physically x is ! ess5ce ( light t x is n a ?+ t travels1 & 9 *oos+ to treat x z a ?+ t does1 ,i d n see h[ we c expect to avoid ! mo/ s]i\s difficulties4 ,( c\rse ! :ole problem ( ! nature ( light is n[ giv+ ! mo/ acute difficulty4 ,! ?+-travell+ po9t ( view1 ev5 z treat$ by ,e9/e91 does n l& u 9 a situation :i* is at all satisfy+ logically4 ,we are famili> ) only two k9ds ( ?+ travell+1 a di/urbance 9 a m$ium1 & a balli/ic ?+ l a projectile4 ,b light is n l a di/urbance 9 a m$ium1 = o!rwise we %\ld f9d a diff]5t velocity :5 we move ) respect to ! m$ium1 & no su* ph5om5on exi/s2 nei!r is light l a projectile1 because ! velocity ( light ) respect to ! obs]v] is indep5d5t ( ! velocity ( ! s\rce4 ,on ! o!r h&1 9 ab]ration we h a ph5om5on simil> to t %[n by projectiles4 ,! prop]ties ( light are m l ^? ( a projectile ?an is p]haps commonly realiz$1 z is %[n 9 ! pap]s ( ,la ,rosa#bg on ! balli/ic !ory ( light4 ,! prop]ties ( light rema9 incongru\s & inconsi/5t :5 we try to ?9k ( !m 9 t]ms ( mat]ial ?+s4 ,footnote #bg3 ,m4 ,la ,rosa1 ,sci5tia1 ,july-,augu/1 #aibd4 ,e9/e9's re/rict$ relativity has made a great contribution 9 s gr\p+ & coord9at+ ! ph5om5a t !y c all be embrac$ 9 a simple ma!matical =mula1 b he does n seem to h pres5t$ !m 9 su* a light t !y are simple or easy to grasp physically4 ,! explanatory aspect is completely abs5t f ,e9/e9's "w4 ,9 view ( all our pres5t difficulties x w\ld seem t we ought at lea/ to try to />t ov] aga9 f ! beg9n+ & devise concepts = ! treatm5t ( all optical ph5om5a :i* come clos] to physical reality4 ,no "o realizes m vividly ?an ,i t ?is is a mo/ difficult ?+ to d4 ,if we are ev] successful 9 c>ry+ ?r\gh su* a modifi$ treatm5t1 x is evid5t t n only w ! /ructure ( mo/ ( our physics be alt]$1 b 9 p>ticul> ! =mal approa* to ^? ph5om5a n[ treat$ by relativity !ory mu/ be *ang$1 & !re=e ! appe>ance ( ! entire !ory alt]$4 ,i believe t x is a v s]i\s "q :e!r we %all n ultimately see su* a *ange1 & :e!r ,e9/e9's :ole =mal /ructure is n a m or less tempor>y affair4 ,al?\gh x is exce$+ly difficult to =see :at ! treatm5t ( ! future w be l1 x is easy to surmise c]ta9 ( its features4 ,9 ess5ce ! elem5t>y process ( all radiation p]ceiv$ z radiation is tw(old4 ,!re is "s process at ! s\rce & "s accompany+ process at ! s9k1 & no?+ else1 z f> z we h any physical evid5ce2 fur!rmore1 ! elem5t>y act is unsymmetrical1 9 t ! s\rce & ! s9k are physically diff]5tiat$ f ea* o!r4 ,?is is ! mo/ complete expression ( ! physical facts2 !re is n[h]e any physical evid5ce = ! inclusion ( a ?ird elem5t 7! e!r74 ,!re=e all ! ph5om5a appreh5d$ by an obs]v] 7& ?is embraces all physical ph5om5a7 c be det]m9$ only by ! s\rce & ! s9k & ! relation to ea* o!r ( s\rce & s9k1 = !re is no?+ else t has physical mean+ 9 t]ms ( op]ations4 ,?is =mula cov]s n only ! possibility ( su* fir/ ord] ph5om5a z ab]ration & ! ,dppl] effect1 b also %[s t su* second ord] effects z t look$ = by ,mi*elson & ,morley mu/ be non-exi/5t4 ,x w ?us be se5 t "s ( ! consequ5ces ( relativity !ory are implicitly conta9$ 9 c]ta9 v broad po9ts ( view4 ,"o int]e/+ "q t mu/ be answ]$ be=e we c get v f> ) a new treatm5t is :e!r ! elem5t>y optical process is ( necessity tw(old1 or :e!r we may h emission )\t absorption1 t is1 radiation into empty space4 ,lewis seems to imply 9 rec5t pap]s t ?is is n possible4#bh ,! a/ronom]s h already po9t$ out difficulties 9 expla9+ ph5om5a l ! temp]ature equilibrium ( ! planets if we suppose ?is is ! case4 ,footnote #bh3 ,= example1 9 ! book3 ,g4 ,n4 ,lewis1 ,! ,anatomy ( ,sci5ce1 ,yale ,univ]sity ,press1 #aibf1 p4 #abi4 ,,o!r ,,relativity ,,concepts ,we n[ turn to "s ( ! o!r concepts ( relativity4 ,"o ( ! mo/ important ( ^! is ! ev5t2 9 fact ?is concept is made fundam5tal by ,:itehead4#bi ,we h already discuss$ ! concept ( ev5t "u ! id5tity concept ) :i* x is closely involv$4 ,! ev5t is usually ?\ght ( by ,e9/e9 z m]ely an aggregate ( f\r coord9ates1 ?ree ( space & "o ( "t4 ,! pr9ciple ( g5]al relativity1 namely1 t ! laws ( nature %all be ( inv>iant =m1 :5 =mulat$ ma!matically1 involves ! assumption t nature may be analyz$ into ev5ts1 & is express$ by ! requirem5t t ! ma!matical relations betwe5 ! coord9ates ( a *a9 ( ev5ts %all be inv>iant4 ,! same idea is also express$ by ,e9/e9 9 ano!r =m1 namely1 t nature may be completely *>act]iz$ 9 t]ms ( space-"t co9cid5ces4 ,9 elaborat+ ?is idea1 ,e9/e9 assumes t ! results ( all measurem5t may be giv5 9 t]ms ( su* co9cid5ces4 ,n[ x appe>s to me mo/ que/ionable :e!r ! analysis ( nature into ev5ts is possible or suffici5t4 ,) reg>d to ! co9cid5ce po9t ( view1 x seems p]fectly obvi\s t ! _w ( our imm$iate s5sation _c be describ$ 9 t]ms ( co9cid5ces2 h[1 = example1 %all we describe 9 t]ms ( space-"t co9cid5ce ! photometric comp>ison ( ! int5sity ( two s\rces ( illum9ation1 or ! comp>ison ( ! pit* ( two s\nds1 or ! location ( a s\nd by ! b9aural effect8 ,footnote #bi3 ,a4 ,n4 ,:itehead1 ,an ,enquiry ,conc]n+ ! ,pr9ciples ( ,natural ,k1 ,cambridge ,univ]sity ,press1 #aiai1 ,*ap4 ,v4 ,to ju/ify ! co9cid5ce po9t ( view we app>5tly h to analyze d[n to ! colorless elem5ts beyond our s5se p]ception4 ,x does n seem unreasonable1 p]haps1 to expect t ! univ]se is completely det]m9$ 9 t]ms ( ! positions z a function ( "t ( all ! positive & negative electrons2 b to introduce su* a !sis n[ c]ta9ly goes beyond pres5t exp]im5tal w>rant1 & is contr>y to ! g5]al _s ( relativity1 :i* n[h]e else involves any ref]5ce to ! small scale /ructure ( ?+s4 ,ev5 if we 7 will+ to ov]look all ^! objections1 we w\ld /ill h ! fact t ! diff]5ce betwe5 a positive & negative electron is n conta9$ 9 any specification ( ! m]e coord9ates4 ,a fur!r v important d\bt 9 pr9ciple z to ! possibility ( ! analysis ( nature into ev5ts is af=d$ by ! "* ( ! concept ( ev5t itself4 ,we h se5 t ! idea ( ev5t involves ! exi/5ce ( discont9uities1 & t ?is c correspond only approximately to ! physical fact1 because discont9uities app>5tly lose _! abruptness z we make our measurem5ts m ref9$4 ,! !sis t nature c be describ$ 9 t]ms ( discont9uities ( a v small scale seems mu* too special to be made a fundam5tal "p ( a !ory ( ! g5]al pret5sions ( t ( relativity4 ,9 fact ?is1 z well z a consid]ation to be m5tion$ lat]1 sugge/s t ! argum5t & result ( g5]al relativity may be intr9sically re/rict$ to l>ge scale ph5om5a4 ,we n[ pass f ^! some:at special que/ions to ask :y x is t ,e9/e9 0 able 9 ! g5]al !ory ( relativity to obta9 new & physically correct results f g5]al reason+ ( an app>5tly purely ma!matical "*4 ,we are conv9c$ t purely ma!matical reason+ nev] c yield physical results--t if any?+ physical comes out ( ma!matics x mu/ h be5 put 9 ano!r =m4 ,our problem is to f9d :]e ! physics got into ! g5]al !ory4 ,!re are two que/ions to be dis5tangl$ "h3 we h to consid] 9 ! fir/ place ! significance ( ! fact t ,e9/e9 has be5 able to describe relations 9 nature 9 ma!matical =m1 & 9 ! second place ( ! fact t he 0 able to arrive at ! ma!matical =mulation ( ^! physical relations by reason+ ( app>5tly a purely ma!matical "*1 f po/ulates ( m]ely =mal ma!matical cont5t 7inv>iance ( natural laws 9 g5]aliz$ coord9ates74 ,n[ ! !ory ( relativity does n seem to diff] 9 ! fir/ respect f any o!r bran* ( ma!matical physics1 su* z ! classical ma!matical !ory ( electricity & magnetism1 = in/ance1 & ?is matt] has already be5 t\*$ 9 an e>li] *apt]4 ,x is a fact t ! behavior ( nature c 9 _m cases be express$ to a high degree ( precision 9 ma!matical language1 & relativity is n unique 9 ?is respect4 ,9 any ev5t1 we mu/ n all[ ?is possibility ( ma!matical =mulation to obscure ! ess5tial fact t all physical k is by its nature only approximate1 s t we may expect at any "t to f9d1 :5 we h c>ri$ our measurem5ts to a high] degree ( precision1 t our ma!matical expression ( ! laws 0 n q exact1 z seems n[ to be ! case ) ,newton's law ( gravitation1 = example4 ,i d n suppose t ,e9/e9 w\ld claim t ! /atem5ts ( relativity diff] 9 ?is respect f any ( our o!r /atem5ts ab\t nature1 al?\gh app>5tly "s ( 8 foll[]s see some?+ m "h4 7,f ! op]ational viewpo9t ! mean+ to be atta*$ to some?+ m is some:at obscure47 ,) respect to ! second "q1 we may /op to notice t ! special !ory /&s 9 q a diff]5t position f ! g5]al !ory4 ,! special !ory is mu* m physical ?r\gh\t2 its po/ulates are physical 9 "*1 & x is obvi\s t ! physics got into ! results ?r\gh ! po/ulates4 ,x seems to me )\t "q t ,e9/e9 %[$ ! intuitive insight ( a great g5ius 9 recogniz+ t !re are mutual relations betwe5 physical ph5om5a :i* c be describ$ 9 v mu* simplifi$ language 9 t]ms ( concepts slightly modifi$ f ^? already 9 common use4 ,9 view ( ! rem>ks made on ! nature ( light1 x is legitimate to wond]1 h[ev]1 :e!r ! =mulations ( ev5 ! special !ory w always /&4 ,x seems to be true t all ! facts ( nature1 ev5 9 ! abs5ce ( a gravitational field1 _c be connect$ by ! simple =mulations ( ! special !ory2 t ! physical relations are simple only 9 a sub-gr\p2 & t if we wi% to deal ) all optical ph5om5a1 we h c>ri$ our simplifications too f>1 = ! emission ( a light signal is n a simple ev5t1 & light is n 9 nature l a ?+ travell+4 ,j ! sorts ( physical ?+ :i* are ignor$ 9 treat+ light z ! special !ory does are com+ to be m & m important 9 ! m9ds ( physici/s1 & ?is is a reason = wond]+ :e!r ultimately ,e9/e9's special !ory may n be reg>d$ m]ely z a v conv5i5t way ( ty+ toge!r a l>ge gr\p ( important physical ph5om5a1 b n z be+ by any means a full or complete /atem5t ( natural relations4 ,) respect to ! g5]al !ory1 h[ev]1 ,i believe ! situation is q diff]5t4 ,! fundam5tal po/ulate t ! laws ( nature are ( inv>iant =m 9 all cord9ate sy/ems is highly ma!matical1 & ( an entirely man-made "*4 ,( :at conc]n ( nature's is x h[ man may *oose to describe h] ph5om5a1 & h[ c we expect ! limitations ( our descriptive process to limit ! ?