392:
31:
405:
641:" for empty space, he invokes the law in situations where space is no longer empty. For the derivation to apply to physical objects requires an additional postulate or "bridging hypothesis", that the geometry derived for empty space also applies when a space is populated. This would be equivalent to stating that we know that the introduction of matter into a region, and its relative motion, have no effect on lightbeam geometry.
522:
The two-postulate basis for special relativity is the one historically used by
Einstein, and it is sometimes the starting point today. As Einstein himself later acknowledged, the derivation of the Lorentz transformation tacitly makes use of some additional assumptions, including spatial homogeneity,
646:
There can be no doubt that this principle is of far-reaching significance; and yet, I cannot believe in its exact validity. It seems to me unbelievable that the course of any process (e.g., that of the propagation of light in a vacuum) could be conceived of as independent of all other events in the
1220:
Under transitions between inertial reference frames, the equations of all fundamental laws of physics stay form-invariant, while all the numerical constants entering these equations preserve their values. Thus, if a fundamental physical law is expressed with a mathematical equation in one inertial
1966:
in all reference frames. This postulate is a subset of the postulates that underlie
Maxwell's equations in the interpretation given to them in the context of special relativity. However, Maxwell's equations rely on several other postulates, some of which are now known to be false (e.g., Maxwell's
619:
in 1911, and many others in subsequent years) that a formula equivalent to the
Lorentz transformation, up to a non-negative free parameter, follows from just the relativity postulate itself, without first postulating the universal light speed. These formulations rely on the aforementioned various
628:
are left to be determined by experiment even when using
Einstein's original postulates. Experiment rules out the validity of the Galilean transformations. When the numerical values in both Einstein's and other approaches have been found then these different approaches result in the same theory.
2383:
when measured in each inertial reference frame. This metric is viewed as one of the physical quantities of the theory; thus it transforms in a certain manner when the frame of reference is changed, and it can be legitimately used in describing the laws of physics. The first postulate is an
3185:
is consistent with
Galilean relativity, but not special relativity. Conversely, Maxwell's equations are not consistent with Galilean relativity unless one postulates the existence of a physical aether. In a number of cases, the laws of physics in special relativity (such as the equation
1950:
767:, leaving special relativity as the only remaining option. Given that SR was similarly unable to reproduce the Fizeau result without introducing additional auxiliary rules (to address the different behaviour of light in a particulate medium), this was perhaps not a fair comparison.
2343:
705:
can be considered constant ... the sole objection that can be raised against the theory is that the equations we have set up might, perhaps, be void of any physical content. But no one is likely to think in earnest that this objection is justified in the present
698:
A similar suggestion that the reduction of GR geometry to SR's flat spacetime over small regions may be "unphysical" (because flat pointlike regions cannot contain matter capable of acting as physical observers) was acknowledged but rejected by
Einstein in 1914
3169:
1221:
frame, it must be expressed by an identical equation in any other inertial frame, provided both frames are parameterised with charts of the same type. (The caveat on charts is relaxed, if we employ connections to write the law in a covariant form.)
713:
It is by no means settled a priori that a limiting transition of this kind has any possible meaning. For if gravitational fields do play an essential part in the structure of the particles of matter, the transition to the limiting case of constant
1763:
1196:
We also assume that the universe obeys a number of physical laws. Mathematically, each physical law can be expressed with respect to the coordinates given by an inertial frame of reference by a mathematical equation (for instance, a
467:
The idea that special relativity depended only on two postulates, both of which seemed to follow from the theory and experiment of the day, was one of the most compelling arguments for the correctness of the theory (Einstein 1912:
603:
is "almost the only hypothesis that can reconcile" the apparent contradictions. Lorentz independently came to similar conclusions, and later wrote "the chief difference being that
Einstein simply postulates what we have deduced".
3012:
2145:
727:
A further argument for unphysicality can be gleaned from
Einstein's solution to the "hole problem" under general relativity, in which Einstein rejects the physicality of coordinate-system relationships in truly empty space.
652:
Including this "bridge" as an explicit third postulate might also have damaged the theory's credibility, as refractive index and the Fizeau effect would have suggested that the presence and behaviour of matter
2747:
2668:
1579:
1500:
661:
the theory. If this bridging hypothesis had been stated as a third postulate, it could have been claimed that the third postulate (and therefore the theory) were falsified by the experimental evidence.
1046:
3222:) can be deduced by combining the postulates of special relativity with the hypothesis that the laws of special relativity approach the laws of classical mechanics in the non-relativistic limit.
1059:
that converts the coordinates from one frame of reference to the coordinates in another frame of reference. This transformation not only provides a conversion for spacetime coordinates
794:(if the object is larger than a point). The worldline or worldsheet only describes the motion of the object; the object may also have several other physical characteristics such as
620:
assumptions such as isotropy. The numerical value of the parameter in these transformations can then be determined by experiment, just as the numerical values of the parameter pair
2874:
2569:
2504:
1401:
1336:
1187:
1122:
948:
879:
2820:
3430:
1263:
885:. Furthermore, this frame of reference also gives coordinates to all other physical characteristics of objects in the spacetime; for instance, it will provide coordinates
2423:
736:
Einstein's special theory is not the only theory that combines a form of light speed constancy with the relativity principle. A theory along the lines of that proposed by
1770:
3220:
2772:
1604:
752:
the bridging hypothesis) are not sufficient to allow us to arrive uniquely at the solution of special relativity (although special relativity might be considered the
2151:
1611:
2589:
1421:
3018:
2881:
436:
1984:
470:
This theory is correct to the extent to which the two principles upon which it is based are correct. Since these seem to be correct to a great extent, ...
644:
Such a statement would be problematic, as
Einstein rejected the notion that a process such as light-propagation could be immune to other factors (1914: "
607:
Following these derivations, many alternative derivations have been proposed, based on various sets of assumptions. It has often been argued (such as by
585:). A more modern example of deriving the Lorentz transformation from electrodynamics (without using the historical aether concept at all), was given by
3473:
670:
Without a "bridging hypothesis" as a third postulate, the 1905 derivation is open to the criticism that its derived relationships may only apply
552:
3867:
429:
679:
The controversial suggestion that the 1905 theory, derived by assuming empty space, might only apply to empty space, appears in
30:
2388:
is given by the
Minkowski metric. One advantage of this formulation is that it is now easy to compare special relativity with
761:
It is on the basis of this hypothesis that Hertz developed an electrodynamics of moving bodies that is free of contradictions.
3629:
953:
1124:, but will also provide a conversion for all other physical coordinates, such as a conversion law for momentum and energy
775:
In the rigorous mathematical formulation of special relativity, we suppose that the universe exists on a four-dimensional
514:
that is independent of the state of motion of the emitting body. Or: the speed of light in free space has the same value
422:
578:
50:
3693:
3411:
3394:
701:
The equations of the new theory of relativity reduce to those of the original theory in the special case where the g
3860:
2392:, in which the same two postulates hold but the assumption that the metric is required to be Minkowski is dropped.
3721:[Do gravitational fields play an essential part in the structure of the elementary particles of matter?].
391:
637:
Einstein's 1905 derivation is not complete. A break in Einstein's logic occurs where, after having established "
2673:
2594:
1505:
1426:
3908:
543:
can be seen as a space-time constant, and the identification with the speed of light is derived from optics.
