[PDF] Histoire de la Relativité Générale dEinstein: Développement

View - Download Histoire de la Relativité Générale dEinstein: Développement

Previous PDF

Next PDF

>G A/, i2H@ykjkRe33 ?iiTb,ff?HXb+B2M+2fi2H@ykjkRe33 am#KBii2/ QM kR P+i kyRN >GBb KmHiB@/Bb+BTHBM`v QT2M ++2bb `+?Bp2 7Q` i?2 /2TQbBi M/ /Bbb2KBMiBQM Q7 b+B@

2MiB}+ `2b2`+? /Q+mK2Mib- r?2i?2` i?2v `2 Tm#@

HBb?2/ Q` MQiX h?2 /Q+mK2Mib Kv +QK2 7`QK

i2+?BM; M/ `2b2`+? BMbiBimiBQMb BM 6`M+2 Q` #`Q/- Q` 7`QK Tm#HB+ Q` T`Bpi2 `2b2`+? +2Mi2`bX /2biBMû2 m /ûTP¬i 2i ¨ H /BzmbBQM /2 /Q+mK2Mib b+B2MiB}[m2b /2 MBp2m `2+?2`+?2- Tm#HBûb Qm MQM-

Tm#HB+b Qm T`BpûbX

.ûp2HQTT2K2Mi *QM+2Tim2H /2 H h?ûQ`B2 hQ +Bi2 i?Bb p2`bBQM,

LLh, X i2H@ykjkRe33

Ph.D. Thesis

d,mKEWdh)>ms>KWDEdmK&m/E^d/Em[^m

This is an authorized facsimile

printed by microfilm/xerography on acid-free paper in 1982 by

UNIVERSITY MICROFILMS INTERNATIONAL

Ann Arbor, Michigan, U.S.A.

London, England

Licrolilmôd by Univ. ot Wi3€onsin-Madison g2_05S30 'ladrdirl Liè(ùt Collacltm Lemlffia Ottica GlMnD, Patrick RalphÎI{E COT{CÊPIIJAL DEVELOPI{€IIT OF EIIIS1EIXIS G€ilERAL

THÉORY OF RËIÂTIVITY

thc Univcr:ity of lJl:con:ln-tladiron, ph.D., l98l

University Microfilms lnternaliOnal

^nn Ârùo., titcntern 48t06 @ l98l Patrick Ralph Girard (ttlts titt e card prepared by the University of l,lisconsin)

PLÊASÊ NOTE:

The negative microfi'lm copy of this dissertatJonwas prepared and lnspected by the school grant.ingthe degree. lJe are using this fl1m withoùt furtËer{nspectlon or chanEe. If there are any questionsabout the fi'lm content, piease wrlte d.r'rectly to theschool .

UNIVERSITY MI CROFILI.IS

GEIENÂI, ÎHEOAT OF R3I,AlrirIlY

À thesi-s subE{tred to the Graduête School of the unLveralty of iflscossts-Hadrson Ln partlal furftllnent of the rêqulre!Êeats for the degree of Doctor of phlloeophy by

PATRISIC NATPH 6TRA.R,

Degree to be awatded: Dece$ber lg_g1_ llay 1g_ August 19

Âpproved by lteelsLead{ag Co!ûDlttee:

t{ lÀ,!r}f^*q__..

THE CONCEPTUAL DEVEtOPilENl OF EINSTEINIS

GENERAI THEORY OF RETATIVITY

by

PATRICK RALPH GIRARD

thesis subrÀitted in requirenentspartial fulfillrnent of thefor the degree of

DOCÎOR OF PHILOSOPHY(Histof)' of Science)

at th€

UNtrVERSITY OF WISCONSIN-MAOISON

I 981 a O Copyrightby Patrick Ralph GirardAll Rights Resèrved198 I 1l

ACKNOI{LEDGMENTS

I would like to thank Ûaniel Siegel for hisoverall advice and particularly for the many hours he spent on editorial work because of my restricted knowledge of the Englisb language. I am also grareful for hi.s petience witlr certain philosophical views sonewhat in contrast wj.th his orrn. Further thanks goto Geoffrey Joseph and Robert March for a few suggestions. Finally, I nant to thank the physics Departnent of the University of l{isconsin-Madison, in Particular C. H. Blanchard, for fj.nancial support inthe forn of a Teaching Assistantship while this dissertation uas in progress, Charles Goebel for reading an early draft of the dissertation, and

Jeanne Zwaska for 1ypi11g the nanuscript.

