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CRITIOQFU E PHYSICS BY L L WHYTE LONDON KEGAN PAUL,TRE NCH, TRUBNER &C O.L,TD . BROADWAY HOUSH: 68-CAR7T4ER LANE. B.C. 1931 PRINTED J:lrf GREAT BRITAIN 9V RL\.DLEY BRoTIR.RS, I8 :OEVOJii'BS illltS'I'RU "''LO,N D0 111JI:1. C.;2 .&ND ILSDl'OR.Dt D:trl'. TO LO'ITE CONTENTS PAGE PREFACE ix QUOTATIONS FROM EINSTEIN,E DDINGTON AND HEISENBERG xi CHAPTER I SPACE-TIME §I.I NTRODUCTORY I §2.U NITARY THEORY 5 §3.T HE STRUCTURE OF MEASURING RODS 8 §4.K INEMATIC SIMILARITYI N CLASSICALP HYSICS 12 §S.T HE ABSENCE OF SIMILARITYI N RELATIVITY PHYSICS 17 §6.T HE UNIVERSAL LENGTHSI N QUANTUM PHYSICS 21 §7. THE FOUR UNIVERSAL LENGTHS IN UNITARY THEORY 24 §8.M EASURING RODS (Contd.) 27 §9. CLOCKS 32 §10.S PACE-TIMEM ETRICAL COORDINATES 35 §IIS.PA CE-TIMET OPOLOGICALO RDER 40 §12.M ETRIC AND ORDER IN PHYSICAL THEORY 46 §13.C OURSE CALCULUS 50 §14.U NITARY COURSE THEORY 54 II CHAPTER COORDINATET HEORIESF ROM THE STANDPOINT OF UNITARY COURSE THEORY §15.B ASIC CONCEPTS OF COORDINATE THEORY 58 §16.G ENERAL FORM OF COORDINATE LAWS 62 §17.S PECIALA ND GENERAL COVARIANCE 67 vii viii CONTENTS PAGE §18.Q UANTUM THEORY 70 §19.G ENERAL PRINCIPLESO F QUANTUM THEORY 76 §20.S PECIAL QUANTUM-MECHANICAL PROBLEMS 83 §2I.P ARTICLESA ND WAVES 8g §22.C LASSICALR,E LATIVITYQ,U ANTUM, AND UNITARY COURSE THEORY g6 §2J.T HE SIX UNIVERSAL DIMENSIONAL CONSTANTS 101 §24.S YMMETRIES IN COORDINATE LAWS 107 §25-UNSOLVED PROBLEMS IN COORDINATE THEORY II2 §26. SUMMARY Il3 III CHAPTER GENERAL FEATURES OF UNITARY COURSE THEORY §27.I NTRODUCTORY II5 §28.T HE THREE NUMBERS a, {3,y OF COORDINATE THEORY 116 §29.L OGIC,C ONCEPT, AND FACT 120 §30.T HE STRUCTURE OF UNITARY COURSE THEORY 124 §31.S IMPLICITYI N PHYSICAL THEORY 128 §32.T HE LIMITED COMPLEXITOYF NATURE 130 §33·T HE EXHAUSTION OF MICRO-ANALYSIS 132 §34·G ENERAL CONCEPTS OF NATURAL SCIENCE 136 §35·G ENERAL PRINCIPLESO F NATURAL SCIENCE 138 §36.LI NES FOR RESEARCH 142 §37·C ONCLUSION 145 NOTES REFERENCES APPENDIX A. EINSTEIN AND THE THEORY OF RELATIVITY 173 APPENDIX B. THE DEVELOPMENT OF QUANTUM THEORY 182 PREFACE THEco mpletioofgn e nerraell atitvhietoy(r Iyg ia6n)do ft he genermaelt hodosfq uantutmh eor(y1 92l7e)a vpehsy sical theoriny as ituatoifso pne ciialn terestt hseisntech ee ories lacakn a dequactoem monf oundatainodnt heiinrt errela tionasr es tillo bscure. TheC ritihqauseb eewnr ittine tnh eb elietfh aat r evision oft hef undamenctoanlc eputnsd erlybiontgh r elativity theorayn dq uantumt heoriysa ne ssentpiralelimin ary toa comprehenstihveeo retsiycnatlh easnidst hatth ee mpirical factrse quirfeodrt h itsas ka ren owa vailabThlee .p urpose oft heC ritiiqsut eom ake thiasi mp recisaen dt os uggest a methowdh iccha nb e usedi nt hep roposreedv ision. Relatiyv aintdq uantutmh