+ describ$8 ,fur!rmore1 ,e9/e9's me?od ( connect+ 8 ma!matical =mulation & nature by way ( co9cid5ces ( #d-;ev5ts 7?ree space1 "o "t coord9ates7 seems to be v f> remov$ f reality1 s9ce x entirely leaves out ! descriptive backgr\nd 9 t]ms only ( :i* ! #d-;ev5t takes on physical significance4 ,nev]!less1 ?ree def9ite conclusions ab\t ! physical univ]se h be5 tak5 out ( ! hat by ! conjuror ,e9/e9 7%ift ( ! p]ihelion ( ,m]cury1 displacem5t ( app>5t position ( />s at ! edge ( ! sun's disk1 & ! %ift t[>d ! infra-r$ ( spectrum l9es f a s\rce 9 a gravitational field71 & ! problem = u z physici/s is to discov] by :at process ^! results 7 obta9$4 ,an exam9ation ( :at ,e9/e9 actually did 9 d]iv+ 8 results w %[1 ,i believe1 t ! situation is really diff]5t f t sugge/$ above4 ,9 ! fir/ place1 ! requirem5t t ! laws ( nature be ( inv>iant =m actually places no re/riction1 z any "o c see by sett+ himself ! task ( express+1 = example1 an inv]se cube law = gravitation 9 t]ms ( g5]aliz$ coord9ates4 ,! "w ( express+ su* a law c be attack$ 9 a p]fectly r\t9e way4 7,! ess5tial diff]5ce betwe5 ! inv>iability requirem5ts ( ! special & g5]al !ories is to be not$2 ! special !ory requires t ! velocity ( light1 = in/ance1 h ! same num]ical value 9 all all[$ sy/ems3 ! g5]al !ory m]ely t all laws h ! same lit]al =m1 b ) v>iable num]ical coeffici5ts47 ,b1 z ,e9/e9 says1 if any "o actually attempts to c>ry ?r\gh ! "w ( express+ an inv]se cube law 9 g5]aliz$ coord9ates1 he w f9d ! task prohibitively complicat$1 & w seek = "s simpl] =mulation4 ,:at ,e9/e9 actually did1 !re=e1 0 to require t ! laws ( nature be simple 9 g5]aliz$ =m4 ,n[ we "k t ! law ( gravitation z =m]ly express$ 9 ord9>y coord9ates z an inv]se squ>e law 0 approximately exact1 & 0 also simple4 ,any deviations f ?is law are small1 & all exp]i5ce leads u to expect t to ! fir/ ord] ( small quantities ! deviations c be tak5 c>e ( ma!matically 9 ! =m ( small correction t]ms to ?is law4 ,?is by itself gives no?+1 h[ev]1 because a small correction t]m c be add$ to our equations 9 an inf9ite numb] ( ways4 ,if1 h[ev]1 we "k t ! equation mu/ be ( a c]ta9 type aft] ! correction t]ms h be5 add$1 ! possibilities are s mu* re/rict$ t ! =m ( ! correction t]m may be det]m9$4 ,9 argu+ z to ! probable type ( ! equation1 ,e9/e9 advanc$ ! consid]ations by :i* physics gets into ! situation4 ,9 ! fir/ place1 ! special !ory _h prep>$ u = ! possibility ( f9d+ t our measur+ in/rum5ts might be modifi$ 9 a gravitational field1 analog\sly to ! %ort5+ ( a met] /ick :5 set into motion4 ,9 fact1 special !ory _h indicat$ t 9 an accel]at$ sy/em ! modifications might be too complicat$ to be treat$ by t !ory4 ,9 ! abs5ce1 !n1 ( specific in=mation we mu/ be prep>$ = ! mo/ g5]al possible alt]ation 9 space-"t 9 a gravitational field4 ,9 describ+ space-"t we mu/ !re=e use cord9ates adapt$ to h&l+ ! mo/ g5]al possible relations1 & ^! are ! g5]aliz$ cord9ates ( ,riemann1 :i* _h be5 already discuss$ by ma!maticians4 ,go+ back n[ to ,e9/e9's crit]ion t ! equations are to be simple1 we h ! dem& t ! equations be simple 9 g5]aliz$ cord9ates1 & ( c\rse !y mu/ also r$uce to ! ord9>y equations 7t is1 ! equations ( special relativity7 9 space :]e !re is no gravitational field4 ,9 decid+ ! fur!r "q z to :at ! type ( equation probably is1 we are influ5c$ by consid]ations ( conv5i5ce z well z by physical consid]ations4 ,practically ! only type ( equation t c be h&l$ ma!matically is l9e>1 s t we %all c]ta9ly try fir/ :e!r ?is type ( equation may n cont9ue to hold4 ,n[ ! ,newtonian law ( ! inv]se squ>e may be express$ 9 t]ms ( a l9e> diff]5tial equation ( ! second ord] 9 ! old ,c>tesian cord9ates 7,poisson's equation71 s t our mo/ imm$iate sugge/ion is t ! equations rema9 l9e> & ( ! second ord] 9 g5]aliz$ cord9ates4 ,z a matt] ( fact1 ?is requirem5t turns out to be suffici5t to det]m9e ! small correction t]m by :i* ! ord9>y equations c be g5]aliz$2 ,e9/e9's pap]s mu/ be /udi$ to see h[ ?is works out 9 detail4 ,all ?is looks pretty ma!matical1 b z a matt] ( fact !re is mu* physical cont5t1 because sy/ems :i* c be describ$ by l9e> equations ( ! second ord] h def9ite physical prop]ties4 ,! requirem5t t ! equations be l9e> corresponds to "o ( ! mo/ fundam5tal prop]ties ( our univ]se--! causality concept w\ld n be possible or w\ld be mu* modifi$ 9 a univ]se gov]n$ by non-l9e> equations1 = ! jo9t effect ( two causes act+ toge!r w\ld n be ! sum ( _! effects act+ sep>ately1 s t ! analysis ( a situation into simple elem5ts w\ld be impossible & ! causality concept probably w\ld n h aris54 ,fur!rmore1 an equation ( ! type ( ,poisson ( ! second ord] means t !re are propagation ph5om5a1 & equations ( me*anics ( ! second ord] involve ! exi/5ce ( a scal> en]gy function4 ,if1 !n1 ! behavior ( ! univ]se c be describ$ by diff]5tial equations at all1 ^! equations mu/ be l9e> ( ! second ord] if ! univ]se is to h ! broade/ physical *>act]i/ics ( our own univ]se4 ,:at ,e9/e9 really did1 !re=e1 0 to dem& t ev5 :5 space-"t is w>p$ by ! pres5ce ( a gravitational field1 ^? physical ph5om5a :i* c be describ$ 9 t]ms ( diff]5tial equations cont9ue to be describ$ by l9e> diff]5tial equations ( ! second ord]2 t is1 t nature cont9ues to be describable 9 t]ms ( a causality concept1 ) propagation ph5om5a1 & a simple en]gy function4 ,! consequ5ces ( a guess l ?is ab\t ! prop]ties ( nature appeal to our physical intuition z be+ wor? foll[+ out1 & ( c\rse we "k ! exp]im5tal ju/ification4 ,sev]al g5]al comm5ts may n[ be made on ! /ructure rea*$ 9 ?is way4 ,9 ! fir/ place1 ! :ole /ructure is only descriptive 9 "*2 we f9d c]ta9 correlations 9 nature :i* we describe ) consid]able complet5ess 9 ma!matical equations1 )\t introduc+ any new elem5t ( explanation or ( me*anism4 ,we h se5 t z we increase our range f ! realm ( ord9>y ph5om5a to ph5om5a ( diff]5t "* we arrive at a /age :]e = a "t ! process ( explanation app>5tly halts1 & we h to be satisfi$ ) a /atem5t ( m]e correlation betwe5 elem5ts2 lat]1 h[ev]1 ^! elem5ts may be accept$ z ! ultimates 9 a broad5$ s*eme ( explanation1 & ! explanatory process resum$4 ,are we at su* a /age n[ ) ! g5]al relativity !ory1 & may lat] a new s*eme ( explanation be e/abli%$ bas$ on ! correlations ( ,e9/e98 ,?is is ( c\rse a matt] ( individual judgm5t2 ,i p]sonally "q :e!r ! elem5ts ( ,e9/e9's =mulation1 su* z curvature ( space-"t1 are closely en\gh connect$ ) imm$iate physical exp]i5ce ev] to be accept$ z an ultimate 9 a s*eme ( explanation1 & ,i v mu* feel ! ne$ = a =mulation 9 m intimate physical t]ms4 ,9 ! second place1 we mu/ repeat ! comm5t already made 9 discuss+ "t1 namely1 t !re is /ill a v wide gap betwe5 ! !ory & its physical application1 9 t we h no way ( id5tify+ our physical clocks & our physical measures ( "t ) ! ?+ call$ "t 9 ! =mulas4 ,?is gap mu/ be fill$ by a specification ( ! physical /ructure ( a clock4 ,x has always be5 v puzzl+ to und]/& :y ,e9/e9 has s /r5u\sly insi/$ t ! %ift t[>d ! infra-r$ is an integral "p ( ! g5]al !ory1 & t if ! %ift is n f\nd1 ! !ory mu/ fall4 ,9 o!r words1 ,e9/e9 insi/s t ! assumption t an atom is a clock is an integral "p ( 8 !ory4 ,i believe t ?is attitude may be due to a realization by ,e9/e9 ( t v flaw 9 ! logical /ructure :i* we are n[ emphasiz+4 ,9 ! abs5ce ( any me?od ( specify+ ! details ( con/ruction ( at lea/ "o clock1 relativity becomes a purely academic affair1 unless !re exi/ 9 nature concrete ?+s :i* may s]ve z clocks4 ,e9/e9 mu/ ei!r be able to tell h[ to con/ruct a clock1 or else be able to po9t to a specific example ( a clock4 ,he *ose ! atom z ! specific ?+4 ,d\btless ! reason 0 ! app>5t simplicity ( ! vibrat+ me*anism ( an atom1 z %[n by ! precise equality ( ! frequ5cies emitt$ by all atoms ( ! same elem5t4 ,if ! atom is n a clock1 :]e 9 nature c "o be f\nd8 ,b 9 ! la/ few ye>s we h come to appreciate ! exce$+ly complicat$ quantum /ructure ( an atom1 & ,e9/e9's !sis loses mu* ( its in/9ctive appeal4 ,s9ce ,e9/e9 creat$ ! !ory ( relativity1 x is p]haps ungraci\s to "q 8 "r to /ipulate t ! assumption t ! atom is a clock is an integral "p ( ! !ory4 ,?is1 h[ev]1 deg5]ates to a m]e matt] ( language1 & does n t\* ! arbitr>y nature ( ! proc$ure4 ,x does n prev5t u f hav+ a second br& ( relativity !ory1 t ( ,x in/ead ( ,e9/e91 exactly l t ( ,e9/e9 except t p]haps n[ ! clock is con/ruct$ 9 t]ms ( ! life p]iod ( a radioactively dis9tegrat+ elem5t4 ,! only way to elim9ate ! arbitr>9ess seems to be to po/ulate t all natural processes1 :i* run naturally ( !mselves indep5d5tly ( :at we may d1 may equally well s]ve z clocks & give ! same results4 ,b 9 answ]+ ! "q ( ! op]ational mean+ ( indep5d5tly ( :at we may d we %all effectively h to answ] ! "q ( :at is a clock4 ,?is po9t ( view may possibly1 h[ev]1 get u a little ne>] to our goal ( f9d+ h[ to specify ! /ructure ( a clock4 ,f9ally1 ! g5]al !ory is n completely g5]al1 b applies only to a c]ta9 range ( ph5om5a1 j z we saw t ! special !ory does n embrace all optical ph5om5a4 ,! g5]al !ory applies only to ^? ph5om5a :i* c be describ$ 9 t]ms ( diff]5tial equations1 t is1 p> excell5ce1 to l>ge scale ph5om5a4 ,if quantum ph5om5a _c be describ$ by diff]5tial equations1#cj z app>5tly n[ !y _c1 g5]al relativity _c by its v nature be applicable4 ,g5]al relativity does n give u a compreh5sive =mulation ( ! behavior ( all nature1 & z f> z we c see1 we are /ill z f> z ev] f su* a g5]al =mulation4 ,footnote #cj3 ,?is /atem5t n[ takes on a v que/ionable aspect 9 view ( ! new quantum wave me*anics 7,m>*1 #aibg74 ,,rotational ,,motion ,,& ,,relativity ,physically !re is a great diff]5ce betwe5 ! behavior ( sy/ems 9 uni=m relative rectil9e> motion & ^? 