247:
2509:
2444:
1341:
1276:
1127:
1062:
888:
819:
489:
3565:
Baccetti, Valentina; Tate, Kyle; Visser, Matt (2012), "Inertial frames without the relativity principle",
4108:
4021:
4006:
3991:
3950:
3853:
810:
596:
409:
152:
137:
127:
75:
4001:
3986:
2426:
2368:
1236:
1206:
1201:) which relates the various coordinates of the various objects in the spacetime. A typical example is
748:
observers. The logical possibility of a Hertzian theory shows that Einstein's two standard postulates (
132:
122:
2384:
assertion that the laws of physics are invariant when represented in any frame of reference for which
1056:
592:
314:
3655:[On the Foundations of the Generalized Theory of Relativity and the Theory of Gravitation].
2429:). In this theory, the first postulate remains unchanged, but the second postulate is modified to:
1945:{\displaystyle \quad {\sqrt {(x'_{1}-y'_{1})^{2}+(x'_{2}-y'_{2})^{2}+(x'_{3}-y'_{3})^{2}}}=c(s'-t')}
2402:
3924:
3890:
2825:
1213:
481:
266:
40:
3741:
3719:"Spielen Gravitationsfelder im Aufber der Materiellen Elementarteilchen eine Wesentliche Rolle?"
3474:"Eine Bemerkung zu meiner Arbeit: "Einige allgemeine Bemerkungen zum Relativitätsprinzip""
1189:, etc. (In practice, these conversion laws can be efficiently handled using the mathematics of
3965:
3960:
3788:
2777:
2357:
1202:
684:
570:
566:
90:
85:
3636:
3189:
2364:
2338:{\displaystyle =c^{2}(s'-t')^{2}-(x'_{1}-y'_{1})^{2}-(x'_{2}-y'_{2})^{2}-(x'_{3}-y'_{3})^{2}}
1198:
1049:
577:
becomes undetectable in agreement with what Poincaré called the principle of relativity (see
3827:
3652:
3284:
3243:
2356:. This can in turn be used to deduce the transformation laws between reference frames; see
1758:{\displaystyle {\sqrt {(x_{1}-y_{1})^{2}+(x_{2}-y_{2})^{2}+(x_{3}-y_{3})^{2}}}=c(s-t)\quad }
573:, which served to explain the negative result of all aether drift measurements. By that the
4069:
3895:
3800:
3753:
3718:
3664:
3584:
3509:
3296:
3255:
1971:
582:
211:
45:
3497:
3448:
8:
3919:
3382:
3178:
2396:
1975:
625:
608:
574:
304:
261:
3804:
3757:
3742:"General covariance and the foundations of general relativity: eight decades of dispute"
3668:
3588:
3546:
Frank, Philipp & Rothe, Hermann (1912). "Zur Herleitung der Lorentztransformation".
3513:
3300:
3259:
2752:
1970:
The second postulate can be used to imply a stronger version of itself, namely that the
1584:
3996:
3876:
3769:
3600:
3574:
3530:
3410:
3320:
2574:
2389:
1406:
600:
453:
117:
22:
3383:"21–6. The potentials for a charge moving with constant velocity; the Lorentz formula"
3164:{\displaystyle ={\sqrt {(x'_{1}-y'_{1})^{2}+(x'_{2}-y'_{2})^{2}+(x'_{3}-y'_{3})^{2}}}}
4054:
4026:
4016:
4011:
3773:
3765:
3699:
3689:
3625:
3604:
3390:
3366:
3324:
3312:
3182:
3007:{\displaystyle \quad {\sqrt {(x_{1}-y_{1})^{2}+(x_{2}-y_{2})^{2}+(x_{3}-y_{3})^{2}}}}
814:
764:
532:
369:
334:
299:
186:
157:
147:
142:
2140:{\displaystyle c^{2}(s-t)^{2}-(x_{1}-y_{1})^{2}-(x_{2}-y_{2})^{2}-(x_{3}-y_{3})^{2}}
783:
562:
506:
As measured in any inertial frame of reference, light is always propagated in empty
329:
3808:
3761:
3688:. John Archibald Wheeler (Second ed.). New York, NY: Freeman. pp. 56–57.
3592:
3517:
3498:"Ăśber die Transformation der Raum-Zeitkoordinaten von ruhenden auf bewegte Systeme"
3304:
3263:
2380:
1978:
under changes of inertial reference frame. In the above notation, this means that
1967:
equations cannot account for the quantum attributes of electromagnetic radiation).
339:
309:
4044:
3929:
3653:"Prinzipielles zur verallgemeinerten Relativitätstheorie und Gravitationstheorie"
3619:
3531:
On the Transformation of Space-Time Coordinates from Stationary to Moving Systems
2371:. The second postulate is then an assertion that the four-dimensional spacetime
803:
680:
586:
558:
536:
449:
324:
319:
294:
271:
181:
3596:
2363:
The postulates of special relativity can be expressed very succinctly using the
4082:
3955:
1765:
737:
528:
498:
396:
364:
225:
80:
4102:
4087:
3981:
3812:
3521:
3316:
3308:
3268:
795:
616:
612:
230:
112:
3703:
3285:"Relativität und Gravitation. Erwiderung auf eine Bemerkung von M. Abraham"
595:
already made an argument similar to Einstein's in 1889, in response to the
359:
3349:
1958:
Informally, the Second Postulate asserts that objects travelling at speed
1055:
We assume that given any two inertial frames of reference, there exists a
4077:
3683:
3564:
344:
220:
3287:[Relativity and Gravitation: Reply to a comment by M. Abraham].
4059:
4049:
3945:
3791:[On the Basic Equations of Electrodynamics for Moving Bodies].
791:
740:(in 1890) allows for light to be fully dragged by all objects, giving
374:
354:
196:
191:
4036:
3845:
787:
776:
461:
172:
3828:"The Principle of Relativity and Its Consequences in Modern Physics"
718:
would, for them, lose its justification, for indeed, with constant g
672:
524:
349:
3789:"Ueber die Grundgleichungen der Electrodynamik für bewegte Körper"
3579:
3412:"Einige allgemeine Bemerkungen über das Relativitätsprinzip"
3447:
809:
In addition to events and physical objects, there are a class of
763:"), but dismissed it on the grounds of a poor agreement with the
759:
Einstein agreed that the Hertz theory was logically consistent ("
3621:
Introduction to Classical Mechanics: With Problems and Solutions
546:
1190:
632:
3472:
770:
665:
507:
3545:
3495:
599:
seeming to show both postulates to be true. He wrote that a
535:
also implicitly used both postulates when he introduced the
3685:
Spacetime physics : Introduction to special relativity
799:
464:, though his derivation implies a few more assumptions.
3723:
Königlich Preußische Akademie der Wissenschaften, Berlin
2399:
is the limiting case of special relativity in the limit
1962:
in one reference frame will necessarily travel at speed
2375:
is a pseudo-Riemannian manifold equipped with a metric
3348:
950:
for the momentum and energy of an object, coordinates
3192:
3021:
2884:
2828:
2780:
2755:
2676:
2597:
2577:
2512:
2447:
2405:
2154:
1987:
1773:
1614:
1587:
1508:
1429:
1409:
1344:
1279:
1239:
1130:
1065:
1041:{\displaystyle (E_{1},E_{2},E_{3},B_{1},B_{2},B_{3})}
956:
891:
822:
460:. Einstein's formulation is said to only require two
3246:[On the Electrodynamics of Moving Bodies].