eorayr et herefeoxraem ineadn d reinterpreint etdh el igohftt hinse waim andm ethodN.o theoretfiocnnalu latiiosrn e achebdu,tt hea nalysilsea ds toa progmrmae forf urtherre search. Thes ummary givaetnt hes taorfte acsecht ionwil l assist ther eadeinr followtihnega rgumenRte.f erenarcee s starr*e idnt het exatn dc ollecotnpe agde 1 65.T hen otes, refertroeb dy n umbersdne1awi,lt h specipalo intwsh eriet isu ndesiratbol ien teprrtu the maina rgumenTtw.o historaipcpale ndihcaesv eb eenin cludeodnt hec haracter istfieca tuorfeE si nstewionr'ksi nr elatitvihteyo rayn do f thed evelopmoefnq tu antuthme ory. Theses urbvreiyesf oft het wogr eatt heoretaichciale vemenotfts h ep eriod I900-193a0p proprialtinekl tyh eh eurisvtiisct oaf t he Crititqout eh ep reviosutasg oefsp hysitchaolu ght. LondonD.e cember1,9 30. NOTATION THEs ix primaryu niverdimseanls ionalc onstants: c thev elocitoyfl ighint v acuo. G theg ravitatcioonnsalt ant. e thee lectrcohnaircg e. M themas s oft hep roton. m them asso ft hee lectron. h Planck'cso nstaonfat c tion. Thet hreep uren umberra ti:o s thefi ne-structure constant. the ratioof p rototno e lectrmasso.n e' the ratioof the electrotsot tahtei c y•GMM gravitatfioorncbaeel t weetnw op rotons. " Thei deoaf th e measuringa nrdot dh ei deoaf t hec lock coordinatweidt hi ti nt het heoroyf r elativdiot noyt fi nd theierx accto rrespondientn hcere e awlo rld. Iti sa lscloear thatth es olibdo dya nd tchleo cdko n oti nt hec onceptual edifice ofp hysipclsa tyh ep arotf i rreduceilbelmee ntbust, thato f composistter uctuwrhesi chm ay noptl aya ny independepnatr ti n theoretical pBhuyts iitci ss.m y convictitohna tin thep resenstt agoef development of theoretical physics tmhuesstse t iibldelee amsp loyeasd independeindte afso,rw e ares tiflla rf romp ossesssiuncgh certakinn owledogfet heoretpircianlc ipalste osbe ablteo givee xactth eoreticcoaln structioofn sso libdo dieasn d clocks(.E"i nste1i9n2.1 .) " Theh iatu(sb etwetehne r ecognitioonft here lativistic relatioofin n tervaanldt hea ssumptiooffn o ru-coordinate ordeprr)o babinldyi catseosm ethimnogr et hana temporary weaknesosft her igoroudse ductioIntm. e anst hastpa ce andt imea reo nlya pproximcaotnec eptiwohnisc.hm ust ultimatgeilvyew a y toa moreg enercaoln ceptoifot nh e orderionfge ventisn n aturneo te xpressini btleerm so fa fourfoclodo rndaite-syste(mE.d.d.i ngto1n9.2 2.) " Ina ddititono t hem odificatioofon usr o rdinasrpya ce timew orldr euqiredb y thet heoroyf relativaintdy characterbiys tehde c onstacn, ta ndt ot hein exactitude relatioofnth se quantutmh eorys ymbolisbeyd P lanck's constahn,st t ilolt helri mitatwililo nasp peacro nnectwedi th theu nivercsoanls tane,tm s, M. Itis not yetp ossibtloe seew hatf orm theslei mitatwiiolntlsa ke."( Heisenberg. 1930.)