9 uni=m relative rotation4 ,! special !ory ( relativity /ates t !re is a triply inf9ite numb] ( sy/ems ) all possible uni=m rectil9e> velocities ) respect to ea* o!r1 9 all ( :i* physical ph5om5a h exactly ! same mutual relations1 t is1 natural laws are ! same4 ,n[ ! m]e =mulation ( ! pr9ciple sugge/s ! s5se 9 :i* sy/em is "h us$4 ,x is obvi\s t sy/em ref]s only to a "p ( ! univ]se2 we are n mak+ a hopelessly academic /atem5t ab\t :at w\ld happ5 if we _h an inf9ite numb] ( univ]ses to exp]im5t )1 b are talk+ ab\t op]ations t may be approximately realiz$ 9 our own univ]se4 ,! sy/em ( ! =mulation we may ?9k ( z a completely equipp$ laboratory1 out 9 empty space1 s f> f ! heav5ly bodies t !y c h no effect4 ,! diff]5t sy/ems ( ! =mulation are diff]5t laboratories1 all built to exactly ! same ar*itectural blue pr9ts4 ,! ph5om5on to :i* ! po/ulates ( relativity apply are ph5om5a :i* p]ta9 entirely only to "o or ano!r ( ^! laboratories4 ,! mean+ ( ?is re/riction is n completely def9ite & has1 9 any special case1 to be judg$ p>tly by ! context4 ,obvi\sly1 to see f ! w9d[ ( a laboratory ano!r laboratory pass+ ) a c]ta9 velocity _c be c\nt$ z "o ( ! all[$ ph5om5a4 ,/ill less is x "o ( ! all[$ ph5om5a to obs]ve t ! c5t] ( gravity ( ! entire /ell> univ]se has a c]ta9 velocity ( translation ) respect to ! laboratory4 ,! special pr9ciple ( relativity conta9s by implication !re=e ! /atem5t t c]ta9 v l>ge & important classes ( physical ph5om5a may be isolat$ & treat$ z tak+ place unaffect$ by ! re/ ( ! univ]se4 ,grant$ n[ ! possibility ( isolation1 we h a second /atem5t1 :i* is usually treat$ z if x 7 ! entire /atem5t ( ! re/rict$ pr9ciple1 namely1 t !re is a triply inf9ite set ( sy/ems 9 :i* ^! ph5om5a run 9 ! same way indep5d5t ( ! relative motion ( ! sy/ems ) respect to ea* o!r4 ,:5 once ! significance ( ! obs]vation is grasp$ t absolute motion has no mean+ 9 t]ms ( op]ations1 we see t ?is la/ /atem5t takes imm$iately a mo/ simple & satisfy+ aspect1 9 fact1 s simple & inevitable t we are incl9$ to see 9 ?is ! complete ess5ce ( ! situation & reg>d ! mean+lessness ( absolute motion z af=d+ p]emptory pro( ( ! re/rict$ pr9ciple4 ,) ?is bias we n[ turn to exam9e ! facts ( rot>y motion1 & are disconc]t$ to f9d !m q diff]5t4 ,no mean+ 9 t]ms ( measur+ op]ations c be giv5 to absolute rot>y motion any m ?an to absolute translation1 b nev]!less ph5om5a are obvi\sly entirely diff]5t 9 diff]5t sy/ems 9 relative rot>y motion 7ph5om5a ( rupture1 = example71 s t app>5tly !re are physical ph5om5a by :i* ! concept ( absolute rot>y motion might be giv5 a c]ta9 physical significance4 ,giv5 two worlds l our own 9 empty space1 b surr\nd$ by imp5etrable cl\ds1 & ea* provid$ ) a ,f\cault p5dulum1 !n we believe t x is physically possible t we may f9d on "o ( ^! worlds ! plane ( rotation ( ! p5dulum gradually *ang+ 9 direction1 :ile on ! o!r x rema9s /ation>y4 ,?is diff]5ce we reg>d z possible )\t o!r accompany+ physical ph5om5a :i* are causally relat$ to ! rotation ( ! p5dulum 7( c\rse we h to make ! two worlds ( inf9itely rigid mat]ial & elim9ate o!r ph5om5a :i* we reg>d z purely incid5tal71 s t we app>5tly h "h a contradiction ( our c>d9al physical pr9ciple ( ess5tial connectivity4 ,we are c]ta9ly n incl9$ to give up our pr9ciple1 & we believe t z a physical fact1 if ! cl\ds c\ld be evaporat$1 an obs]v] 9 "o _w w\ld f9d t he 0 rotat+ ) respect to ! sy/em ( ! fix$ />s1 :]eas ! correspond+ obs]v] on ! o!r _w w\ld f9d t he 0 /ation>y4 ,our pr9ciple ( ess5tial connectivity is !re=e ma9ta9$1 9 t ! rotation ( ! plane ( ! p5dulum is connect$ ) a rotation ) respect to ! re/ ( ! univ]se ( ! entire _w 9 :i* ! p5dulum is m\nt$4 ,z f> z ,i am aw>e1 no o!r way ( ma9ta9+ our pr9ciple has ev] be5 sugge/$4 ,b ?is dem&s t we give up our physical hypo!sis ( ! possibility ( isolat+ a sy/em4 ,!re is "h no "q ( limit+ behavior2 we believe t no matt] h[ f> our rotat+ _w gets f ! re/ ( ! univ]se ! ,f\cault p5dulum w\ld always behave 9 ! same way2 ! sy/em c nev] be isolat$1 b su* local ph5om5a z ! inv>iance ( ! plane ( ! p5dulum are always ess5tially det]m9$ by ! re/ ( ! univ]se4 ,if n[ our sy/em _c be isolat$1 we mu/ return to ! ph5om5a ( translational motion4 ,9 pr9ciple ! act ( isolation _c be p]=m$1 ! re/ ( ! univ]se _c be disreg>d$1 & we %\ld expect t diff]5t /ates ( translational motion z well z diff]5t /ates ( rotational motion ) respect to ! re/ ( ! univ]se w\ld h an effect on ph5om5a4 ,we set ourselves ! problem ( und]/&+ ?is app>5t enorm\s diff]5ce betwe5 ph5om5a ( translation & rotation4 ,we rem>k t :at app>5tly is a diff]5ce 9 pr9ciple may1 9 virtue ( ! approximate "* ( all measurem5t1 be only a diff]5ce 9 magnitude1 & t translational effects may exi/ too small to detect4 ,a physical basis = su* a diff]5ce may be f\nd 9 ! enorm\sly diff]5t num]ical values ( translational & rotational velocities ) respect to ! re/ ( ! univ]se atta9able 9 practice4 ,9 describ+ ph5om5a ( cosmic magnitude1 we may plausibly measure ! ph5om5a 9 units comm5surable ) ! scale ( ! ph5om5a4 ,?us 9 measur+ l9e> di/ances1 we may p]haps *oose z ! unit ( l5g? ! diamet] ( ! /ell> univ]se1 & 9 measur+ rotation1 a complete rev]sal ( direction ) respect to ! entire univ]se4 ,?is la/ means a *ange ( angul> ori5tation ( #b 1 ! fir/ means a l5g? ( ! ord] ( #ajf light ye>s4 ,measur$ 9 su* cosmic units ! angul> velocities atta9able 9 practice are incomp>ably great] ?an l9e> velocities4 ,we n[ see t x is possible t ! real /ate ( affairs is z foll[s3 namely1 ph5om5a 9 any sy/em are affect$ by motion ) respect to ! entire univ]se1 :e!r t motion is ( translation or ( rotation1 & ! magnitude ( ! effect is connect$ ) ! velocity ( ! motion by a factor :i* is ( ! g5]al ord] ( unity :5 velocity is measur$ 9 cosmic units4 ,?is la/ is m]ely an application ( ! argum5t s (t5 made 9 physics z to ! ord] ( magnitude ( unkn[n num]ical factors1 & w be f\nd exp&$ on page #hh ( my book on ,dim5sional ,analysis4 ,! l9e> velocities atta9able 9 practice are n[ s exce$+ly l[ t _! effect has n yet be5 detect$ exp]im5tally1 b angul> velocities are high1 & ! effect is easily demon/rable4 ,9 ?is light ! special pr9ciple ( relativity is no diff]5t 9 "* f any o!r physical law2 x is only approximate1 & "s day our measurem5ts may become ref9$ en\gh to detect its limitations4 ,we h made a hypo!sis "h1 :i* we may call ! hypo!sis ( ! imman5ce ( ! entire univ]se1 namely1 t isolation is impossible1 or t ! re/ ( ! univ]se1 no matt] h[ di/ant1 always has a local effect on at lea/ "s ph5om5a4 ,?is is ess5tially ! hypo!sis ( ,ma*1#ca & leads to a situation :i* c1 ,i ?9k1 be contemplat$ ) logical equanimity1 al?\gh x has always seem$ to _m physici/s mo/ highly antiphysical 9 "*4 ,footnote #ca3 ,e4 ,ma*1 ,! ,sci5ce ( ,me*anics1 translat$ by ,mc,cormack1 ,! ,op5 ,c\rt ,publi%+ ,co41 ,*icago1 #ahic4 ,see especially p4 #bce4 ,x mu/ c]ta9ly be admitt$ t mo/ physical exp]i5ce ju/ifies u 9 ?9k+ t effects may be made z small z we please by gett+ f> en\gh away f ! cause ( ! effect4 ,b if we accept ! consid]ations ( ! prec$+ pages1 we mu/ be prep>$ to admit t z ph5om5a *ange 9 range _! "* may *ange1 & t 9 ^! new realms we mu/1 at fir/ at lea/1 be satisfi$ ) a m]e /atem5t ( correlations4 ,c]ta9ly we h v /rong physical evid5ce ( a =mal correlation betwe5 ! ,f\cault p5dulum & ! re/ ( ! univ]se4 ,b a correlation ( ?is sort may be )\t significance because ( its v bread?2 we nev] c prove ! significance ( ! correlation by p]=m+ an exp]im5t ) ! re/ ( ! univ]se abs5t4 ,h we really done any?+ m ?an m]ely get ?+s into su* a =mal situation t !y _c be assail$1 a possibility :i* ! m]e laws ( our ?9k+ seem always to leave op51 z has be5 sugge/$1 or is !re any physical cont5t to :at we h done8 ,we h se5 t if our correlation is also sugge/$ by o!r ph5om5a1 !n we may accept x z hav+ physical cont5t4 ,n[ !re is j a glimm] ( a sugge/ion t our hypo!sis ( ! imman5ce ( ! univ]se may be ne$$ 9 o!r ways4 ,! gravitational con/ant & ! velocity ( light are always treat$ z arbitr>y magnitudes ?ru/ on ! univ]se f outside ) no connection ) o!r ph5om5a4 ,nev]!less1 ,i suppose t no "o reg>ds ?is situation z ultimately satisfactory & does n ent]ta9 ! hope t "s day we may be able to give "s sort ( acc\nt ( ! num]ical magnitude ( ^! con/ants4 ,we h n hi!rto succe$$ 9 f9d+ any connection betwe5 ^! con/ants & small scale ph5om5a su* z ! *>ge on ! electron1 its mass1 etc41 s t !re is "s plausibility 9 expect+ t a connection may be sometime f\nd ) cosmic ?+s2 inde$ g5]al relativity !ory already prep>es u = exactly ?is possibility4 ,n[ ! velocity ( light & ! gravitational con/ant control small scale exp]im5ts1 = ( c\rse ^! two con/ants c be measur$ by local exp]im5ts1 s t if ! cosmic connection is f\nd1 we %\ld h a control ( local behavior by cosmic ?+s1 & !re=e ano!r example ( ! imman5ce ( ! entire univ]se4 ,!re is no ne$ = me to wa/e "t 9 apologiz+ = ! highly speculative "* ( all ?is4 ,x is wor? :ile to emphasize1 h[ev]1 t our g5]al consid]ations on ! mean+ ( explanation h prep>$ u to admit z reasonable j ! sort ( explanation conta9$ 9 ! hypo!sis ( ! imman5ce ( ! univ]se1 & !re=e to res]ve a place 9 our physical ?9k+ = possibilities ( ?is sort1 9 spite ( ! fact t su* consid]ations are n usually ent]ta9$1 & may seem to _m oppos$ to ! _s ( physics4 ,,quantum ,,concepts#cb ,! hi/ory ( quantum !ory up to ! pres5t is a repetition 9 _m respects ( t ( ! e>ly !ories ( electricity1 9 t all our ?9k+ has be5 9 me*anical t]ms4 ,z f> z we n[ "k1 quantum ph5om5a are always associat$ ) atoms4 ,we make = ! atom a m5tal model ) all ! prop]ties ( ! me*anisms ( ! ord9>y scale ( magnitude & ) a few impress$ prop]ties 9 addition :i* repres5t ! new quantum relations4 ,z we n[ ?9k ( x1 ! atom has a massive core ab\t :i* electrons revolve "u an inv]se squ>e law1 ! connection betwe5 ! mass ( ! electron1 its accel]ation1 & ! =ce act+ on x be+ t usual 9 ,newtonian me*anics4 ,footnote #cb3 ,?is section 0 writt5 e>ly 9 #aibf )\t access to rec5t lit]ature4 ,our attitude t[>d quantum ph5om5a has be5 s mu* *ang$ s9ce !n by ! new quantum me*anics1 t a numb] ( ! foll[+ /atem5ts are sup]s$$ z a /atem5t ( pres5t op9ion4 ,h[ev] x has seem$ wor? :ile to let ! section /& z writt51 because _m ( ! developm5ts actually tak5 9 ! new me*anics foll[ ! l9es t x is "h urg$ !y ought to take1 & 9 s f> af=d int]e/+ confirmation ( ! po9t ( view ( ?is essay4 ,! space 9 :i* ! electron circulates is ?\ght ( z ,euclidean1 & ! motion is describ$ 9 "t1 :i* may be measur$ ) clocks 9 ! usual way4 ,! g5]al equations ( electrodynamics d n apply2 !re are no propagation effects inside ! atom1 ! motion ( ! electrons does n produce a magnetic field1 & !re is no radiation :5 ! electron is 9 "o ( its possible /able /ates1 9 spite ( ! accel]ation4 ,we may1 if we please1 9 work+ out ! "* ( ! motion1 entirely neglect ! electrical orig9 ( ! inv]se squ>e law1 & treat ?is m]ely z an impress$ =ce )\t fur!r implications4 ,sup]pos$ on ! ord9>y spatial1 temporal1 & me*anical *>act]i/ics ( ! model are additional quantum prop]ties1 "o :i* det]m9es ! p>ticul> orbit 9 :i* ! electron moves pdq nh1 & ano!r :i* det]m9es ! frequ5cy ( ! radiation emitt$ :5 ! electron passes f "o all[$ orbit to ano!r4 ,no me*anism is sugge/$ to acc\nt = ^! quantum conditions1 al?\gh ! conditions are =mulat$ 9 me*anical t]ms4 ,we n[ h to ask :at is ! mean+ 9 t]ms ( op]ations ( our usual concepts ( space-"t & me*anics :5 appli$ to ph5om5a ( ?is ord]4 ,x is ( c\rse evid5t1 z has already be5 emphasiz$1 t ! concepts h entirely *ang$ 9 "*1 because we d n measure an electron orbit1 = example1 by /epp+ (f ! diamet] ) met] /icks1 or by measur+ ! "t requir$ = light to travel across ! diamet]4 ,! p>ticul> feature ( imm$iate int]e/ 9 ?is *ang$ situation is ! *ange 9 numb] ( our concepts on ! atomic level4 ,i %all n attempt to f9d by an exact analysis ! numb] ( indep5d5t concepts at ?is level2 probably su* an analysis is n possible4 ,we may1 h[ev]1 make an approximate sugge/ion4 ,app>5tly ! mo/ important concept 9 describ+ relations inside a quantum sy/em corresponds to t ( en]gy on ! ord9>y scale4 ,*anges ( en]gy det]m9e ! frequ5cy ( emitt$ radiation1 z well z ! relations dur+ collisions ( atoms & electrons2 ^! collisional relations make direct connection ) exp]im5t ?r\gh ! voltages appli$ to electrons 9 collision exp]im5ts4 ,! analogue ( ! mom5tum concept also seems to h indep5d5t significance1 z %[n by ! ,compton effect4 ,! frequ5cy ( emitt$ radiation is also some?