TABLE OF CONTENTS

of the the 111
Page I 4 4 5 11 t2 23
25
28
31
J5 37
41
43
43

INTRODUCTION

CHAPTER

I. THE

A.

SPECIAI ?HEORY OF RELAÎIVITY

Einstein and the DevelopnentSpeciat Theory of nerativiii

1. Historical Backgrouad ofPrinciples of SiR

Z. Einstei.n,s Approach

a. Einsteiafs earJ.y doubts about theçoncept of absolute velocity b. Vain attempts to reconcileelectronagnetism with theprinciple of relativity c. Rejection of the ether d. Epistemological breakthrough

5. Einstein's Âchievement

Einstein's EpistenologicalDissatisfaction with sTR

1. Historical Debate about the Conceptof Absolute Acceleration

?. Einstein's Rejection of the Conceptof Absolute Réceleratiôn

II. THE EXTENSION OF THE SPECIAT THEORY OFRELATIVITY VIA THE EQUIVALENCÈPRTNCTPTE (1907-1912i . . . .-.

A. !.Tfy-Use of rhe EquivalencePrinciple (1907-19i1) . . .- 8. 7-

CHAPTER

1V Page 43

1.The ldea of the EquivalencePrinci.ple

4-Fron the relatiyity of electricand nagneti.c fie1d3 to therelativity of the gravita-

b. From the rel.ativity of thegravitational fielâ to theequivalence principle Z. Extension of the princiole ofRelativity to Uniformly' AcceieratedSys tens a. Space and tine_in a unifornlyaccelerated reference systern b. Electrornagnetic effects in auniforn gravitational field

3. Fu11 Confidence in the EquivalencePrinciple and in a Generâ1Relativity (1911)

Further Use of the EquivalencePrinciple: The Statii The;;t- tional. field of Grairitation l. Historical Background .

Prerelativisticof gravi.tation

the force lawsand l'{inkowski .

Einstein t s relativisticfield approach

d. Abrahamt s theories e. Nordstrômts and Mie's theories 43
48
55
58
63
67
B. 82
82
82
85
o? b" theories of Poincaré 97
104

CHAPTÊR

Z. Einstein's Static Theory ofGravitation

a. Development of the theory . b. Consequences c. Problens and rnodificat.ionsof the theory 120 d. Debate r*ith I'lax Abrahan . llz iil. FIRST SKÊTCH OF THE GENERAT THEORY OFRELATTVTTY (1913*1915) 131

A. Historical Renarks on Tensor Calculus 132

1. Tensors with Respect to rheGroups O(3) and O(4) 1S3

2. Tensors with Respect to the GrouosAssociared with à QuadraticDifferentialForn.. 141

B. The Einstei.n-Grossmann TensorTheory (191 S) 147 . 1. The Generally Covari.antEquation of I'totion 14g

Z" lhe Linearly CovariantField Equations l5g

3. Consequences of the Theory 166

a. The Newtonian gravitetionalfield approximation . 166 b. The relativity of i.nerria . . 169

C. Further Elaboration of the Theory 175

1. the Problem of the Covarianceof the Field Equarions 17S

2. New Hope for an Extended Covarianceof the Field Equations . 182

v Page 109
l.10 114

CHAPTER

D.

IV. THË

v1 Page Einsteinrs philosophical Views and,the Reception of the Theory . . -. -. 187

1. Ëinstei.n's Epistemological Idealisn 1g7

?. Reception of the Theory . .

