403:
1893:
1585:). In special relativity its explanation is as follows: In its rest frame the interferometer can be regarded as at rest in accordance with the relativity principle, so the propagation time of light is the same in all directions. Although in a frame in which the interferometer is in motion, the transverse beam must traverse a longer, diagonal path with respect to the non-moving frame thus making its travel time longer, the factor by which the longitudinal beam would be delayed by taking times
3048:
573:
1609:) for the forward and reverse trips respectively is even longer. Therefore, in the longitudinal direction the interferometer is supposed to be contracted, in order to restore the equality of both travel times in accordance with the negative experimental result(s). Thus the two-way speed of light remains constant and the round trip propagation time along perpendicular arms of the interferometer is independent of its motion & orientation.
628:: Three blue rods are at rest in S, and three red rods in S'. At the instant when the left ends of A and D attain the same position on the axis of x, the lengths of the rods shall be compared. In S the simultaneous positions of the left side of A and the right side of C are more distant than those of D and F, while in S' the simultaneous positions of the left side of D and the right side of F are more distant than those of A and C.
42:
1677:
6623:
1534:. As the electrons in the opposite wire are moving as well, they do not contract (as much). This results in an apparent local imbalance between electrons and protons; the moving electrons in one wire are attracted to the extra protons in the other. The reverse can also be considered. To the static proton's frame of reference, the electrons are moving and contracted, resulting in the same imbalance. The electron
416:
2043:. Meanwhile the proper length of this object, as measured in its rest frame S', can be calculated by using the Lorentz transformation. Transforming the time coordinates from S into S' results in different times, but this is not problematic, since the object is at rest in S' where it does not matter when the endpoints are measured. Therefore the transformation of the spatial coordinates suffices, which gives:
622:
461:
2698:
1846:, as measured on x' and x" respectively. Let them move in opposite directions along the x* axis, considered at rest, at the same speed with respect to it. Endpoints A'A" then meet at point A*, and B'B" meet at point B*. Einstein pointed out that length A*B* is shorter than A'B' or A"B", which can also be demonstrated by bringing one of the rods to rest with respect to that axis.
3420:
4466:
3043:{\displaystyle {\begin{aligned}x_{1}^{'}&=\gamma \left(x_{1}-vt_{1}\right)&\quad \mathrm {and} \quad &&x_{2}^{'}&=\gamma \left(x_{2}-vt_{2}\right)\\t_{1}^{'}&=\gamma \left(t_{1}-vx_{1}/c^{2}\right)&\quad \mathrm {and} \quad &&t_{2}^{'}&=\gamma \left(t_{2}-vx_{2}/c^{2}\right)\end{aligned}}}
921:). It turns out that the proper length remains unchanged and always denotes the greatest length of an object, and the length of the same object measured in another inertial reference frame is shorter than the proper length. This contraction only occurs along the line of motion, and can be represented by the relation
640:
transport velocity. Now, when the synchronization process is finished, the object is moved along the clock row and every clock stores the exact time when the left or the right end of the object passes by. After that, the observer only has to look at the position of a clock A that stored the time when
1904:
Length contraction refers to measurements of position made at simultaneous times according to a coordinate system. This could suggest that if one could take a picture of a fast moving object, that the image would show the object contracted in the direction of motion. However, such visual effects are
2691:
Conversely, if the object rests in S and its proper length is known, the simultaneity of the measurements at the object's endpoints has to be considered in another frame S', as the object constantly changes its position there. Therefore, both spatial and temporal coordinates must be transformed:
464:
Wheels which travel at 9/10 the speed of light. The speed of the top of a wheel is 0.994 c while the speed of the bottom is always zero. This is why the top is contracted relative to the bottom. This animation is made with the assumption that the spokes of a wheel are much more elastic than its
5550:
besteht oder nicht, ist irrefĂŒhrend. Sie besteht nĂ€mlich nicht "wirklich", insofern sie fĂŒr einen mitbewegten
Beobachter nicht existiert; sie besteht aber "wirklich", d. h. in solcher Weise, daĂ sie prinzipiell durch physikalische Mittel nachgewiesen werden könnte, fĂŒr einen nicht mitbewegten
1565:
experimental confirmations of length contraction are hard to achieve, because (a) at the current state of technology, objects of considerable extension cannot be accelerated to relativistic speeds, and (b) the only objects traveling with the speed required are atomic particles, whose spatial
1638:
ability of electrically charged particles with large relative velocities is higher than expected. In pre-relativistic physics the ability should decrease at high velocities, because the time in which ionizing particles in motion can interact with the electrons of other atoms or molecules is
500:. Length contraction is only in the direction in which the body is travelling. For standard objects, this effect is negligible at everyday speeds, and can be ignored for all regular purposes, only becoming significant as the object approaches the speed of light relative to the observer.