+ ) indep5d5t exp]im5tal significance4 ,i believe t ^! ?ree ?+s are all t h direct significance = quantum exp]im5ts made up to ! pres5t "t4 ,9 any ev5t1 x is p]fectly evid5t t on ! quantum level ! concepts :i* at pres5t h op]ational significance are consid]ably few] ?an on ! level ( ord9>y exp]i5ce4 ,ap>t f ! "q ( conv5i5ce1 !re may be ju/ification 9 cont9u+ to use our old me*anical =ms ( ?\ght if new exp]im5tal relations are !reby sugge/$4 ,t a v l>ge numb] ( su* z yet undiscov]$ relations may be sugge/$ 9 "s su* way is at once evid5t4 ,?us we h no pres5t k ( any ph5om5on associat$ ) :at ! electron does :5 pass+ f "o en]gy level to ano!r4 ,h[ long does x take to make ! passage8 ,:at is its pa? dur+ passage8 ,is x subject to ! ord9>y laws ( electrodynamics dur+ passage8 ,:5 & :]e is ! radiation emitt$ t corresponds to passage8 ,:5 ! electron leaves "o /able orbit is ! orbit on :i* x w ev5tually l& already det]m9$8 ,does ! radiation tra9 emitt$ dur+ a *ange f "o en]gy level to ano!r h a def9ite l5g? 9 space1 or may x h a v>iable l5g? & correspond+ly some?+ t corresponds to v>iable amplitude8 ,:at happ5s to ! radiation :5 ! electron passages are int]f]$ ) be=e ! emission ( a quantum has be5 complet$8 ,:at is ! me*anism by :i* ! quantum conditions are impos$8 ,is x n possible t "p ( ! clew to ! riddle ( ! mann] ( transition f purely quantum behavior to ! behavior ( classical me*anics may be f\nd 9 ! behavior ( ! electron dur+ passage f "o en]gy level to ano!r8 ,c]ta9ly we h a t5d5cy to ! classical behavior "u ^? conditions1 su* z at high temp]ature or 9 /rongly cond5s$ sy/ems1 9 :i* ! "t occupi$ 9 passage might be expect$ to become a m important "p ( ! total "t4 ,correspond+ to ^! que/ions !re %\ld be _m z yet undiscov]$ ph5om5a1 & ! me*anical po9t ( view !re=e has its value 9 sugge/+ exp]im5ts to detect su* effects4 ,x is ( c\rse too e>ly to see :at ! f9al result w be "h2 we _c tell :e!r ev5tually en\gh new exp]im5tal k9ds ( behavior w be f\nd to re/ore ! numb] ( indep5d5t concepts to t ( ! level ( ord9>y exp]i5ce or n1 or :e!r inde$ x w turn out t a great] numb] ( concepts is requir$4 ,x is contr>y to our in/9cts to expect a great] numb]1 & a small] numb] n[ seems to u n unnatural1 b ! consid]ations ( ?is essay %\ld prep>e u = ei!r possibility4 ,x is (t5 said t quantum ph5om5a are inconsi/5t ) ord9>y me*anics1 & pro(s ( ?is ass]tion are (t5 (f]$4 ,i believe t no su* pro(1 9 ! _s 9 :i* ! attempt is usually made1 c be correct1 = x seems to me t ! rem>k ( ,po9c> applies1 namely1 t any sort ( behavior c be imitat$ by a me*anical sy/em1 provid$ x is only complicat$ en\gh4 ,a p]emptory pro( ( ?is c be giv5 to any "o :o is n a believ] 9 vitalism4 ,if a s5ti5t be+ c be reg>d$ z a me*anical sy/em1 we m]ely h to /ation inside ea* atom a ,maxwell demon1 ) in/ructions to make ! atom react accord+ to quantum rules4 ,oppos$ to ! _s ( ?is sort ( r$uction ( quantum ph5om5a to me*anical t]ms1 we h to rememb] t x makes s5se to talk ab\t ! "* ( our conceptual /ructure only :5 ! numb] ( concepts is r$uc$ to ! numb] t h indep5d5t op]ational significance1 t is1 to ! m9imum numb]4 ,9 ! meantime let u exam9e :at may be ! significance 9 ! light ( pres5t exp]im5t ( /atem5ts l ^? ascrib$ to ,bohr t our usual concepts ( space & "t may be inapplicable 9 deal+ ) quantum ph5om5a4 ,?is idea is (t5 giv5 ! m explicit =m t space & "t may be ess5tially discont9u\s at ! quantum level4 ,f ! op]ational po9t ( view1 x is mo/ difficult to see exactly :at ?is m explicit /atem5t means1 at lea/ 9 t]ms ( ^? op]ations by :i* l5g? & "t 7 orig9ally def9$4 ,?us if space 7 discont9u\s1 x might mean t a po9t exi/s :i* may be rea*$ by lay+ (f a met] /ick f\rte5 times1 = example1 & ano!r po9t by lay+ (f sixte5 times1 b t no po9t c be f\nd ) fifte5 applications4 ,su* a /ate ( affairs seems to be inconsi/5t ) our def9ition ( ! c\nt+ op]ation & to h no conc]n ) any prop]ties ( space2 = :at %all we mean by lay+ (f a met] /ick sixte5 times if x _c be laid (f fifte5 times8 ,x is conceivable t space might end1 9 ! s5se t beyond a c]ta9 limit !re might be "s irremovable physical h9drance to ! cont9u$ lay+ (f ( di/ances ) a met] /ick 7al?\gh ,i ?9k t we %\ld be incl9$ to describe su* a /ate ( affairs 9 t]ms ( matt] enclos+ empty space r ?an z ! end ( space71 b to say t space may be discont9u\s seems to be mean+less4 ,9 ! same way1 ,i believe x mean+less to speak ( discont9u\s "t4 ,we may h ph5om5a discont9u\s 9 space & "t1 b n discont9u\s space or "t4 ,x seems !n t we mu/ give up ! idea t 9 ! quantum doma9 ! usual concepts ( space & "t may fail1 9 ! specific s5se t !y may become discont9u\s4 ,:at may we und]/& by ! failure ( ^! concepts 9 a m g5]al s5se8 ,no "o ( c\rse w\ld expect t ev5 ev5tually ! concepts w h ! same op]ational significance = ! inside ( an atom t !y h on ! ord9>y scale2 x mu/ be a modifi$ sort ( concept ) :i* we are conc]n$1 su* z we h already se5 is giv5 by ! field equations ( electrodynamics4 ,if n[ ! numb] ( op]ationally indep5d5t concepts on ! quantum level turns out to be ! same z on ! level ( ord9>y exp]i5ce1 & if !re is also ! possibility ( cont9u\s transition f ! op]ations ( ! quantum doma9 to ^? ( ord9>y exp]i5ce1 !n x seems to me t we %\ld say t our usual concepts ( space & "t /ill apply 9 ! quantum doma94 ,b if ! numb] ( op]ationally indep5d5t concepts is ei!r great] or less ?an on ! ord9>y level1 !n ,i believe we mu/ say t ! ord9>y concepts ( space & "t _c apply4 ,"o might /ill look = ! possibility ( sep>at+ out f ! complex ( concepts on ! quantum level a gr\p :i* might *ange cont9u\sly to ^? ( space & "t on ! ord9>y level1 b ,i ?9k t su* a possibility is v remote :5 "o consid]s t ! total numb] ( concepts *anges1 & t 9 ! zone :]e ! numb] *anges ! def9itions are n unique by :i* "o extrapolates a concept f "o doma9 to ano!r4 ,if ,bohr's idea is true t space & "t _c be us$ 9 describ+ ultimate quantum ph5om5a1 "o ( ! mo/ imm$iate implications 9 t]ms ( exp]im5t might be t ph5om5a correspond+ to int]m$iate positions ( ! electron betwe5 /able orbits d n exi/4 ,f9ally1 we mu/ comm5t on ! g5]al tactics ( ! quantum situation4 ,x w\ld seem t !re h already be5 a suffici5t numb] ( unsuccessful attempts to =mulate quantum behavior 9 t]ms ( ord9>y me*anics to ju/ify ! expectation t ultimately some?+ q diff]5t mu/ evolve4 ,! difficulties ( an unmodifi$ c>ry+ ov] ( ord9>y me*anical notions to quantum ph5om5a may be illu/rat$ by a simple example4 ,consid] a p>ticle ( mass m rotat+ 9 a frictionless circul> track ( radius r4 ,!n accord+ to quantum conditions x c move /ably on ?is track only ) c]ta9 def9ite velocities1 su* t pdq mv #br nh4 ,suppose n[ ! p>ticle rotat+ ) "o ( ! all[$ velocities1 & a tang5tial =ce appli$4 ,if ! usual me*anical notions ( =ce are /ill valid1 ! p>ticle mu/ respond by mov+ 9 its track ) cont9ually increas+ velocity4 ,aft] ! velocity has be5 increas$ by a small am\nt1 we remove ! =ce4 ,! motion is n[ no long] "o ( ! all[$ ones1 & ! p>ticle mu/ 9 "s way *ange its velocity2 x mu/ ei!r sl[ d[n or spe$ up4 ,9 ! fir/ case x mu/ ei!r radiate en]gy1 :i* a sy/em ( ! simple me*anical prop]ties we h suppos$ is n capable ( do+1 or else ! law ( cons]vation ( en]gy fails1 & also ,newton's fir/ law ( motion dur+ ! process ( acquir+ ! /eady condition4 ,if1 on ! o!r h&1 ! p>ticle spe$s up1 x mu/ increase its en]gy f n[h]e1 & aga9 ord9>y me*anics does n apply4 ,x seems !n a mi/ake to attempt to =mulate ! quantum conditions 9 t]ms ( ! notions ( ord9>y me*anics 7mom5tum1 & position cord9ates 9 ei!r ! ord9>y or ! g5]aliz$ ,lagrangean s5se74 ,x w\ld seem1 on ! o!r h&1 plausible to expect t me*anics is n a fundam5tal ?+1 b is 9 "s way an effect produc$ by ! aggregate action ( a great _m elem5t>y quantum processes4 ,amplitude ( radiational vibration1 = example1 may be su* a /ati/ical aspect ( a great _m processes1 9 "s su* way z on ! ord9>y level ( exp]i5ce temp]ature is a /ati/ical aspect ( ! av]age k9etic en]gy ( ! atoms4 ,"o possibility ( ?is k9d has already be5 m explicitly indicat$2 9 ! elem5t>y process ( emission ( radiation1 frequ5cy & en]gy are n two indep5d5tly assignable v>iables1 b are connect$ ,e h4 ,t is1 on ! quantum level radiation has only a s+le prop]ty1 :i* is prop]ly nei!r en]gy or frequ5cy4 ,we are n[ neglect+ ! pol>ization aspect ( radiation4 ,on a high] level1 t ( ord9>y radiation1 ! s+le elem5t>y prop]ty has exp&$ itself into two 7en]gy & frequ5cy7 ?r\gh ! additional v>iable ( ! numb] ( elem5t>y quantum processes 9 ! complex radiation4 ,! program ( ! imm$iate future %\ld be an ext5sion ( some?+ ( ?is sort1 namely1 to inv5t new concepts correspond+ to ! exp]im5tally indep5d5t ?+s on ! quantum level 7su* p]haps z ! resultant ( ! fusion ( ! en]gy & frequ5cy concepts = radiation71 & !n to %[ h[ ! ord9>y concepts ( me*anics 7& v likely ^? also ( space & "t7 are g5]at$ by /ati/ical effects 9 aggregates ( great numb]s4 ,p]haps x is yet too e>ly = an attempt ( ?is sort1 because x may seem t !re are /ill too _m possibilities ( new exp]im5tal discov]ies :i* might upset ! results ( elaborate !oretical speculation4 ,if ?is %\ld really be felt to be ! case1 ,i believe t physics ought = ! pres5t to hold 9 p>tial abeyance its !oretical activities 9 ?is field1 & devote itself to acquir+ z rapidly z possible ! necess>y exp]im5tal facts4 ,we may emphasize aga9 t ! possibility ( c>ry+ out ?is plausible program c be prov$ only by exp]im5t2 x may be t m concepts w be requir$ on ! quantum level ?an = ord9>y exp]i5ce4 ,! inv5tion ( new concepts is c]ta9ly n an easy ?+1 & is some?+ :i* physics has always delib]ately1 & p]haps ju/ifiably1 %irk$1 z %[n by ! p]si/5t attempts to c>ry ! notions ( me*anics d[n into ! f9e/ /ructure ( ?