475:
3346:
3214:
3163:
3006:
2868:
2814:
2766:
2741:
2662:
2583:
2563:
2498:
2417:
2337:
2139:
1944:
1757:
1598:
1573:
1494:
1415:
1395:
1330:
1257:
1181:
1116:
1040:
942:
873:
731:
3470:
3445:
3408:
786:; physical objects in spacetime are described by
4100:
3431:Some General Remarks on the Relativity Principle
3389:, vol. 2, Reading: Addison Wesley Longman,
813:. Each inertial frame of reference provides a
782:. Individual points in spacetime are known as
693:The Principle of Relativity Rests on Emptiness
639:the law of the constancy of the speed of light
553:Alternative formulations of special relativity
488:The laws of physics take the same form in all
3861:
3832:Archives des sciences physiques et naturelles
3380:
547:Alternative derivations of special relativity
430:
3496:Frank, Philipp & Rothe, Hermann (1910),
3365:Various English translations on Wikisource:
633:Insufficiency of the two standard postulates
3624:. Cambridge University Press. p. 549.
722:there could not be any particles of matter.
3868:
3854:
2379:of signature (1,3), which is given by the
771:Mathematical formulation of the postulates
437:
423:
3578:
3267:
2742:{\displaystyle (y'_{1},y'_{2},y'_{3},s')}
2663:{\displaystyle (x'_{1},x'_{2},x'_{3},t')}
1574:{\displaystyle (y'_{1},y'_{2},y'_{3},s')}
1495:{\displaystyle (x'_{1},x'_{2},x'_{3},t')}
711:Einstein revisited the problem in 1919 ("
539:formulation, even though he showed that
3825:
3716:
3650:
3282:
3241:
3637:Chapter "Relativity without c" page 549
2425:(which is sometimes referred to as the
790:(if the object is a point particle) or
456:in 1905, from principle now called the
4101:
3875:
3739:
3681:
3337:Albert Einstein, Morgan document, 1921
2441:are two events which have coordinates
1273:are two events which have coordinates
3849:
3786:
3646:
3644:
3617:
2564:{\displaystyle (y_{1},y_{2},y_{3},s)}
2499:{\displaystyle (x_{1},x_{2},x_{3},t)}
1396:{\displaystyle (y_{1},y_{2},y_{3},s)}
1331:{\displaystyle (x_{1},x_{2},x_{3},t)}
1182:{\displaystyle (p_{1},p_{2},p_{3},E)}
1117:{\displaystyle (x_{1},x_{2},x_{3},t)}
943:{\displaystyle (p_{1},p_{2},p_{3},E)}
874:{\displaystyle (x_{1},x_{2},x_{3},t)}
676:, that is, in the absence of matter.
657:seem to influence light-propagation,
3244:"Zur elektrodynamik bewegter körper"
3237:
3235:
518:in all inertial frames of reference.
1225:2. Second Postulate (Invariance of
496:2. Second postulate (invariance of
13:
3641:
2412:
1252:
1233:There exists an absolute constant
579:History of Lorentz transformations
14:
4120:
3232:
1265:with the following property. If
1258:{\displaystyle 0<c<\infty }
3454:Archiv der Mathematik und Physik
3429:English Wikisource translation:
666:The 1905 system as "null theory"
476:Postulates of special relativity
458:postulates of special relativity
404:
403:
390:
29:
3819:
3780:
3733:
3710:
3675:
3611:
3558:
3539:
3449:"Das Relativitätsprinzip"
3387:The Feynman Lectures on Physics
2885:
1774:
1754:
732:Alternative relativistic models
3746:Reports on Progress in Physics
3608:; See references 5–25 therein.
3567:Journal of High Energy Physics
3489:
3464:
3439:
3402:
3374:
3340:
3331:
3276:
3150:
3117:
3105:
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2191:
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2128:
2101:
2089:
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2023:
2011:
1998:
1939:
1917:
1900:
1867:
1855:
1822:
1810:
1777:
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1739:
1722:
1695:
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1568:
1509:
1489:
1430:
1390:
1345:
1325:
1280:
1176:
1131:
1111:
1066:
1035:
957:
937:
892:
868:
823:
1:
3793:Annalen der Physik und Chemie
3177:The physical theory given by
2418:{\displaystyle c\to \infty }
881:for events in the spacetime
811:inertial frames of reference
490:inertial frames of reference
7:
4007:Relativistic Doppler effect
3951:Inertial frame of reference
3347:Minkowski, Hermann (1909),
2869:{\displaystyle s-t=s'-t'=0}
2369:pseudo-Riemannian manifolds
597:Michelson-Morley experiment
138:Relativistic Doppler effect
76:Inertial frame of reference
10:
4125:
4002:Relativity of simultaneity
3766:10.1088/0034-4885/56/7/001
3471:Ignatowsky, W. v. (1911).
3446:Ignatowsky, W. v. (1911).
3409:Ignatowsky, W. v. (1910).
2749:in another inertial frame
1581:in another inertial frame
550:
133:Relativity of simultaneity
4068:
4035:
3974:
3938:
3904:
3883:
3826:Einstein, Albert (1910).
3717:Einstein, Albert (1916).
3682:Taylor, Edwin F. (1992).
3657:Physikalische Zeitschrift
3651:Einstein, Albert (1914).
3548:Physikalische Zeitschrift
3479:Physikalische Zeitschrift
3417:Physikalische Zeitschrift
3355:Physikalische Zeitschrift
3242:Einstein, Albert (1905).
2815:{\displaystyle s-t=s'-t'}
1057:coordinate transformation
593:George Francis FitzGerald
510:with a definite velocity
4022:Bell's spaceship paradox
3813:10.1002/andp.18902771102
3522:10.1002/andp.19113390502
3309:10.1002/andp.19123431014
3269:10.1002/andp.19053221004
3225:
3215:{\displaystyle E=mc^{2}}
565:(1892–1905) derived the
153:Bell's spaceship paradox
3992:Mass–energy equivalence
3925:Galilean transformation
3891:Principle of relativity
3597:10.1007/JHEP05(2012)119
2591:, and have coordinates
1423:, and have coordinates
1214:Principle of relativity
482:principle of relativity
267:Galilean transformation
128:Mass–energy equivalence
41:Principle of relativity
3966:Lorentz transformation
3381:Feynman, R.P. (1970),
3216:
3165:
3008:
2870:
2816:
2768:
2743:
2664:
2585:
2571:in one inertial frame
2565:
2500:
2427:non-relativistic limit
2419:
2358:Lorentz transformation
2339:
2141:
1946:
1759:
1600:
1575:
1496:
1417:
1403:in one inertial frame
1397:
1332:
1259:
1183:
1118:
1042:
944:
875:
685:John Archibald Wheeler
567:Lorentz transformation
452:derived the theory of
91:Lorentz transformation
3618:Morin, David (2008).