GENERAL THEORY OF RELATTVTTy (1915-1917) 2r4

The Generally CovariantTheory (1915-1916) 215

1. The Return to the Riernann-Christoffel Tensor ZI5

2. The Generally Covariant Fieldrquatlons . ZZ2

Covariant field equations wi.threspect to transformationsofJacobianl .Z?3

6enera1ly covarj.ant fi.eldequati.ons with the assumptionTuu=O. .z3l

Generally covariant fieldequations without the assuxlptionTlu'o .n3 Consequences of the Theory andExperimental Verification .

1. First Order Effects: Newton's Law ofGrayitation, Deflection of fieÈiRays, Behavior of Clocks .na Foàsin a Gravitat,ional Fie1d . . ;-.

2. Second Order Effect: Resi.dualPrecession of the perihelionof Mercury

3. Experinental Verification . .

Extension of the Theory: TheCosmological Csnstant ttsiT) A. a. b. c. B. 240
240
255
245
248
c.

CHAPTËR

CONCIUSION

APPÊNDI X:

1. 2, vii Page Einstein' s Epistemologicalrrlssatlstaction . . Z5S a. EpistenologicaL background ZS5 b. The.problem of the relativityof inertia . 263

Modification of the Field Equat.ions 265

. 275 EINSTEIN'S PRIORITYIN THE }IATTER OFTHE FIELD EQUATIONS

BlBL IOGRAPHY

)'r', 294

INTRODUCTION

Anong all the physical theories developed by

Albert Einstein, the general theory of relativi.ty (GTR) is generally considered as his nasterpiece. îhis theory has yielded the tnost successful treatnent of gravitat.ion known so far, and has, to the present day (1981), briLliantly withstood alL the experinental. tests to which j.t has been submitted, while nany competing theories have been elirninated.

Despite i.ts success, the history of the general

theory of relativity has received much less attention than the history of the special theory. Two basic clrcurnstances are probabLy responsible for this. First between the 1930s and the 1950s, the general theory of reJ.ativity was relatively neglected by the scientists thenselves because experimental methods had not yet reached the sophistication required for the further, study of general-relativistic effects, Second, the technicaliq, of the subject matter has hindered historical study of GTR.

Though various aspects of the history of

the general theory of relativity have been treated elsewhere,l rro "o*prehensive, detailed historical

account of the sucçessive stâges in the development ofthe general theory of re1atiyity lras, to my knowledge,

been publi.shed. It is the purpose of this dissertationto fill that gep. The dissertation will not only analyze

the nrathernatical developnent of the theory in detail,fron 1g07 to 1912, but nill also pay close attention roEinstein's notivations, Though it is generally knownthat Einstein was noti.vated by epistenological reasonsin the development of GTR, this is the first tine thatthis clain is thoroughly docunented. By 1905, Einstein

had already successfully applied epistemological con-siderati.ons to physics; it was his rejection of the

concept of absolute tine t.hat nad,e the special theory ofrelativity (STR) possible. Einstein,s nÉxt nove Has toattenpt to eliminate the concept of absolute space (inparticular the concept of absolute acceleration) byextending the principle of relativity.

In order to show the cont.inuity of Einstein,s

concerns in the developnent of STR and 6TR, I nill. in the

1 1 and/

For other accounts,

aga ins tequationssee the

1-ùeeert, and

ton, U. S.Mehrats clainindependentlvbibliography. rneory (uordrecht.4). I sha1l argué1915? ?? 2 S S P