+s4 ,?is %irk+ has n _h bad results1 b on ! contr>y good results1 z long z physics has be5 prim>ily conc]n$ ) ph5om5a ne> ! range ( ord9>y exp]i5ce1 b ,i believe t z we get f>!r & f>!r away f ord9>y exp]i5ce1 ! inv5tion ( new concepts w become an increas+ necessity4 ,,*apt] ,,iv ,,special ,,views ,,( ,,nature ,,9 ?is la/ *apt] we propose to discuss c]ta9 special hypo!ses ab\t ! /ructure ( nature1 & c]ta9 o!r matt]s t c\ld be/ be left until we _h exam9$ our fundam5tal concepts4 ,we h se5 t 9 sett+ up ! g5]al rules :i* are to guide u 9 describ+ & correlat+ nature1 we h to take extreme c>e to all[ no special hypo!ses to creep 91 z o!rwise we might be re/ra9+ possible future exp]i5ce4 ,ev5 "h !re is no h>d & fa/ l9e ( sep>ation ( ! g5]al f ! special1 & "o might entangle himself 9 inextricable difficulties if 8 ideals 7 too meticul\s4 ,h[ = example is ! critic to be answ]$ :o says3 ,y\r v endeavor to =mulate pr9ciples s broad z n to re/rict future exp]i5ce means1 :5 exam9$ 9 ! light ( op]ations1 t y are seek+ = pr9ciples :i* pa/ exp]i5ce sugge/s w n limit ! future4 ,x is 9 ! v nature ( ?+s impossible to escape all ! implications ( pa/ exp]i5ce & !re=e to f9d any completely g5]al pr9ciple4 ,i believe t we mu/ admit ! critic is "r1 & t rigor\sly our goal is impossible ( atta9m5t4 ,we may say 9 p>tial self-def5se t all ! discussion ( ?is essay has be5 subject to "o explicit assumption1 namely1 t ! work+ ( our m9ds is und]/ood1 :i* ( c\rse involves ! assumption t our m9ds cont9ue to function 9 ! future 9 ! same way z 9 ! pa/4 ,ev5 ) ?is proviso we c n rigor\sly avoid ! implications ( ! pa/1 b !re c be no practical "q t we recognize c]ta9 assumptions ab\t ! behavior ( nature to be s special z to limit s]i\sly ! physical possibilities1 & o!r assumptions to be less re/rict+4 ,9 ! previ\s discussion we _h to make assumptions1 b ,i hope ^! assumptions w be recogniz$ by all ) physical exp]i5ce to be s broad z n to re/rict u s]i\sly4 ,m special assumptions or hypo!ses h _! v great use1 h[ev]1 :5 we attempt to pu% =w>d ! doma9s ( exp]im5tal k1 because !y may sugge/ new exp]im5ts or aid 9 correlat+ in=mation already obta9$4 ,^! special hypo!ses may cov] a v wide range ( g5]ality2 "s ( !m are g5]al en\gh 9 "* to be discuss$ "h4 ,among ^! special hypo!ses !re is a gr\p :i* play an important "p 9 ! speculation ( mo/ physici/s1 & :i* h features 9 common4 ,^! are3 ! hypo!ses ( ! simplicity ( nature1 ( ! f9it5ess ( nature 9 ! direction ( ! v small1 & ( ! det]m9at5ess ( ! future 9 t]ms ( ! pres5t4 ,t ^! views h po9ts ( simil>ity is obvi\s if we consid] a hypo!tical special case4 ,suppose t no physical /ructure beyond ! electrons & protons c be discov]$1 or is ev5 sugge/$ by any kn[n ph5om5on1 s t ! entire future behavior ( a sy/em c be det]m9$ by a specification ( ! pres5t relations ( all its protons & electrons2 9 ?is case nature w\ld be bo? simple & f9ite & ! future det]m9$ by ! pres5t4 ,,! ,,simplicity ,,( ,,nature ,( ^! hypo!ses1 p]haps ! mo/ important is t ( ! simplicity ( nature1 because ( its wide spread diffusion & ! effect x has _h on physical ?\ght4 ,! hypo!sis ( simplicity assumes sev]al =ms2 "s physici/s are conv9c$ t ! laws :i* gov]n nature are simple1 o!rs t ! ultimate /uff ( :i* nature is compos$ is simple 7p]haps protons & electrons & en]gy71 or !re may be a comb9ation ( bo? views into ! belief t ultimately we %all f9d simple ultimate elem5ts behav+ accord+ to simple laws4 ,9 "o respect x is obvi\s t nature is n simple1 namely num]ically--try c\nt+ ! electrons or atoms or />s6 ,consid] n[ ! fir/ ( ^! aspects ( ! !sis ( simplicity1 :i* may be express$ z ! conviction t ! behavior ( ! entire univ]se c be compreh5d$ 9 a few pr9ciples ( great bread? & simplicity1 su* z ! inv]se squ>e law ( =ce1 or ! second law ( !rmodynamics1 or p]haps /ill bett] ! equality ( ! elem5t>y positive & negative *>ges1 :i* app>5tly holds to an enorm\s degree ( precision4 ,9 explanation ( a view l ?is !re is 9 ! fir/ place ! m5tal urge1 because we c take a satisfaction almo/ /hetic 9 contemplat+ su* a univ]se1 & !re is 9 ! second place a /rong sugge/ion f exp]i5ce4 ,practically all ! hi/ory ( physics is a hi/ory ( ! r$uction ( ! complicat$ to ! simpl]4 ,= example1 ! behavior ( a l>ge "p ( ! _w ( imm$iate exp]i5ce c be r$uc$ to ! simple laws ( me*anics4 ,! behavior ( ano!r v l>ge gr\p ( natural ph5om5a c be r$uc$ to !rmodynamics4 ,! behavior ( ! heav5ly bodies1 :i* at fir/ 0 describ$ 9 a r complicat$ way 9 ! ,ptolemaic sy/em ( a/ronomy1 c be r$uc$ to ^? same laws ( me*anics :i* we f9d 9 our imm$iate neighborhood1 ) ! "o addition ( ! univ]sal law ( gravitation1 :i* lat] ref9$ exp]im5t discloses is really active 9 our imm$iate surr\nd+s4 ,simil>ly ! laws ( !rmodynamics 7except t "p deal+ ) radiation7 are r$uc$ to ! ord9>y laws ( me*anics ?r\gh ! additional assumption ( ! atomic /ructure ( matt]4 ,truly a /up5d\s accompli%m5t t may well color our :ole future outlook4 ,"o may f9d great ju/ification "h = ! belief t all nature w ultimately be r$uc$ to a simil> simplicity1 &1 9 p>ticul>1 ju/ification = ! attempt to f9d ! explanation ( all nature 9 ! action ( me*anical laws4 ,n[1 ( c\rse1 z a matt] ( physical & hi/orical fact1 ?is program c\ld n be c>ri$ ?r\gh1 b obdurate physical ph5om5a 7 discov]$4 ,electric ph5om5a1 :i* at fir/ seem$ s promis+1 refus$ to fit into ! s*eme1 & ! conv]se attempt1 to expla9 me*anical effects 9 t]ms ( electrical effects1 also fail$4 ,we /ill c>ry our ord9>y me*anical notions d[n into ! realm ( small electric effects1 & /ill talk1 = in/ance1 ab\t non-electrical =ces :i* hold an electron toge!r4 ,nor are !re exp]im5ts af=d+ suffici5t basis = believ+ t all ! mass ( a positive nucleus is electrical 9 "*4 ,we also ?9k ( electrical *>ges z hav+ ! prop]ty ( id5tifiability1 :i* involves ! possession ( %>p edges & a *ange 9 ! law ( =ce at small di/ances1 & ?is is c]ta9ly a prop]ty c>ri$ ov] f our l>ge scale exp]i5ce4 ,x seems fairly evid5t !n t ! laws ( nature _c be r$uc$ to ei!r ^? ( me*anics or ( electricity1 nor probably1 z is sugge/$ by quantum ph5om5a1 to a comb9ation ( bo?4 ,?is ( c\rse does n preclude ! possibility t ! laws /ill may be simple :5 express$ 9 o!r =ms4 ,an example ( su* a broad g5]al law t goes deep] ?an me*anics or electrodynamics is probably af=d$ by ! second law ( !rmodynamics :5 ext5d$ to include radiation ph5om5a4 ,examples ( attempts to f9d o!r su* simple laws are ,tolman's ,pr9ciple ( ,similitude1#cc & ,lewis's !ory ( ,ultimate ,rational ,units1#cd & 8 rec5tly enunciat$ pr9ciple ( ,complete ,rev]sibility4#ce ,! fir/ two ( ^! attempts ,i d n believe are successful1 = reasons ,i h /at$ else:]e1#cf ! ?ird also seems some:at d\btful4 ,footnote #cc3 ,r4 ,c4 ,tolman1 ,phys4 ,rev4 #c1 #bdd-bee1 #aiad2 #f1 #bai-bcc1 #aiae2 #ae1 #eba1 #aibj2 ,j\r4 ,am]4 ,*em4 ,soc41 #dc1 #hff-hge1 #aiba4 ,footnote #cd3 ,g4 ,n4 ,lewis4 ,vol4 #ae1 #aiba ( ! ,contributions f ! ,jeff]son ,physical ,laboratory1 d$icat$ to ,pr(essor ,hall1 ,cambridge1 ,mass42 ,phil4 ,mag41 #di1 #gci-gej1 #aibe4 ,footnote #ce3 ,g4 ,n4 ,lewis1 ,proc4 ,nat4 ,acad4 ,sci41 #aa1 #agi-ahc1 #dbb-dbh1 #aibe4 ,footnote #cf3 ,p4 ,w4 ,bridgman1 ,phys4 ,rev4 #h1 #dbc-dca1 #aiaf2 ,dim5sional ,analysis1 p4 #aje4 ,) reg>d to ! g5]al "q ( simple laws1 !re are at lea/ two attitudes2 "o is t !re are probably simple g5]al laws /ill undiscov]$1 ! o!r is t nature has a pr$ilection = simple laws4 ,i d n see h[ !re c be any qu>rel ) ! fir/ ( ^! attitudes4 ,let u exam9e ! second4 ,we h 9 ! fir/ place to notice t simple means simple to u1 :5 /at$ 9 t]ms ( our concepts4 ,?is is 9 itself suffici5t to raise a presumption aga9/ ?is g5]al attitude4 ,x is evid5t t our ?9k+ mu/ foll[ ^? l9es impos$ by ! nature ( our ?9k+ me*anism3 does x seem likely t all nature accepts ^! same limitations8 ,if ?is 7 ! case1 our conceptions ought to /& 9 c]ta9 simple & def9ite relations to nature4 ,n[ if our discussion has br\ght out any "o ?+1 x is t our concepts are n well def9$ ?+s1 b !y are hazy & d n fit nature exactly1 & _m ( !m fit ev5 approximately only )9 re/rict$ range4 ,! task ( f9d+ concepts :i* %all adequately describe nature & at ! same "t be easily h&l$ by u1 t is1 be simple1 is ! mo/ important & difficult ( physics1 & we nev] a*ieve m ?an approximate & tempor>y success4 ,consid] ! example ( "t4 ,! orig9al concept ( local "t1 :i* = long seem$ satisfactory1 turns out to be inadequate1 & has to be replac$ by ext5d$ "t1 :i* is s complicat$ t x is que/ionable :e!r we %all ev] be able to grasp x ) ! confid5ce t we mu/ dem& 9 a useful concept 7by grasp ,i mean intuitive comm& ( all ! implications ( ! op]ations :i* are involv$74 ,! concept has n yet be5 f\nd :i* describes simply ! temporal relations ( ! univ]se4 ,n only are concepts hazy ar\nd ! edges & s incapable ( fitt+ nature exactly1 b !re is always ! *ance t !re are concepts o!r ?an ^? :i* we h adopt$ :i* w\ld fit our pres5t ph5om5a4 ,f9d+ concepts to fit nature is mu* l solv+ a cross-^w puzzle4 ,9 ! puzzle !re may be "s p>ts ( ! patt]n :i* we fill completely & easily1 b sometimes we f9d p>ts 9 :i* we c fill 9 ev]y?+ except "o or two ob/9ate def9itions1 s t we are sure we are on ! "r track1 & rack our bra9s = ! miss+ words1 :5 ) a fla% ( inspiration we see t ! ob/9ate words c be fitt$ 9 by a complete *ange 9 ^? :i* we _h already accept$4 ,x may be t we are soon to witness a simil> *ange 9 our concept ( ! nature ( light4 ,an important diff]5ce betwe5 ! cross-^w puzzle & nature is t we c nev] tell :5 we h fill$ 9 all ! squ>es 9 any ( ! p>ts ( nature's puzzle2 !re is always ! possibility ( new ph5om5a :i* our pres5t s*eme does n t\*4 ,consid]+1 !n1 ! nature ( our conceptual mat]ial1 x seems to me t ! ov]:elm+ presumption is aga9/ ! laws ( nature hav+ any pr$isposition to simplicity z =mulat$ 9 t]ms ( our concepts 7:i* is ( c\rse all t simplicity means71 & ! wond] is t !re are app>5tly s _m simple laws4 ,!re is ?is obs]vation to be made ab\t all ! simple laws ( nature t h hi!rto be5 =mulat$2 !y apply only ov] a c]ta9 range4 ,we h n ext5d$ ! laws ( gravitation to small bodies1 nor h we f\nd t our electrical laws w "w on a cosmic scale4 ,x does n seem s v surpris+ t ov] a limit$ doma91 9 :i* ! mo/ important ph5om5a are ( a re/rict$ type1 ! conduct ( nature %\ld foll[ comp>atively simple rules4 ,a tempt+ "q is :e!r !re may n be "s laws ( nature t are really simple1 )\t relation to our mode ( =mulation1 su* z ! law ( ! inv]se squ>e4 ,i leave x to ! read] to decide :e!r ?is "q has mean+4 ,9 ?is connection x is possibly significant t ! av]age physici/ is /rangely reluctant to tamp] ) ! inv]se squ>e law4 ,i f9d 9 myself a lack ( sympa?y1 :i* ,i _c ju/ify by any ( ! consid]ations ( ?is essay1 ) attempts l ! rec5t "o ( ,swann1#cg = example1 to expla9 a wide v>iety ( hi!rto