3529:English translation:
3350:"Raum und Zeit"
3283:Einstein, A. (1912).
3217:
3166:
3009:
2871:
2817:
2769:
2744:
2665:
2586:
2566:
2501:
2420:
2365:mathematical language
2340:
2142:
1947:
1760:
1601:
1576:
1497:
1418:
1398:
1333:
1260:
1199:differential equation
1184:
1119:
1050:electromagnetic field
1043:
945:
876:
71:Einstein's postulates
3896:Theory of relativity
3740:Norton, J D (1993).
3190:
3019:
2882:
2826:
2778:
2753:
2674:
2595:
2575:
2510:
2445:
2403:
2152:
1985:
1771:
1612:
1585:
1506:
1427:
1407:
1342:
1277:
1237:
1212:1. First Postulate (
1128:
1063:
954:
889:
820:
744:c-constancy for all
583:Lorentz ether theory
480:1. First postulate (
46:Theory of relativity
4045:Minkowski spacetime
3961:Maxwell's equations
3920:Galilean relativity
3805:1890AnP...277..369H
3758:1993RPPh...56..791N
3669:1914PhyZ...15..176E
3589:2012JHEP...05..119B
3514:1911AnP...339..825F
3301:1912AnP...343.1059E
3260:1905AnP...322..891E
3179:classical mechanics
3148:
3132:
3103:
3087:
3058:
3042:
2822:. Furthermore, if
2724:
2708:
2692:
2645:
2629:
2613:
2397:Galilean relativity
2348:for any two events
2324:
2308:
2279:
2263:
2234:
2218:
1898:
1882:
1853:
1837:
1808:
1792:
1556:
1540:
1524:
1477:
1461:
1445:
1203:Maxwell's equations
626:Vacuum permittivity
609:Vladimir Ignatowski
575:luminiferous aether
571:Maxwell's equations
262:Galilean relativity
182:Minkowski spacetime
86:Maxwell's equations
4109:Special relativity
4055:Spacetime diagrams
3997:Length contraction
3877:Special relativity
3787:Hertz, H. (1890).
3502:Annalen der Physik
3289:Annalen der Physik
3248:Annalen der Physik
3212:
3161:
3136:
3120:
3091:
3075:
3046:
3030:
3004:
2866:
2812:
2767:{\displaystyle F'}
2764:
2739:
2712:
2696:
2680:
2660:
2633:
2617:
2601:
2581:
2561:
2496:
2415:
2390:general relativity
2335:
2312:
2296:
2267:
2251:
2222:
2206:
2137:
1972:spacetime interval
1942:
1886:
1870:
1841:
1825:
1796:
1780:
1755:
1599:{\displaystyle F'}
1596:
1571:
1544:
1528:
1512:
1492:
1465:
1449:
1433:
1413:
1393:
1328:
1255:
1207:Newton's first law
1179:
1114:
1038:
940:
871:
601:length contraction
454:special relativity
397:Physics portal
118:Length contraction
23:Special relativity
16:Concept in physics
4096:
4095:
4027:Ehrenfest paradox
4017:Relativistic disk
4012:Thomas precession
3987:Relativistic mass
3631:978-1-139-46837-4
3295:(10): 1059–1064.
3183:Newtonian gravity
3159:
3002:
2584:{\displaystyle F}
1909:
1731:
1416:{\displaystyle F}
815:coordinate system
689:Spacetime Physics
533:Hermann Minkowski
447:
446:
187:Spacetime diagram
158:Ehrenfest paradox
148:Relativistic disk
143:Thomas precession
123:Relativistic mass
4116:
3870:
3863:
3856:
3847:
3846:
3840:
3839:
3823:
3817:
3816:
3784:
3778:
3777:
3737:
3731:
3730:
3714:
3708:
3707:
3679:
3673:
3672:
3648:
3639:
3635:
3615:
3609:
3607:
3582:
3562:
3556:
3555:
3543:
3537:
3524:
3493:
3487:
3486:
3476:
3468:
3462:
3461:
3451:
3443:
3437:
3424:
3414:
3406:
3400:
3399:
3378:
3372:
3362:
3352:
3344:
3338:
3335:
3329:
3328:
3280:
3274:
3273:
3271:
3239:
3221:
3219:
3218:
3213:
3211:
3210:
3170:
3168:
3167:
3162:
3160:
3158:
3157:
3144:
3128:
3113:
3112:
3099:
3083:
3068:
3067:
3054:
3038:
3026:
3013:
3011:
3010:
3005:
3003:
3001:
3000:
2991:
2990:
2978:
2977:
2962:
2961:
2952:
2951:
2939:
2938:
2923:
2922:
2913:
2912:
2900:
2899:
2887:
2875:
2873:
2872:
2867:
2859:
2848:
2821:
2819:
2818:
2813:
2811:
2800:
2773:
2771:
2770:
2765:
2763:
2748:
2746:
2745:
2740:
2735:
2720:
2704:
2688:
2669:
2667:
2666:
2661:
2656:
2641:
2625:
2609:
2590:
2588:
2587:
2582:
2570:
2568:
2567:
2562:
2551:
2550:
2538:
2537:
2525:
2524:
2505:
2503:
2502:
2497:
2486:
2485:
2473:
2472:
2460:
2459:
2424:
2422:
2421:
2416:
2381:Minkowski metric
2344:
2342:
2341:
2336:
2334:
2333:
2320:
2304:
2289:
2288:
2275:
2259:
2244:
2243:
2230:
2214:
2199:
2198:
2189:
2178:
2167:
2166:
2146:
2144:
2143:
2138:
2136:
2135:
2126:
2125:
2113:
2112:
2097:
2096:
2087:
2086:
2074:
2073:
2058:
2057:
2048:
2047:
2035:
2034:
2019:
2018:
1997:
1996:
1951:
1949:
1948:
1943:
1938:
1927:
1910:
1908:
1907:
1894:
1878:
1863:
1862:
1849:
1833:
1818:
1817:
1804:
1788:
1776:
1764:
1762:
1761:
1756:
1732:
1730:
1729:
1720:
1719:
1707:
1706:
1691:
1690:
1681:
1680:
1668:
1667:
1652:
1651:
1642:
1641:
1629:
1628:
1616:
1605:
1603:
1602:
1597:
1595:
1580:
1578:
1577:
1572:
1567:
1552:
1536:
1520:
1501:
1499:
1498:
1493:
1488:
1473:
1457:
1441:
1422:
1420:
1419:
1414:
1402:
1400:
1399:
1394:
1383:
1382:
1370:
1369:
1357:
1356:
1337:
1335:
1334:
1329:
1318:
1317:
1305:
1304:
1292:
1291:
1264:
1262:
1261:
1256:
1188:
1186:
1185:
1180:
1169:
1168:
1156:
1155:
1143:
1142:
1123:
1121:
1120:
1115:
1104:
1103:
1091:
1090:
1078:
1077:
1052:, and so forth.