SP(mPm)mK

2K ??!f=m! t 0=t x 0=xvt y 0=y z 0=z t=t0 x=x0+vt0 y=y0 z=z0 ds

2=dx2+dy2+dz2

=ds02 x

0=xvt;y0=y;z0=z

????? ???v=c? ??? ?????? ?????? ?????1905? 19 ???? ????1897 2 S S P SP(mP 2) t

0=tvxc

2Sq 1v2c 2 x

0=(xvt)q

1v2c 2 y 0=y z 0=z t= t

0+vx0c

2q 1v2c 2 x=(x0+vt0)q 1v2c 2 y=y0 z=z0 ds

2=c2dt2dx2dy2dz2

=ds02 )??????? ?? ?? ??????? ???? ?? ???? ?c0=c? ????1721? ????? ?19071911? E

0x=Ex;E0y=(EyBzv)q

1v2c 2;E

0z=(Ez+Byv)q

1v2c 2 B

0x=Bx;B0y=By+Ezvc

2Sq 1v2c 2;B

0z=BzEzvc

2Sq 1v2c 2 E x=E0x;Ey=E0y+B0zvSq 1v2c 2;E z=E0zB0yvSq 1v2c 2 B x=B0x;By= B 0yE0 zvc 2q 1v2c 2;B z= B 0z+E0 zvc 2q 1v2c 2 !E 2c 2!B 2;2!E :!Bc 2 S S

P(m)KM

SP(m)KM

2 2 S S S 2 1 P P ??? ??????? ??????? ?? ??????? ????? ???? ?? ???? ??? ??????? ??1922??? t 1vc

2x1=t2vc

2x2: x

2x1=x02x01=21;

t 1=1=; t 2=2; x P (SS, PmP (x, (ms1=ts2 ()(K

M)MK)K

Mt v= t1= 21=
c

2(21);

1 + c 2 1 +c 2 ???? ???? ?? ??????? ??????? ??????? ???? ???????1 + 2:106S???? ???? ?????? 2S??? c 0=L =L 1c 2S=c 1 +c 2 ?18671895???? S2 K 1=2 1 + hc 2 hc 1=2 1 +c 2 S 21 +c
c=c0 1 +c 2 ????1??????? ???u=12 !Eg 2+!Bg 2 ?????!F?????? ??? ?? ?????A?????? ?? ?????!r0+!r?? ?????t0+t? ??? ?? t (t;r;!vA;!vB) = 0: r

2t2;t!r :!vAp1v2A;t!r :!vBp1v2B;1!vA:!vBp(1v2A)(1v2B)

q= (r;!r); f= k

0T;k0!F

u

B= (k0;k0!vB);

u

A= (k1;k1!vA);

????k0=1p1v2B;k

1=1p1v2A??T=!F :!vB#??

f=q+uB+ uA v2c f=qB 3AB 3uA; v2c

2? ??? ??????? ? ?? ??? ?? ?????? ?? ?????? ???

???? ????? ??1907?? ??1908? 1c 2@2@t = 4G; 2@x

2+@2@y

2+@2@z

21c
2@ 2@t 2; !F=m!grad; ??????? ?? ??1875? ??????? ?????? ? ?????? ???? ??? ?????? = 4G; ?????=@2@x

2+@2@y

2+@2@z

21c
2@2@t

F=Grad;

@@x ;@@y ;@@z ;@@(ict) dxd 2 +dyd 2 +dzd 2 +dictd 2 =c2??quotesdbs_dbs46.pdfusesText_46

[PDF] la religion au moyen age en france

[PDF] La religion dans Vipère Au Poing d'Hervé Bazin

[PDF] la religion des temps moderne

[PDF] La religion est elle la honte de l'intelligence humaine

[PDF] la religion n'est elle qu'une affaire privée

[PDF] la religion un obstacle a la religion

[PDF] la remédiation pédagogique pdf

[PDF] la remise en cause de l absolutisme

[PDF] La remise en cause de l'absolutismeau XVIIème et XVIIIème siècle

[PDF] la remise en cause de la monarchie absolue 4eme

[PDF] La rempailleuse de Maupassant

[PDF] la rempailleuse de maupassant

[PDF] la rempailleuse de maupassant analyse

[PDF] la rempailleuse lecture analytique

[PDF] la rempailleuse maupassant pdf