ob/9ate effects by ! assumption ( slightly unequal dep>tures f ! inv]se squ>e law by ! electrons & protons4 ,( c\rse ,i hope t ?is feel+ w turn out n to be prejudice1 b w p]haps be ju/ifi$ by "s su* g5]al obs]vation z t a dep>ture f ! inv]se squ>e law s slight z by def9ition to be =ev] beyond detection by direct exp]im5t is mean+less2 b ( ?is ,i am n at all sure4 ,footnote #cg3 ,w4 ,f4 ,g4 ,swann1 ,phys4 ,rev41 #be1 #bec1 #aibe4 ,we are n[ ready to consid] ! second respect 9 :i* nature may be simple1 namely1 because ! mat]ial ( :i* x is built may r$uce to a few sorts ( elem5ts4 ,9 ?is discussion x w be conv5i5t to consid] also at ! same "t ! m inclusive simplicity aris+ f simple laws act+ on simple elem5ts4 ,! imm$iate "q = u "h is "o ( fact3 does nature seem to be gett+ intr9sically simpl] z we get t[>d small scale ph5om5a8 ,!re is mu* room = diff]5ce ( op9ion "h2 p]sonally ,i feel t ?is expect$ simplicity is n 9 evid5ce1 at lea/ to ! ext5t t we c\ld desire4 ,= in/ance1 ! fact t ! electrons mu/ h bo? electrical & me*anical prop]ties is a /raw 9 ?is direction4 ,x mu/ also be rememb]$ t a c]ta9 simulation ( simplicity is inevitable z we approa* ! limits ( exp]im5tal k1 :atev] ! actual /ructure ( nature1 = ! m]e reason t ne> ! limit our possible exp]im5tal op]ations become few] 9 numb]1 & our concepts few] also4 ,! "q :i* we are try+ to answ] has1 !re=e1 its real mean+ only 9 t]ms ( ! possible future4 ,d we believe t if we drive 9 our /akes at a c]ta9 po9t on our pres5t fronti]s1 ?is po9t w gradually1 z physics advances1 become possess$ ( a cont9ually ri*] exp]i5ce1 s t nature at ?is po9t w appe> increas+ly complicat$8 ,or d we expect a t]m9ation ( ?is process ( expansion fairly soon8 ,x seems to me t z a matt] ( exp]im5tal fact !re is no d\bt t ! univ]se at any def9ite level is on ! av]age becom+ increas+ly complicat$1 & t ! region ( app>5t simplicity cont9ually rec$es4 ,?is1 h[ev]1 is n ! op9ion ( all obs]v]s4 ,?us ,b]tr& ,russell1 9 ,:at ,i ,believe1 page #aj1 writes1 ,physical ,sci5ce is !n approa*+ ! /age :]e x w be complete1 & !re=e un9t]e/+4 ,?is is p]haps a p>ticul>ly favorable epo* 9 ! hi/ory ( physics to urge ! ess5tial complexity ( nature1 because all our new quantum ph5om5a indicate a va/ weal? ( hi!rto unsuspect$ relations on ! v edge ( ! atta9able4 ,!re is "o aspect ( quantum relations1 z also ( our ideas ( ! nature ( ! /ructure ( ! nucleus ( ! atom1 :i* is p>ticul>ly significant 9 ?is respect1 namely1 t we h to describe ph5om5a by /ati/ical me?ods4 ,n[ a /ati/ical me?od is us$ ei!r to conceal a va/ am\nt ( actual ignorance1 or else to smoo? out ! details ( a va/ am\nt ( actual physical complication1 mo/ ( :i* is uness5tial = our purposes4 ,!re c be no d\bt ( ! am\nt ( ignorance t ! /ati/ical me?od conceals :5 appli$ to ^! ph5om5a1 b !re are also /rong indications1 p>ticul>ly :5 appli$ to ! nucleus1 t x cov]s a va/ am\nt ( actual physical complications4 ,! nucleus ( a radium atom becomes un/able on ! av]age e #ajd ye>s1 :i* may be plausibly tak5 to indicate t e #ajd ye>s ! radium nucleus gets itself into "s p>ticul> configuration4 ,consid]+ ! "t scale on :i* we suppose ev5ts 9 ! atom to take place1 & also consid]+ ! fact t radioactive dis9tegration seems unaffect$ by outside ag5cies1 ?is w\ld indicate a p]fectly appall+ am\nt ( /ructure4 ,we are simil>ly driv5 to /ati/ical me?ods 9 quantum !ory1 z = example1 9 ,e9/e9's analysis ( ! details ( equilibrium betwe5 emitt+ & absorb+ atoms & radiation4 ,9 g5]al1 we _c admit = a m9ute t a /ati/ical me?od1 unless us$ to smoo? out irrelevant details1 c ev] m>k m ?an a tempor>y /age 9 our progress1 because ! assumption ( ev5ts tak+ place accord+ to pure *ance con/itutes ! complete negation ( our fundam5tal assumption ( connectivity2 su* /ati/ical me?ods always indicate ! pres5ce ( physical complications :i* x mu/ be our aim to dis5tangle ev5tually4 ,x appe>s !n t pres5t exp]im5tal evid5ce makes v probable /ructures beyond ! electron & ! quantum2 we may g ev5 fur!r & say t !re is no exp]im5tal evid5ce t ! sequ5ce ( ph5om5a 9 nature z we g to ev] small] scales is a t]m9at$ sequ5ce1 or t a drop ( wat] is n 9 itself ess5tially inf9ite4 7,?is /atem5t conta9s by implications ! mean+ t we atta* to inf9ite47 ,all ! m1 !n1 !re is no evid5ce t nature r$uces to simplicity z we burr[ d[n into ! small scale4 ,:atev] may be "o's op9ion z to ! simplicity ( ei!r ! laws or ! mat]ial /ructure ( nature1 !re c be no "q t ! possessors ( "s su* conviction h a real advantage 9 ! race = physical discov]y4 ,d\btless !re are _m simple connections /ill to be discov]$1 & he :o has a /rong conviction ( ! exi/5ce ( ^! connections is mu* m likely to f9d !m ?an he :o is n at all sure !y are !re1 & is m]ely hunt+ = any?+ t may turn up4 ,x is l>gely a matt] ( psy*ology4 ,ev]yone kn[s t ! m]e sugge/ion t a problem has a solution1 or ! k t someone has already solv$ x1 is (t5 suffici5t to sugge/ a relation t o!rwise might n h be5 notic$4 ,! *ances are1 !re=e1 t ! relations betwe5 ph5om5a w be f\nd by ^? :o are previ\sly conv9c$ t ! relations exi/4 ,! obs]vation t mo/ ( ! discov]ies are made by m5 ) p>ticul> sorts ( conviction naturally /r5g!ns ! belief t _! convictions are true4 ,b ?is picture has an obv]se side4 ,! man :o is conv9c$ t !re is a relation :]e none exi/s may wa/e all 8 "t 9 va9 seek+ = x4 ,grant$ t nature has no p>ticul> pr$isposition to simple relations1 ! conviction t !re are su* relations is1 f ! po9t ( view ( any "o individual1 z likely to be a h9drance z a help4 ,f ! po9t ( view ( physical society1 on ! o!r h&1 x is desirable t !re be su* convictions1 = 9 su* a society !re w be m discov]ies ?an 9 a society )\t su* convictions4 ,we h "h aga9 ! old conflict betwe5 ! individual & society4 ,z 9 all o!r simil> conflicts1 society w n be able to dem& p]man5tly f ! individual ! acceptance ( any conviction or cre$ :i* is n true1 no matt] :at ! ga9 9 o!r ways to society4 ,if nature is n simple1 physici/s w n cont9ue to believe t x is1 ev5 if su* a conviction does increase ! total numb] ( discov]ies4 ,x is an impossible attitude to expect t "o c ma9ta94 ,does ?is !n mean t physics is to face a drab future1 becom+ cont9ually m prosaic1 ) new discov]ies ev] r>]1 made by a cont9ually decreas+ numb] ( misguid$ b =tunate en?usia/s8 ,!re may be su* a dang]1 b ! greate/ "p ( ! dang] is avoid$ if its nature is cle>ly recogniz$4 ,"o ( ! problems ( ! future is ! self-consci\s developm5t ( a m p[]ful te*nique = ! discov]y ( new relations )\t ! necessity = preconceiv$ op9ions on ! "p ( ! obs]v]4 ,!re is an aspect "h ( our physical rese>* t is (t5 lo/ sight (1 namely1 ! small proportion ( successful discov]ies comp>$ ) ! numb] ( inve/igators4 ,c]ta9ly ! numb] ( unsuccessful attempts1 ev5 9 ! case ( ^? =tunate individuals :o make ! great discov]ies1 is v mu* great] ?an ! numb] ( _! successful attempts4 7,f>aday's reput$ satisfaction ) a return comes to m9d47 ,?is mu/ always be tak5 into acc\nt 9 e/imat+ ! probable *ances ( correctness ( any new !ory4 ,) s _m physici/s work+ to devise new !ories1 ! *ances are high t _m false !ories w be f\nd1 9 :i* a numb] ( ph5om5a may app>5tly fit toge!r into a new relation1 b :i* ev5tually prove to be inconsi/5t ) o!r ph5om5a1 s t ! propos$ !ory has to be ab&on$4 ,z physics advances & ! numb] ( inve/igators & ! am\nt ( physical mat]ial increases1 "o has to be m & m exact+ 9 "o's requirem5ts ( a new !ory4 ,"o mu/ be p>ticul>ly on gu>d aga9/ num]ical co9cid5ces4 ,an int]e/+ *apt] might be writt5 on num]ical relations :i* h be5 hopefully publi%$1 b lat] _h to be ab&on$ z )\t significance4 ,,det]m9ism ,if we are "r 9 suppos+ t physical evid5ce gives no w>rant = ! idea t nature is f9ite d[nw>d1 we h n only repudiat$ ! !sis ( simplicity b we h also made a v important obs]vation on ! o!r g5]al !sis m5tion$ at ! beg9n+ ( ?is *apt]1 namely1 ! !sis ( physical det]m9ism4 ,by det]m9ism we und]/& ! belief t ! future ( ! :ole univ]se1 or ( an isolat$ "p ( x1 is det]m9$ 9 t]ms ( a complete description ( its pres5t condition4 ,:at we mean by pres5t condition w be discuss$ lat]4 ,x is popul>ly assum$ t e physici/ subscribes to "s su* !sis z ?is4 ,b n[ if !re is inf9ite /ructure ev5 9 a small isolat$ "p ( ! univ]se1 a complete description ( x is impossible1 & ! doctr9e z /at$ mu/ be ab&on$4 ,x seems to me t all pres5t physical evid5ce prep>es u to admit ?is possibility4 ,i suppose1 h[ev]1 t mo/ physici/s w\ld subscribe to "s modification ( ! orig9al !sis1 p]haps along ! foll[+ l9es4 ,giv5 a description ( an isolat$ "p ( ! physical univ]se 9 ! mo/ complete t]ms t h physical mean+1 t is1 d[n to ! smalle/ elem5ts ( :i* our physical op]ations give u cognizance1 !n ! future hi/ory ( ! sy/em is det]m9$ )9 a c]ta9 p5umbra ( unc]ta9ty1 ?is p5umbra gr[+ broad] z we p5etrate to f9] details ( ! /ructure ( ! sy/em or z times goes on1 until ev5tually all b c]ta9 v g5]al prop]ties ( ! orig9al sy/em1 su* z its total en]gy1 are =ev] lo/ 9 ! haze1 & we h a sy/em :i* 0 unpr$ictable4 ,i suppose t x is a fur!r conviction ( at lea/ _m physici/s t by suffici5tly ref9+ our measurem5ts1 ! am\nt ( haze at any fix$ po9t 9 ! future may be made indef9itely small1 & _m might ev5 g fur!r & hope by /udy+ ! haze 7p]haps /ati/ically7 to obta9 "s inf]5tial evid5ce ( /ructure beyond t yet exp]i5c$4 ,9 fact x may be t ?is la/ conta9s ! g]ms ( ! ultimate me?od ( inve/igation1 if we ev] rea* a /age :5 we c no long] ref9e our me?ods ( measurem5t4 ,det]m9ism to ! physici/ is simply a way ( /at+ c]ta9 implications ( 8 conviction ( ! connectivity ( nature4 ,we h se5 t ! broade/ possible /atem5t ( ! !sis ( connectivity is3 ,giv5 two isolat$ sy/ems ) id5tical pa/ hi/ories up to a c]ta9 epo*1 !n ! future hi/ories w also be id5tical4 ,! !sis ( ! det]m9ism ( ! future by ! pres5t con/itutes a specialization ( ?is g5]al !sis 9 t we suppose t id5tity ( all pa/ hi/ory is n necess>y = id5tity ( future behavior1 b only id5tity ( pres5t condition4 ,! g5]al & ! special !sis are n equival5t by any means3 if pa/ hi/ories are id5tical !n pres5t conditions are also id5tical1 b ! conv]se does n necess>ily hold at all4 ,n[ ,i believe t ! g5]al !sis 7:i* ,i suppose all physici/s w admit1 b ^: tru? is nev]!less subject to ! v]ification ( exp]i5ce7 gets turn$ into ! special !sis by a feel+ ( some:at metaphysical cont5t1 :i* we may p]haps /ate by say+ t we c see no way by :i* ! pa/ c affect ! future except ?r\gh ! pres5t4 ,we d n l to ?9k ( ! effect ( a cause di/ant 9 ! pa/ jump+ ov] ! pres5t & affect+ ! future )\t t\*+ ! pres5t at all4 ,x is ! analogue ( t attitude ( m9d to :i* action at a di/ance 9 space is inconceivable2 j z x is difficult to conceive ( a body "h affect+ a body !re )\t 9 "s way an action propagat$ ?r\gh int]m$iate space1 s we d n l to ?9k ( a pa/ cause jump+ ov] "t & produc+ a future effect )\t "s sort ( cont9uity 9 ! causal *a9 ?r\gh all int]m$iate "t4 ,s f> our discussion has be5 purposely loose3 x is evid5t t :at we mean by pres5t /ate is cry+ = def9ition4 ,:at is meant by ?is may dep5d some:at on ! specific hypo!sis t "o adopts ab\t ! /ructure ( nature4 ,hi/orically ! conviction ( future det]m9ism has be5 mo/ intimately associat$ ) a me*anical picture ( ! /ructure ( ! univ]se1 s t x may be well to beg9 f ?is po9t ( view4 ,suppose ! simple/ possible sy/em compos$ ( po9t masses )\t /ructure1 z 9 ! k9etic !ory ( gases4 ,:at sort ( specifications d we believe necess>y to fix ! pres5t /ate ( su* a sy/em8 ,! me*anical view ( nature gives a def9ite answ]4 ,by pres5t /ate we mean ! positions & velocities ( all ! masses4 ,?is is suffici5t = ! complete det]m9ation ( any purely me*anical sy/em1 9 :i* ! =ces betwe5 ! elem5ts are kn[n functions ( only _! relative positions4 ,by a sort ( ext5sion ( ^! ideas valid = me*anical sy/ems1 x seems to be (t5 ?