1047:
1045:
1044:
1039:
1034:
1033:
1021:
1020:
1008:
1007:
995:
994:
982:
981:
969:
968:
949:
947:
946:
941:
930:
929:
917:
916:
904:
903:
880:
878:
877:
872:
861:
860:
848:
847:
835:
834:
439:
432:
425:
412:
407:
406:
399:
395:
394:
287:
214:
175:
106:
64:
33:
19:
18:
4124:
4123:
4119:
4118:
4117:
4115:
4114:
4113:
4099:
4098:
4097:
4092:
4064:
4031:
3970:
3946:Relative motion
3934:
3930:Aether theories
3913:
3900:
3879:
3874:
3844:
3843:
3824:
3820:
3799:(11): 369–399.
3785:
3781:
3738:
3734:
3715:
3711:
3696:
3680:
3676:
3649:
3642:
3632:
3616:
3612:
3563:
3559:
3544:
3540:
3494:
3490:
3469:
3465:
3444:
3440:
3407:
3403:
3397:
3379:
3375:
3345:
3341:
3336:
3332:
3281:
3277:
3254:(10): 891–921.
3240:
3233:
3228:
3206:
3202:
3191:
3188:
3187:
3153:
3149:
3140:
3124:
3108:
3104:
3095:
3079:
3063:
3059:
3050:
3034:
3025:
3020:
3017:
3016:
2996:
2992:
2986:
2982:
2973:
2969:
2957:
2953:
2947:
2943:
2934:
2930:
2918:
2914:
2908:
2904:
2895:
2891:
2886:
2883:
2880:
2879:
2852:
2841:
2827:
2824:
2823:
2804:
2793:
2779:
2776:
2775:
2756:
2754:
2751:
2750:
2728:
2716:
2700:
2684:
2675:
2672:
2671:
2649:
2637:
2621:
2605:
2596:
2593:
2592:
2576:
2573:
2572:
2546:
2542:
2533:
2529:
2520:
2516:
2511:
2508:
2507:
2481:
2477:
2468:
2464:
2455:
2451:
2446:
2443:
2442:
2404:
2401:
2400:
2329:
2325:
2316:
2300:
2284:
2280:
2271:
2255:
2239:
2235:
2226:
2210:
2194:
2190:
2182:
2171:
2162:
2158:
2153:
2150:
2149:
2131:
2127:
2121:
2117:
2108:
2104:
2092:
2088:
2082:
2078:
2069:
2065:
2053:
2049:
2043:
2039:
2030:
2026:
2014:
2010:
1992:
1988:
1986:
1983:
1982:
1931:
1920:
1903:
1899:
1890:
1874:
1858:
1854:
1845:
1829:
1813:
1809:
1800:
1784:
1775:
1772:
1769:
1768:
1725:
1721:
1715:
1711:
1702:
1698:
1686:
1682:
1676:
1672:
1663:
1659:
1647:
1643:
1637:
1633:
1624:
1620:
1615:
1613:
1610:
1609:
1588:
1586:
1583:
1582:
1560:
1548:
1532:
1516:
1507:
1504:
1503:
1481:
1469:
1453:
1437:
1428:
1425:
1424:
1408:
1405:
1404:
1378:
1374:
1365:
1361:
1352:
1348:
1343:
1340:
1339:
1313:
1309:
1300:
1296:
1287:
1283:
1278:
1275:
1274:
1238:
1235:
1234:
1164:
1160:
1151:
1147:
1138:
1134:
1129:
1126:
1125:
1099:
1095:
1086:
1082:
1073:
1069:
1064:
1061:
1060:
1029:
1025:
1016:
1012:
1003:
999:
990:
986:
977:
973:
964:
960:
955:
952:
951:
925:
921:
912:
908:
899:
895:
890:
887:
886:
856:
852:
843:
839:
830:
826:
821:
818:
817:
796:energy-momentum
773:
754:most minimalist
734:
721:
717:
704:
681:Edwin F. Taylor
668:
635:
587:Richard Feynman
559:Hendrik Lorentz
555:
549:
537:Minkowski space
478:
450:Albert Einstein
443:
402:
389:
388:
381:
380:
379:
289:
288:
285:
277:
276:
272:Aether theories
257:
256:
255:
236:
235:
216:
215:
210:
202:
201:
177:
176:
171:
163:
162:
108:
107:
104:
96:
95:
66:
65:
62:
17:
12:
11:
5:
4122:
4112:
4111:
4094:
4093:
4091:
4090:
4085:
4080:
4074:
4072:
4066:
4065:
4063:
4062:
4057:
4052:
4047:
4041:
4039:
4033:
4032:
4030:
4029:
4024:
4019:
4014:
4009:
4004:
3999:
3994:
3989:
3984:
3978:
3976:
3972:
3971:
3969:
3968:
3963:
3958:
3956:Speed of light
3953:
3948:
3942:
3940:
3936:
3935:
3933:
3932:
3927:
3922:
3916:
3914:
3912:
3911:
3905:
3902:
3901:
3899:
3898:
3893:
3887:
3885:
3881:
3880:
3873:
3872:
3865:
3858:
3850:
3842:
3841:
3838:: 5–28, 125–1.
3818:
3779:
3752:(7): 791–858.
3732:
3709:
3694:
3674:
3640:
3630:
3610:
3557:
3538:
3536:
3535:
3534:
3533:
3508:(5): 825–855,
3488:
3463:
3438:
3436:
3435:
3434:
3433:
3401:
3395:
3373:
3371:
3370:
3367:Space and Time
3339:
3330:
3275:
3230:
3229:
3227:
3224:
3209:
3205:
3201:
3198:
3195:
3175:
3174:
3173:
3172:
3156:
3152:
3147:
3143:
3139:
3135:
3131:
3127:
3123:
3119:
3116:
3111:
3107:
3102:
3098:
3094:
3090:
3086:
3082:
3078:
3074:
3071:
3066:
3062:
3057:
3053:
3049:
3045:
3041:
3037:
3033:
3029:
3024:
3014:
2999:
2995:
2989:
2985:
2981:
2976:
2972:
2968:
2965:
2960:
2956:
2950:
2946:
2942:
2937:
2933:
2929:
2926:
2921:
2917:
2911:
2907:
2903:
2898:
2894:
2890:
2865:
2862:
2858:
2855:
2851:
2847:
2844:
2840:
2837:
2834:
2831:
2810:
2807:
2803:
2799:
2796:
2792:
2789:
2786:
2783:
2762:
2759:
2738:
2734:
2731:
2727:
2723:
2719:
2715:
2711:
2707:
2703:
2699:
2695:
2691:
2687:
2683:
2679:
2659:
2655:
2652:
2648:
2644:
2640:
2636:
2632:
2628:
2624:
2620:
2616:
2612:
2608:
2604:
2600:
2580:
2560:
2557:
2554:
2549:
2545:
2541:
2536:
2532:
2528:
2523:
2519:
2515:
2495:
2492:
2489:
2484:
2480:
2476:
2471:
2467:
2463:
2458:
2454:
2450:
2414:
2411:
2408:
2395:The theory of
2346:
2345:
2332:
2328:
2323:
2319:
2315:
2311:
2307:
2303:
2299:
2295:
2292:
2287:
2283:
2278:
2274:
2270:
2266:
2262:
2258:
2254:
2250:
2247:
2242:
2238:
2233:
2229:
2225:
2221:
2217:
2213:
2209:
2205:
2202:
2197:
2193:
2188:
2185:
2181:
2177:
2174:
2170:
2165:
2161:
2157:
2147:
2134:
2130:
2124:
2120:
2116:
2111:
2107:
2103:
2100:
2095:
2091:
2085:
2081:
2077:
2072:
2068:
2064:
2061:
2056:
2052:
2046:
2042:
2038:
2033:
2029:
2025:
2022:
2017:
2013:
2009:
2006:
2003:
2000:
1995:
1991:
1956:
1955:
1954:
1953:
1941:
1937:
1934:
1930:
1926:
1923:
1919:
1916:
1913:
1906:
1902:
1897:
1893:
1889:
1885:
1881:
1877:
1873:
1869:
1866:
1861:
1857:
1852:
1848:
1844:
1840:
1836:
1832:
1828:
1824:
1821:
1816:
1812:
1807:
1803:
1799:
1795:
1791:
1787:
1783:
1779:
1766:if and only if
1753:
1750:
1747:
1744:
1741:
1738:
1735:
1728:
1724:
1718:
1714:
1710:
1705:
1701:
1697:
1694:
1689:
1685:
1679:
1675:
1671:
1666:
1662:
1658:
1655:
1650:
1646:
1640:
1636:
1632:
1627:
1623:
1619:
1594:
1591:
1570:
1566:
1563:
1559:
1555:
1551:
1547:
1543:
1539:
1535:
1531:
1527:
1523:
1519:
1515:
1511:
1491:
1487:
1484:
1480:
1476:
1472:
1468:
1464:
1460:
1456:
1452:
1448:
1444:
1440:
1436:
1432:
1412:
1392:
1389:
1386:
1381:
1377:
1373:
1368:
1364:
1360:
1355:
1351:
1347:
1327:
1324:
1321:
1316:
1312:
1308:
1303:
1299:
1295:
1290:
1286:
1282:
1254:
1251:
1248:
1245:
1242:
1223:
1222:
1205:. Another is
1178:
1175:
1172:
1167:
1163:
1159:
1154:
1150:
1146:
1141:
1137:
1133:
1113:
1110:
1107:
1102:
1098:
1094:
1089:
1085:
1081:
1076:
1072:
1068:
1037:
1032:
1028:
1024:
1019:
1015:
1011:
1006:
1002:
998:
993:
989:
985:
980:
976:
972:
967:
963:
959:
939:
936:
933:
928:
924:
920:
915:
911:
907:
902:
898:
894:
870:
867:
864:
859:
855:
851:
846:
842:
838:
833:
829:
825:
772:
769:
738:Heinrich Hertz
733:
730:
719:
715:
702:
667:
664:
634:
631:
563:Henri Poincaré
557:Historically,
548:
545:
529:memorylessness
520:
519:
494:
493:
477:
474:
445:
444:
442:
441:
434:
427:
419:
416:
415:
414:
413:
400:
383:
382:
378:
377:
372:
367:
362:
357:
352:
347:
342:
337:
332:
327:
322:
317:
312:
307:
302:
297:
291:
290:
284:
283:
282:
279:
278:
275:
274:
269:
264:
258:
254:
253:
250:
244:
243:
242:
241:
238:
237:
234:
233:
228:
223:
217:
209:
208:
207:
204:
203:
200:
199:
194:
189:
184:
178:
170:
169:
168:
165:
164:
161:
160:
155:
150:
145:
140:
135:
130:
125:
120:
115:
109:
103:
102:
101:
98:
97:
94:
93:
88:
83:
81:Speed of light
78:
73:
67:
61:
60:
59:
56:
55:
54:
53:
48:
43:
35:
34:
26:
25:
15:
9:
6:
4:
3:
2:
4121:
4110:
4107:
4106:
4104:
4089:
4086:
4084:
4081:
4079:
4076:
4075:
4073:
4071:
4067:
4061:
4058:
4056:
4053:
4051:
4048:
4046:
4043:
4042:
4040:
4038:
4034:
4028:
4025:
4023:
4020:
4018:
4015:
4013:
4010:
4008:
4005:
4003:
4000:
3998:
3995:
3993:
3990:
3988:
3985:
3983:
3982:Time dilation
3980:
3979:
3977:
3973:
3967:
3964:
3962:
3959:
3957:
3954:
3952:
3949:
3947:
3944:
3943:
3941:
3937:
3931:
3928:
3926:
3923:
3921:
3918:
3917:
3915:
3910:
3907:
3906:
3903:
3897:
3894:
3892:
3889:
3888:
3886:
3882:
3878:
3871:
3866:
3864:
3859:
3857:
3852:
3851:
3848:
3837:
3834:(in German).
3833:
3829:
3822:
3814:
3810:
3806:
3802:
3798:
3795:(in German).
3794:
3790:
3783:
3775:
3771:
3767:
3763:
3759:
3755:
3751:
3747:
3743:
3736:
3728:
3725:(in German).
3724:
3720:
3713:
3705:
3701:
3697:
3695:0-7167-2327-1
3691:
3687:
3686:
3678:
3670:
3666:
3662:
3659:(in German).
3658:
3654:
3647:
3645:
3638:
3633:
3627:
3623:
3622:
3614:
3606:
3602:
3598:
3594:
3590:
3586:
3581:
3576:
3572:
3568:
3561:
3553:
3549:
3542:
3532:
3528:
3527:
3526:
3525:
3523:
3519:
3515:
3511:
3507:
3503:
3499:
3492:
3484:
3480:
3475:
3467:
3459:
3455:
3450:
3442:
3432:
3428:
3427:
3426:
3425:
3422:
3418:
3413:
3405:
3398:
3396:0-201-02115-3
3392:
3388:
3384:
3377:
3368:
3364:
3363:
3360:
3356:
3351:
3343:
3334:
3326:
3322:
3318:
3314:
3310:
3306:
3302:
3298:
3294:
3290:
3286:
3279:
3270:
3265:
3261:
3257:
3253:
3249:
3245:
3238:
3236:
3231:
3223:
3207:
3203:
3199:
3196:
3193:
3184:
3180:
3154:
3145:
3141:
3137:
3133:
3129:
3125:
3121:
3114:
3109:
3100:
3096:
3092:
3088:
3084:
3080:
3076:
3069:
3064:
3055:
3051:
3047:
3043:
3039:
3035:
3031:
3022:
3015:
2997:
2987:
2983:
2979:
2974:
2970:
2963:
2958:
2948:
2944:
2940:
2935:
2931:
2924:
2919:
2909:
2905:
2901:
2896:
2892:
2878:
2877:
2863:
2860:
2856:
2853:
2849:
2845:
2842:
2838:
2835:
2832:
2829:
2808:
2805:
2801:
2797:
2794:
2790:
2787:
2784:
2781:
2760:
2757:
2732:
2729:
2725:
2721:
2717:
2713:
2709:
2705:
2701:
2697:
2693:
2689:
2685:
2681:
2653:
2650:
2646:
2642:
2638:
2634:
2630:
2626:
2622:
2618:
2614:
2610:
2606:
2602:
2578:
2555:
2552:
2547:
2543:
2539:
2534:
2530:
2526:
2521:
2517:
2490:
2487:
2482:
2478:
2474:
2469:
2465:
2461:
2456:
2452:
2440:
2436:
2432:
2431:
2430:
2428:
2406:
2398:
2393:
2391:
2387:
2382:
2378:
2374:
2370:
2366:
2361:
2359:
2355:
2351:
2330:
2321:
2317:
2313:
2309:
2305:
2301:
2297:
2290:
2285:
2276:
2272:
2268:
2264:
2260:
2256:
2252:
2245:
2240:
2231:
2227:
2223:
2219:
2215:
2211:
2207:
2200:
2195:
2186:
2183:
2179:
2175:
2172:
2163:
2159:
2155:
2148:
2132:
2122:
2118:
2114:
2109:
2105:
2098:
2093:
2083:
2079:
2075:
2070:
2066:
2059:
2054:
2044:
2040:
2036:
2031:
2027:
2020:
2015:
2007:
2004:
2001:
1993:
1989:
1981:
1980:
1979:
1977:
1973:
1968:
1965:
1961:
1935:
1932:
1928:
1924:
1921:
1914:
1911:
1904:
1895:
1891:
1887:
1883:
1879:
1875:
1871:
1864:
1859:
1850:
1846:
1842:
1838:
1834:
1830:
1826:
1819:
1814:
1805:
1801:
1797:
1793:
1789:
1785:
1781:
1767:
1748:
1745:
1742:
1736:
1733:
1726:
1716:
1712:
1708:
1703:
1699:
1692:
1687:
1677:
1673:
1669:
1664:
1660:
1653:
1648:
1638:
1634:
1630:
1625:
1621:
1608:
1607:
1592:
1589:
1564:
1561:
1557:
1553:
1549:
1545:
1541:
1537:
1533:
1529:
1525:
1521:
1517:
1513:
1485:
1482:
1478:
1474:
1470:
1466:
1462:
1458:
1454:
1450:
1446:
1442:
1438:
1434:
1410:
1387:
1384:
1379:
1375:
1371:
1366:
1362:
1358:
1353:
1349:
1322:
1319:
1314:
1310:
1306:
1301:
1297:
1293:
1288:
1284:
1272:
1268:
1249:
1246:
1243:
1240:
1232:
1231:
1230:
1228:
1219:
1218:
1217:
1215:
1210:
1208:
1204:
1200:
1194:
1192:
1173:
1170:
1165:
1161:
1157:
1152:
1148:
1144:
1139:
1135:
1108:
1105:
1100:
1096:
1092:
1087:
1083:
1079:
1074:
1070:
1058:
1053:
1051:
1030:
1026:
1022:
1017:
1013:
1009:
1004:
1000:
996:
991:
987:
983:
978:
974:
970:
965:
961:
934:
931:
926:
922:
918:
913:
909:
905:
900:
896:
884:
865:
862:
857:
853:
849:
844:
840:
836:
831:
827:
816:
812:
807:
805:
801:
797:
793:
789:
785:
781:
778:
768:
766:
765:Fizeau result
762:
757:
755:
751:
747:
743:
739:
729:
725:
723:
709:
707:
696:
694:
691:" (Box 3-1: "
690:
686:
682:
677:
675:
674:
663:
660:
656:
650:
648:
642:
640:
630:
627:
623:
618:
617:Hermann Rothe
614:
613:Philipp Frank
610:
605:
602:
598:
594:
590:
588:
584:
580:
576:
572:
568:
564:
560:
554:
544:
542:
538:
534:
530:
526:
517:
513:
509:
505:
504:
503:
501:
500:
491:
487:
486:
485:
483:
473:
471:
465:
463:
459:
455:
451:
440:
435:
433:
428:
426:
421:
420:
418:
417:
411:
401:
398:
393:
387:
386:
385:
384:
376:
373:
371:
368:
366:
363:
361:
358:
356:
353:
351:
348:
346:
343:
341:
338:
336:
333:
331:
328:
326:
323:
321:
318:
316:
313:
311:
308:
306:
303:
301:
298:
296:
293:
292:
281:
280:
273:
270:
268:
265:
263:
260:
259:
251:
249:
246:
245:
240:
239:
232:
231:Four-momentum
229:
227:
224:
222:
219:
218:
213:
206:
205:
198:
195:
193:
190:
188:
185:
183:
180:
179:
174:
167:
166:
159:
156:
154:
151:
149:
146:
144:
141:
139:
136:
134:
131:
129:
126:
124:
121:
119:
116:
114:
113:Time dilation
111:
110:
100:
99:
92:
89:
87:
84:
82:
79:
77:
74:
72:
69:
68:
58:
57:
52:
49:
47:
44:
42:
39:
38:
37:
36:
32:
28:
27:
24:
21:
20:
3975:Consequences
3835:
3831:
3821:
3796:
3792:
3782:
3749:
3745:
3735:
3726:
3722:
3712:
3684:
3677:
3660:
3656:
3620:
3613:
3570:
3566:
3560:
3551:
3547:
3541:
3505:
3501:
3491:
3482:
3478:
3466:
3457:
3453:
3441:
3420:
3416:
3404:
3386:
3376:
3358:
3354:
3342:
3333:
3292:
3288:
3278:
3251:
3247:
3176:
2438:
2434:
2394:
2385:
2376:
2372:
2362:
2353:
2349:
2347:
1969:
1963:
1959:
1957:
1270:
1266:
1226:
1224:
1211:
1195:
1054:
882:
808:
779:
774:
760:
758:
756:solution).
753:
749:
745:
741:
735:
726:
712:
710:
700:
697:
692:
688:
678:
671:
669:
658:
654:
651:
645:
643:
638:
636:
621:
611:in 1910, or
606:
591:
556:
540:
521:
515:
511:
497:
495:
479:
469:
466:
457:
448:
105:Consequences
70:
51:Formulations
4083:Proper mass
4078:Proper time
3939:Foundations
3663:: 176–180.
792:worldsheets
226:Proper mass
221:Proper time
63:Foundations
4088:4-momentum
4060:Light cone
4050:World line
3729:: 349–356.
3573:(5): 119,
3554:: 750–753.
3423:: 972–976.
788:worldlines
551:See also:
462:postulates
315:FitzGerald
300:Sommerfeld
252:Precursors
197:Light cone
192:World line
4037:Spacetime
3884:Overviews
3774:250902085
3605:118695037
3580:1112.1466
3325:120162895
3317:0003-3804
3134:−
3089:−
3044:−
2980:−
2941:−
2902:−
2850:−
2833:−
2802:−
2785:−
2413:∞
2410:→
2310:−
2291:−
2265:−
2246:−
2220:−
2201:−
2180:−
2115:−
2099:−
2076:−
2060:−
2037:−
2021:−
2005:−
1976:invariant
1929:−
1884:−
1839:−
1794:−
1746:−
1709:−
1670:−
1631:−
1253:∞
777:spacetime
687:'s book "
365:Ehrenfest
335:Minkowski
305:Michelson
173:Spacetime
4103:Category
4070:Dynamics
3704:25165077
3460:: 17–40.