\ght t ! pres5t /ate ( any sy/em is det]m9$ by a complete specification ( ! positions & velocities ( all ! ultimate elem5ts ( ! sy/em 7provid$ always ( c\rse t ?is numb] is f9ite74 ,?is pr9ciple1 h[ev]1 does n appe> to be> ! *eck ( exp]im5t :5 appli$ to electrical sy/ems ) radiation4 ,! !orems ( ! ret>d$ pot5tial %[ t su* sy/ems are det]m9$ by ! pres5t position & velocities ( ! *>ges 9 ! imm$iate vic9ity1 & by ! correspond+ data at remote po9ts giv5 = prop] epo*s 9 ! pa/2 9 ?is case1 !re=e1 pa/ & pres5t hi/ory are necess>y to det]m9e ! future4 ,b if we consid] ! electrical field z "p ( ! sy/em1 we may fix ! future 9 t]ms ( ! pres5t positions ( ! *>ges1 _! velocities1 & ! values ( ! field vectors all ov] space1 ?us return+ to a c]ta9 =mal resemblance to me*anical sy/ems1 & sugge/+ a reason = ascrib+ physical reality to ! electric field4 ,?is analogy ) a me*anical sy/em is1 h[ev]1 loose2 complete analogy w\ld all[ ! in/antane\s values ( ! "t d]ivatives ( ! field to be giv5 also1 & ?is is n possible4 ,h[ is x t velocity c /rictly be reg>d$ z *>act]i/ic ( ! pres5t /ate ( ! sy/em8 ,c]ta9ly ! usual op]ations = measur+ velocity dem& t we "k ! configuration ( ! sy/em at two diff]5t times1 & calculate ! velocity f c]ta9 diff]5ces ( ! sy/em at ^! two times4 ,! velocity is def9$ z a limit+ result1 b ev5 9 ! limit ! ess5tial physical fact does n disappe> t we mu/ "k ! positions ( ! sy/em at two times4 ,we may n[ g fur!r2 if ! velocity is prop]ly includ$ 9 ! pres5t attributes ( ! sy/em1 we c see no reason = n includ+ a specification ( all ! high] "t d]ivatives also4 ,9 ! case ( ! simple gase\s sy/em "u pres5t consid]ation we c answ] ?is "q by exam9+ ! op]ations by :i* we actually g to "w to det]m9e ! future ( su* a sy/em4 ,! problem ( det]m9+ ! future condition ( su* a sy/em r$uces to ! problem ( writ+ ! diff]5tial equations ( motion ( all its p>ts4 ,if ! sy/em is a me*anical sy/em1 z 9 ?is case1 ^! equations are ( ! second ord] 9 ! "t d]ivatives ( ! position coord9ates1 & also involve ! =ces1 :i* we suppose are kn[n 9 t]ms ( ! relative positions ( ! p>ts ( ! sy/em4 ,giv51 !n1 ! positions & ! way 9 :i* ! =ces dep5d on ! relative positions ( ! p>ts1 ! equations ( motion c be writt5 d[n = any configuration ( ! sy/em1 & ^! equations may be integrat$ 7at lea/ approximately7 9 t]ms ( ! prop] initial conditions4 ,n[ ! only b\nd>y conditions on a second ord] equation are ! initial positions & velocities4 ,?is is ! reason t velocities h to be specifi$ 9 giv+ ! pres5t condition ( ! sy/em1 & t x is n necess>y to give ! high] d]ivatives4 ,app>5tly ! reason :y we in/9ctively include velocity among ! pres5t prop]ties ( ! sy/em is n because velocity is by its nature /rictly a pres5t prop]ty ( ! elem5ts ( ! sy/em1 b r because our wide exp]i5ce ) me*anical sy/ems has %[n t z a matt] ( fact velocity is necess>y 9 su* sy/ems to det]m9e future motion4 ,b n[ if ! equations ( motion ( ! p>ts ( ! sy/em are n ^? ( me*anics1 !y w 9 g5]al be mu* m complicat$ 9 appe>ance & w involve high] d]ivatives ( ! "t ?an ! second4 ,suppose = ! mom5t t ! equations conta9 only d]ivatives & ! mutual positions ( ! p>ts ( ! sy/em4 ,!n to integrate ! equations & det]m9e ! motion we h to "k ! initial positions & ! initial values ( all ! d]ivatives up to an ord] "o l[] ?an ! highe/ :i* occurs 9 ! equations4 ,! equations ( motion ( an electron are ev5 m complicat$ ?an ?is1 9 t ! positions ( di/ant p>ts ( ! sy/em h to be giv5 ?r\gh\t an int]val ( "t in/ead ( m]ely an in/ant4 ,x w\ld seem t ! feel+ t ! pres5t /ate ( a sy/em may be det]m9$ 9 t]ms ( positions & velocities does n z a matt] ( fact apply to all ! sy/ems ( our exp]i5ce4 ,! discussion up to ?is po9t has be5 subject to ! fundam5tal assumption t ! behavior ( ! sy/em is entirely det]m9$ if we c give ! position ( ea* "p z a function ( "t4 ,?is assumption is implicitly conta9$ 9 ,e9/e9's =mulation ( ! g5]al pr9ciple ( relativity1 namely1 t !re is no?+ m to a physical sy/em ?an a set ( space-"t co9cid5ces1 & t ! sy/em is fix$ 9 t]ms ( ! space "t cord9ates ( all its p>ts4 ,already 9 discuss+ ! assumption ( relativity we h indicat$ reasons = dissatisfaction ) ?is z a means ( reproduc+ all exp]i5ce1 because 9 giv+ only ! space-"t coord9ates ( ev5ts we h entirely omitt$ ! descriptive backgr\nd ( ! equations1 :i* gives physical color to ! sy/em 9 "q4 ,?is discussion also assumes t a specification ( ! positions1 velocities1 & high] d]ivatives 7if necess>y7 ( ! elem5ts ( ! sy/em is possible1 :i* am\nts ess5tially to ! assumption t ! sy/em conta9s only a f9ite numb] ( elem5ts4 ,n[ 9 view ( ! exp]im5tal fact t !re is no reason = suppos+ t ! /ructure ( ! univ]se is f9ite1 ?is conclusion mu/ be modifi$1 b ,i d n believe t ! necess>y modification affects ! ess5tial argum5t4 ,9 view ( ! possible inf9ite /ructure x w\ld seem t we _c expect m ?an t ! future is det]m9$ by ! pres5t )9 a c]ta9 p5umbra ( unc]ta9ty1 & ?is p5umbra may be made less important by digg+ d[n deep] into ! /ructure :5 specify+ ! pres5t condition4 ,we h also slurr$ ov] ! ambiguities 9 pres5t condition :5 ! sy/em is spread ov] space4 ,probably a unique ascription ( mean+ to pres5t is n possible = an ext5d$ sy/em1 b at lea/ "o possibility is indicat$ by relativity !ory4 ,imag9e a /aff ( assi/ants di/ribut$ ?r\gh\t space1 ea* equipp$ ) clocks syn*roniz$ & set ) ! ma/] clock by light signals 9 ! conv5tional mann]1 & ea* fully equipp$ ) ! necess>y measur+ in/rum5ts4 ,!n :at we mean at ?is po9t ( ! argum5t by pres5t /ate ( ! sy/em is ! aggregate ( all ! in=mation ab\t ! positions & velocities ( ! ultimate elem5ts :i* ,i det]m9e 9 my imm$iate vic9ity at my orig9 ( "t plus ! reports ( simil> obs]vations made by all ! assi/ants1 ea* local obs]vation be+ made at ! "t orig9 ( ea* local clock4 ,go+ back n[ to ! ma9 argum5t1 we h %[n t ! feel+ t ! pres5t condition ( ! univ]se may be specifi$ 9 t]ms ( positions & velocities arose f exp]i5ce ) purely me*anical sy/ems1 & t ! m g5]al =mulation1 9 :i* we add to ! velocities ! high] "t d]ivatives1 applies only to sy/ems 9 :i* ! ultimate elem5ts move accord+ to diff]5tial equations ( high] ord] ?an ! second4 ,fur!rmore1 our analysis seems to h %[n t sy/ems 9 :i* !re is radiation d n all[ a det]m9ation ( ! future 9 t]ms ( a pres5t condition specifi$ 9 t]ms su* z ^!4 ,x seems1 h[ev]1 t ! g5]al pr9ciple ( ! det]m9ism ( ! future by ! pres5t may be sav$ by a *ange 9 ! def9ition ( :at we mean by ! pres5t condition ( ! sy/em1 ridd+ x ( its me*anical & o!r special implications1 & mak+ m imm$iate connection ) direct exp]im5t4 ,let u und]/& by pres5t condition ( a sy/em ! aggregate ( all in=mation t c be obta9$ by any physical means :atev]1 ) any sort ( physical in/rum5t1 n attempt+ to get out ( ?is analysis in=mation ab\t hypo!tical ultimate physical elem5ts1 ) ! proviso t ! measurem5ts are to be made n[1 ext5d+ ! concept ( n[ to po9ts di/ant 9 space 9 ! way intimat$ above4 ,) su* a g5]al def9ition ( ! mean+ ( pres5t we c n[ deal ) sy/ems 9 :i* !re is radiation1 notic+ t our assi/ant obs]v]s mu/ be /ation$ ?r\gh\t app>5tly empty space z well z 9 ! neighborhood ( matt]4 ,t ?is does adequately cov] ! case ( radiation is sugge/$ by consid]+ aga9 ! two sy/ems ( d>k lant]ns ) scre5s & di/ant mirrors :i* we h previ\sly consid]$1 9 "o sy/em a light signal hav+ be5 despat*$ #j4e second ago & 9 ! o!r #a4e seconds ago4 ,our !sis dem&s t !re be "s pres5t diff]5ce 9 ^! two sy/ems1 because _! future hi/ory is diff]5t1 9 "o ( !m a light signal arriv+ aft] ! lapse ( #a4e seconds1 & 9 ! o!r aft] only #j4e second4 ,n[ !re is a pres5t diff]5ce z report$ by our assi/ants1 = ! assi/ant /ation$ half way betwe5 lant]n & mirror reports 9 "o sy/em a fla% ( light on ! side ( a scre5 :i* is turn$ t[>d ! lant]n1 & 9 ! o!r sy/em on ! side ( ! scre5 turn$ t[>d ! mirror4 ,?is m g5]al po9t ( view answ]s ! "q :e!r velocity may be reg>d$ z a pres5t attribute ( ! sy/em1 = ! p>ts ( a sy/em :i* are 9 motion h mom5tum1 & mom5tum may be detect$ by plac+ aga9/ su* p>ts comp>atively rigid memb]s :i* w receive a m9ute de=mation1 s t velocity has a mean+ 9 t]ms ( physical measurem5ts made at a s+le in/ant ( "t4 ,!re is a subtle & difficult "q "h1 namely1 :e!r 9 talk+ ab\t op]ations ( measurem5t we c ev] get rid ( temporal implications1 & !re=e1 :e!r a condition ( ! sy/em 9 :i* temporal implications rema9 c prop]ly be describ$ z pres5t4 ,i %all n attempt to answ] ?is "q3 !re mu/ be "s practically satisfy+ answ]1 involv+ p]haps ! physical analogue ( diff]5tials ( diff]5t ord]s 9 ma!matics1 %ort ( c>ry+ ! analysis to su* a degree ( ref9em5t t ! concept ( pres5t becomes mean+less1 z we c see might easily happ54 ,) ?is enl>g$ und]/&+ ( :at we mean by pres5t /ate ( ! sy/em1 x seems to me t physical evid5ce is n[ r favorable to ! view t ! pres5t det]m9es ! future1 subject to qualification ab\t ! p5umbra1 at lea/ z f> z l>ge scale ph5om5a are conc]n$4 ,x appe>s mu* m d\btful :5 we come to small scale ph5om5a1 & 9 p>ticul> x is d\btful :e!r ! pr9ciple c be appli$ to ! details ( ! quantum process1 & 9 fact x is n c]ta9 t x has mean+4 ,x is c]ta9 t if x is true an enorm\s am\nt ( /ructure beyond any t has yet be5 detect$ is impli$4 ,,on ,,! ,,possibility ,,( ,,describ+ ,,nature ,,completely ,,9 ,,t]ms ,,( ,,analysis ,!re is a c]ta9 !sis t is loosely relat$ to ! view t nature is f9ite d[nw>d1 namely1 t an explanation ( ! univ]se is possible 9 :i* we />t ) small scale ?