3146:′
3130:′
3101:′
3085:′
3056:′
3040:′
2857:′
2846:′
2809:′
2798:′
2761:′
2733:′
2722:′
2706:′
2690:′
2654:′
2643:′
2627:′
2611:′
2322:′
2306:′
2277:′
2261:′
2232:′
2216:′
2187:′
2176:′
1936:′
1925:′
1896:′
1880:′
1851:′
1835:′
1806:′
1790:′
1593:′
1565:′
1554:′
1538:′
1522:′
1486:′
1475:′
1459:′
1443:′
746:physical
673:in vacuo
624:and the
525:isotropy
410:Category
360:von Laue
330:Poincaré
320:Herglotz
295:Einstein
212:Dynamics
3909:History
3801:Bibcode
3754:Bibcode
3665:Bibcode
3585:Bibcode
3510:Bibcode
3361:: 75–88
3297:Bibcode
3256:Bibcode
2876:, then
2774:, then
1606:, then
1191:tensors
1048:for an
806:, etc.
750:without
345:Abraham
325:Lorentz
248:History
3772:
3702:
3692:
3628:
3603:
3485:: 779.
3393:
3323:
3315:
3181:, and
804:charge
784:events
708:").
659:contra
649:")
647:world.
527:, and
408:
370:Tolman
355:Planck
340:Fizeau
310:Morley
286:People
3770:S2CID
3601:S2CID
3575:arXiv
3321:S2CID
3226:Notes
742:local
695:").
569:from
508:space
375:Dirac
3700:OCLC
3690:ISBN
3626:ISBN
3571:2012
3391:ISBN
3313:ISSN
2670:and
2506:and
1502:and
1338:and
1250:<
1244:<
800:mass
724:")
706:case
683:and
655:does
615:and
581:and
561:and
350:Born
3809:doi
3797:277
3762:doi
3593:doi
3518:doi
3506:339
3305:doi
3293:343
3264:doi
2433:If
2367:of
1974:is
1193:.)
472:")
4105::
3836:29
3830:.
3807:.
3768:.
3760:.
3750:56
3748:.
3744:.
3698:.
3661:15
3643:^
3599:,
3591:,
3583:,
3569:,
3552:13
3550:.
3516:,
3504:,
3500:,
3483:12
3481:.
3477:.
3458:18
3456:.
3452:.
3421:11
3419:.
3415:.
3385:,
3359:10
3357:,
3353:,
3319:.
3311:.
3303:.
3291:.
3262:.
3252:17
3250:.
3234:^
2437:,
2360:.
2352:,
1269:,
1229:)
1216:)
1209:.
802:,
798:,
720:μν
716:μν
703:μν
699:("
589:.
531:.
502:)
484:)
3869:e
3862:t
3855:v
3815:.
3811::
3803::
3776:.
3764::
3756::
3727:-
3706:.
3671:.
3667::
3634:.
3595::
3587::
3577::
3520::
3512::
3369:.
3327:.
3307::
3299::
3272:.
3266::
3258::
3208:2
3204:c
3200:m
3197:=
3194:E
3171:.
3155:2
3151:)
3142:3
3138:y
3126:3
3122:x
3118:(
3115:+
3110:2
3106:)
3097:2
3093:y
3081:2
3077:x
3073:(
3070:+
3065:2
3061:)
3052:1
3048:y
3036:1
3032:x
3028:(
3023:=
2998:2
2994:)
2988:3
2984:y
2975:3
2971:x
2967:(
2964:+
2959:2
2955:)
2949:2
2945:y
2936:2
2932:x
2928:(
2925:+
2920:2
2916:)
2910:1
2906:y
2897:1
2893:x
2889:(
2864:0
2861:=
2854:t
2843:s
2839:=
2836:t
2830:s
2806:t
2795:s
2791:=
2788:t
2782:s
2758:F
2737:)
2730:s
2726:,
2718:3
2714:y
2710:,
2702:2
2698:y
2694:,
2686:1
2682:y
2678:(
2658:)
2651:t
2647:,
2639:3
2635:x
2631:,
2623:2
2619:x
2615:,
2607:1
2603:x
2599:(
2579:F
2559:)
2556:s
2553:,
2548:3
2544:y
2540:,
2535:2
2531:y
2527:,
2522:1
2518:y
2514:(
2494:)
2491:t
2488:,
2483:3
2479:x
2475:,
2470:2
2466:x
2462:,
2457:1
2453:x
2449:(
2439:B
2435:A
2407:c
2386:g
2377:g
2373:M
2354:B
2350:A
2331:2
2327:)
2318:3
2314:y
2302:3
2298:x
2294:(
2286:2
2282:)
2273:2
2269:y
2257:2
2253:x
2249:(
2241:2
2237:)
2228:1
2224:y
2212:1
2208:x
2204:(
2196:2
2192:)
2184:t
2173:s
2169:(
2164:2
2160:c
2156:=
2133:2
2129:)
2123:3
2119:y
2110:3
2106:x
2102:(
2094:2
2090:)
2084:2
2080:y
2071:2
2067:x
2063:(
2055:2
2051:)
2045:1
2041:y
2032:1
2028:x
2024:(
2016:2
2012:)
2008:t
2002:s
1999:(
1994:2
1990:c
1964:c
1960:c
1952:.
1940:)
1933:t
1922:s
1918:(
1915:c
1912:=
1905:2
1901:)
1892:3
1888:y
1876:3
1872:x
1868:(
1865:+
1860:2
1856:)
1847:2
1843:y
1831:2
1827:x
1823:(
1820:+
1815:2
1811:)
1802:1
1798:y
1786:1
1782:x
1778:(
1752:)
1749:t
1743:s
1740:(
1737:c
1734:=
1727:2
1723:)
1717:3
1713:y
1704:3
1700:x
1696:(
1693:+
1688:2
1684:)
1678:2
1674:y
1665:2
1661:x
1657:(
1654:+
1649:2
1645:)
1639:1
1635:y
1626:1
1622:x
1618:(
1590:F
1569:)
1562:s
1558:,
1550:3
1546:y
1542:,
1534:2
1530:y
1526:,
1518:1
1514:y
1510:(
1490:)
1483:t
1479:,
1471:3
1467:x
1463:,
1455:2
1451:x
1447:,
1439:1
1435:x
1431:(
1411:F
1391:)
1388:s
1385:,
1380:3
1376:y
1372:,
1367:2
1363:y
1359:,
1354:1
1350:y
1346:(
1326:)
1323:t
1320:,
1315:3
1311:x
1307:,
1302:2
1298:x
1294:,
1289:1
1285:x
1281:(
1271:B
1267:A
1247:c
1241:0
1227:c
1177:)
1174:E
1171:,
1166:3
1162:p
1158:,
1153:2
1149:p
1145:,
1140:1
1136:p
1132:(
1112:)
1109:t
1106:,
1101:3
1097:x
1093:,
1088:2
1084:x
1080:,
1075:1
1071:x
1067:(
1036:)
1031:3
1027:B
1023:,
1018:2
1014:B
1010:,
1005:1
1001:B
997:,
992:3
988:E
984:,
979:2
975:E
971:,
966:1
962:E
958:(
938:)
935:E
932:,
927:3
923:p
919:,
914:2
910:p
906:,
901:1
897:p
893:(
883:M
869:)
866:t
863:,
858:3
854:x
850:,
845:2
841:x
837:,
832:1
828:x
824:(
780:M
714:g
622:c
541:c
516:c
512:c
499:c
492:.
468:"
438:e
431:t
424:v
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