+s1 & expla9 l>ge scale ph5om5a 9 t]ms ( _! small scale con/itu5ts1 ! !sis1 9 o!r words1 t all ! prop]ties ( ! l>ge are conta9$ 9 ! prop]ties ( ! small & t ! l>ge may be con/ruct$ out ( ! small4 ,"s su* !sis z ?is seems impli$ 9 ! g5]al attitude ( _m physici/s4 ,let u exam9e ! physical basis = ?is4 ,to ma9ta9 ?is !sis w\ld dem& t aggregates ( ?+s nev] acquire prop]ties 9 virtue ( _! numb]s :i* !y d n already possess z individuals4 ,is ?is true8 ,consid]1 = example1 ! two-dim5sional geometry on ! surface ( a sph]e4 ,?is is non-,euclidean4 ,is ! geometry ( ! individual elem5ts ( ! surface ( ! sph]e non-,euclidean1 or d !y acquire ?is prop]ty 9 *ang+ scale8 ,is ! k9etic en]gy ( a numb] ( electrons all mov+ toge!r 9 su* a way z to con/itute an electric curr5t ! sum ( ! k9etic en]gies ( ! individual electrons1 or is !re an additional t]m8 ,is ! mass ( an electron ! sum ( ! masses ( its elem5ts8 ,a ma!matical consid]ation is sugge/ive "h4 ,^? prop]ties ( a sy/em :i* c be describ$ 9 t]ms ( l9e> diff]5tial equations h ! prop]ty ( additivity2 ! effect ( a numb] ( elem5ts is ! sum ( ! effects sep>ately1 & no new prop]ties appe> 9 ! aggregate :i* 7 n pres5t 9 ! individual elem5ts4 ,b if !re are comb9ation t]ms 7z 9 ! electrical en]gy1 :i* conta9s ! squ>e ( ! field71 !n ! sum is m ?an 7or diff]5t f7 its p>ts1 & new effects may appe> 9 ! aggregate4 ,n[ ( c\rse ! l9e> equation is ( enorm\s importance 9 describ+ nature1 b _m examples ( sy/ems ) o!r types ( equation c be f\nd1 z t above = electromagnetic mass4 ,9 expect+ to f9d 9 nature su* non-additive effects1 we ne$ n commit ourselves at all to ! view t nature is gov]n$ by diff]5tial equations1 b by analogy may expect simil> effects if diff]5ce equations1 = in/ance1 %\ld prove to be fundam5tal1 or ev5 some?+ beyond pres5t ma!matical =mulation4 ,x is c]ta9ly v mu* easi] to h&le a sy/em physically if ! total action c be built up f t ( its p>ts1 because ! analysis :i* e/abli%es ! connection betwe5 ! elem5ts is easi] to p]=m4 ,x is obvi\sly easi] to %[ t an explanation 9 su* t]ms is correct1 because we h se5 t explanation involves mak+ exp]im5ts ) repres5tative elem5ts abs5t or alt]$1 & x is easi] to v>y ! small ?+s ?an ! l>ge ?+s4 ,^? explanations :i* involve work+ f ! small up w !re=e be made fir/1 & w appe> to be ( disproportionate importance4 ,places :]e ,i look = an explanation f ! l>ge to ! small are p]haps 9 acc\nt+ = ! values ( ! gravitational con/ant & ! velocity ( light & 9 ^? ph5om5a :i* g5]al relativity !ory indicates may dep5d on all ! matt] 9 ! univ]se1 z ! ,f\cault p5dulum exp]im5t4 ,we mu/1 ( c\rse1 also be prep>$ = su* non-l9e> effects 9 ! doma9 ( unexplor$ quantum ph5om5a4 ,a ,,glimpse ,,ahead ,"s ( ! g5]al consid]ations ( ?is essay may1 ) consid]able plausibility1 be expect$ to play a "p 9 ! future ( bo? speculative & exp]im5tal physics4 ,! mo/ important effect may be expect$ f ! cle>] recognition ( ! op]ational "* ( our physical concepts4 ,inde$ dur+ ! writ+ ( ?is essay !re has be5 a v m>k$ increase 9 emphasis on ! necessity ( und]/&+ 9 t]ms ( physical op]ations su* fundam5tal concepts z t ( ! electron1 by ! new quantum me*anics ! me*anics ( ,heis5b]g-,born & ,s*rd+] ( #aibe-bf4 ,we are to expect !n 9 ! fir/ place a m self-consci\s & detail$ analysis ( ! op]ational /ructure ( all our physical concepts4 ,x has be5 beyond ! scope ( ?is essay ev5 to beg9 to attempt a sy/ematic & ?or\ghgo+ analysis ( ?is "*4 ,?is future analysis w %[ precisely h[1 z we ext5d ! range ( exp]i5ce1 ! physical "* ( ! op]ations *anges by :i* we def9e our concepts1 z1 = example1 9 me*anics ! notion ( =ce disappe>s at high velocity & is replac$ p]haps by ! notion ( mom5tum4 ,9 ! region ( *ange 9 ! nature ( our concepts1 special /udy w be made ( ! accuracy ( our physical measurem5ts1 & new exp]im5ts devis$ ( great] accuracy1 9 ord] t we may "k precisely to :at ext5t ! new concepts are equival5t to ! old4 ,pa/ exp]i5ce sugge/s t we may p]haps expect to f9d new ph5om5a especially 9 ^? regions :]e ! difficulty ( c>ry+ out ! usual op]ation =ces u to *ange ! op]ational "* ( our concepts4 ,!re w be que/ions ( a m or less =mal nature to answ]1 z = example ! be/ way ( ext5d+ concepts :5 !re are sev]al possible c\rses op5 to u4 ,we may expect m int]e/+ results1 h[ev]1 :5 we get s f> beyond ord9>y exp]i5ce t ! "* ( ! possible physical op]ations has become s re/rict$ z to result 9 an app>5t decrease 9 ! numb] ( indep5d5t concepts4 ,x seems plausible to expect t ! /ructure ( nature is m fundam5tally connect$ ) ! numb] ( indep5d5t concepts necess>y = a complete description ?an ) ! precise details ( ! /ructure ( ! individual concepts1 su*1 = example1 z :e!r space is measur$ optically or tactually4 ,9 ^? regions :]e ! numb] ( concepts decreases1 we mu/ make ! mo/ ?or\ghgo+ exp]im5tal exam9ation to discov] if possible new sorts ( op]ations by :i* ! numb] ( concepts may be br\ght back to normal4 ,9 se>*+ = su* new exp]im5tal op]ations x seems to me t by f> ! greate/ promise = ! imm$iate future is (f]$ by improvem5ts 9 our p[]s ( deal+ ) individual atomic & electronic processes1 su* z we n[ h to a limit$ ext5t 9 ! v>i\s sp9?>iscope me?ods ( c\nt+ radioactive dis9tegrations1 or ,wilson's -track exp]im5ts4#ch ,9 ?is self-consci\s se>* = ph5om5a :i* increase ! numb] ( op]ationally indep5d5t concepts1 we may expect to f9d a p[]ful sy/ematic me?od direct+ ! discov]y ( new & ess5tially important physical facts4 ,footnote #ch3 ,c4 ,t4 ,r4 ,wilson1 ,proc1 ,roy4 ,soc41 #hg1 #bgg1 #aiab4 ,we c only conjecture :e!r ! numb] ( fundam5tal concepts w prove impossible ( fur!r increase or n1 b pres5t exp]i5ce seems to give great] probability to ! view t z we p5etrate deep] ! numb] ( fundam5tal concepts w always t5d to become few]4 ,we h already c]ta9ly "o example 9 t ! temp]ature concept disappe>s :5 we get to ! atomic scale ( magnitude1 & possibly a second example 9 ! build+ up ( sep>ate concepts = en]gy & frequ5cy by ! comb9ation ( great numb]s ( t "o op]ationally simple ?+ :i* *>act]izes ! elem5t>y quantum process 9 ord9>y radiation4 ,diff]5t sorts ( relations betwe5 concepts are conceivable 9 ! transition zone :]e ! numb] *anges4 ,we may f9d t o!r examples are l t ( temp]ature1 :i* is simply a /ati/ical effect ( a great _m ph5om5a :i* may be describ$ individually 9 t]ms ( ! ord9>y concepts ( me*anics1 s t 9 ?is case ! numb] ( concepts *anges m]ely by temp]ature dropp+ out1 leav+ ! o!rs m or less unaffect$4 ,or all ! concepts may be m closely int]wov51 s t :5 ! total numb] ( concepts *anges x may n be possible to sep>ate out a gr\p ( concepts ^: def9+ op]ations are un*ang$4 ,9 su* a case we mu/ say t ! orig9al concepts are n applicable on ! new level4 ,! mo/ imm$iate application ( ?is idea has be5 already m5tion$1 namely1 to ! concepts ( space & "t4 ,if ! op]ations by :i* space & "t are measur$ on ! ord9>y scale ( magnitude _c be c>ri$ d[n z a :ole into ! region ( quantum ph5om5a1 !n we mu/ say t ! ord9>y concepts ( space & "t are n applicable to ^! ph5om5a4 ,closely connect$ ) ! %>p] analysis ( ! op]ational /ructure ( our concepts1 we may expect 9 ! future also a clos] analysis ( our inv5tions4 ,?is w take ! =m ( a se>* = new physical facts :i* %all give to our inv5tions ! "* ( physical reality4 ,9 case prolong$ se>* fails to disclose su* ph5om5a 7z is probably n[ ! case ) ! field concept ( electrodynamics71 we mu/ !n f9d "s way ( embody+ explicitly 9 our ?9k+ ! fact t we are deal+ ) pure inv5tions & n realities4 ,,index ,absolute1 #bf ,absolute "t1 #d ,action at a di/ance1 #df ,analysis ( l>ge into small1 #ea1 #bbj ,ari?metic1 #ce ,atom1 #ei ,bell1 #hd ,birkh(f1 #gb ,black body1 #aab ,bohr1 #aij1 #aib ,born1 #bbb ,boscovit*1 #df ,bo! & ,geig]1 #aaf ,bridgman1 #bja ,br[nian movem5t1 #ajg1 #abi1 #adc ,bu%1 #adb ,caloric fluid1 #ei ,campbell1 #aag ,c>not eng9e1 #abe ,causality1 #hj ff ,causal tra9 ( ev5ts1 #he ,clif=d1 #bh ,clock1 #gj ff1 #agf ,compton1 #aaf1 #ahh ,cont9uity1 #id ,cons]vation ( *>ge1 #ace1 #acf ,cons]vative functions1 #aac ,con/ructs1 #ec ,correlation1 #cg ,cosmic units1 #ahb ,cross ^w puzzle1 #bjb ,descriptive backgr\nd1 #fd ,det]m9ism1 #aad1 #bji ff ,discont9u\s space1 #aia ,dppl] effect1 #aff ds1 #gb ,edd+ton1 #ic ,e9/e91 vii1 #a1 #b1 #c1 #d1 #g1 #h1 #i1 #ab1 #ac1 #ad1 #fd1 #ajj1 #aee1 #afb1 #afc1 #afd1 #afg1 #afi1 #agj1 #aga1 #agb1 #agc1 #age1 #agf1 #agg1 #bjf ,electrical concepts1 #aca ff ,electrical explanation ( univ]se1 #ej ,electrical mass1 #aci ,electric field1 #ef1 #acc ,empiricism1 #c ,en]gy1 #ajh ff1 #abf ff ,euclidean space1 #ad1 #ae1 #af1 #ah1 #bc1 #eb1 #fa1 #fg ,ev5t1 #ie1 #afg ,explanation1 #cg ,explanatory crisis1 #da ,ext5d$ "t1 #gg ,f>aday1 #dd1 #eg1 #eh1 #bji ,f9al explanations1 #dh ,fir/ law ( !rmodynamics1 #abf ff ,=ce1 #ajb ff ,f\cault p5dulum1 #ahj1 #ahd ,f\r? dim5sion1 #gd ,future1 #bbb ,gauss1 #ae1 #cd ,g & come "t1 #aab ,gravitational con/ant1 #ia ,haldane1 #be ,heat fl[1 #acj ,heis5b]g1 #bbb ,h]tz1 #dd ,ho]nl1 vi ,id5tity1 #ia ff ,isolation1 #hb ,j\le1 #abd ,kelv91 #de1 #aaj ,k9etic !ory ( gases1 #dj ,lagrangean equations1 #aab ,l>mor1 #adi ,la ,rosa1 #afd ,l5g?1 #i ff ,lewis1 #aff1 #bja ,light1 #aej ff ,local "t1 #ge ,lor5tz1 #adc1 #adg1 #adh1 #adi ,ma*1 #ahc ,mass1 #ajb ff ,ma!matics1 #fj ff ,maxwell1 #dd1 #eh1 #aab1 #acg1 #adh ,mean+less que/ions1 #bh ff ,measurem5t approximate1 #cc ,me*anism1 #de ,m]cury1 #aje ,mi*elson1 #ae1 #bf ,mi*elson & ,morley1 #ff ,models1 #de1 #eb ,newton1 #d1 #aaj ,op]ational "* ( concepts1 #e ,op]ational ?9k+1 #cb ,optical space1 #fg ,o/wald1 #aji ,p5umbra1 #cd ,p]r91 #ajg ,physical reality1 #ei ,planck1 #fi ,po9c>1 #dh1 #aae1 #aaf1 #aij ,py?agoras1 #fa ,quantum act1 #aef ,quantum !ory1 #dj1 #dg1 #ahf ,radiation & temp]ature1 #abc ,relative "* ( k1 #be ,relativity1 #aej ff ,reynolds1 #ic ,rotational motion1 #agh ,russell1 #bje ,s*rd+]1 #bbb ,space1 #ff ,silb]/e91 #aa ,simplicity ( nature1 #aih ,simultaneity1 #g1 #h ,spr+ balance1 #ajc ,/ati/ical me?ods1 #aae1 #aag ,/ress1 #ed ,swann1 #bjd ,table top1 #ajf ,tactual space1 #fg ,temp]ature1 #aah ff ,!rmodynamics1 #aag ,?+ travel+1 #aja1 #aeb1 #aeg1 #afd ,"t1 #fi ,tolman1 #bja ,tru?1 #gh ,turbul5t motion1 #abj1 #abd ,velocity1 #ig ff1 #bac ff ,velocity ( light1 #ajj ,:itehead1 #afg ,wilson1 #bbd