2187:
465:
circumference. Otherwise there could be a rupture of the spokes or of the circumference. In the rest frame of the center of a wheel, wheels are circular and their spokes are straight and equidistant, but their circumference is contracted and exerts a pressure on the spokes.
1807:
asserted that one sees the length contraction in an objective way, according to
Lorentz, while it is "only an apparent, subjective phenomenon, caused by the manner of our clock-regulation and length-measurement", according to Einstein. Einstein published a rebuttal:
3246:
1313:
are measured parallel to the object's line of movement. For the observer in relative movement, the length of the object is measured by subtracting the simultaneously measured distances of both ends of the object. For more general conversions, see the
1556:
Any observer co-moving with the observed object cannot measure the object's contraction, because he can judge himself and the object as at rest in the same inertial frame in accordance with the principle of relativity (as it was demonstrated by the
1521:
Magnetic forces are caused by relativistic contraction when electrons are moving relative to atomic nuclei. The magnetic force on a moving charge next to a current-carrying wire is a result of relativistic motion between electrons and protons.
1616:' extremely short lifespan shouldn't allow them to make the trip to the surface, even at the speed of light, but they do nonetheless. From the Earth reference frame, however, this is made possible only by the muon's time being slowed down by
1662:
is generated. In the proper frame of the electrons, the undulator is contracted which leads to an increased radiation frequency. Additionally, to find out the frequency as measured in the laboratory frame, one has to apply the
1905:
completely different measurements, as such a photograph is taken from a distance, while length contraction can only directly be measured at the exact location of the object's endpoints. It was shown by several authors such as
858:
destroys this equality. In the first method an observer in one frame claims to have measured the object's endpoints simultaneously, but the observers in all other inertial frames will argue that the object's endpoints were
4147:
1529:
showed that parallel wires having currents in the same direction attract one another. In the electrons' frame of reference, the moving wire contracts slightly, causing the protons of the opposite wire to be locally
1140:
1838:
definitions concerning the way clock regulations and length measurements are performed. He presented the following thought experiment: Let A'B' and A"B" be the endpoints of two rods of the same proper length
1538:
is relatively very slow, on the order of a meter an hour but the force between an electron and proton is so enormous that even at this very slow speed the relativistic contraction causes significant effects.
3845:. Since, according to the principle of relativity, the magnitude of relative velocity is the same in either reference frame, the respective travel times of the clock between the rod's endpoints are given by
3185:
1747:
3115:
1363:
The principle of relativity (according to which the laws of nature are invariant across inertial reference frames) requires that length contraction is symmetrical: If a rod is at rest in an inertial frame
2356:
4977:
580:
First it is necessary to carefully consider the methods for measuring the lengths of resting and moving objects. Here, "object" simply means a distance with endpoints that are always mutually at rest,
3251:
2703:
2418:
2049:
1913:
in a
Physics Today article. For instance, for a small angular diameter, a moving sphere remains circular and is rotated. This kind of visual rotation effect is called Penrose-Terrell rotation.
6326:
3481:
2592:
1261:
976:
2518:
2536:
Likewise, according to the principle of relativity, an object that is at rest in S will also be contracted in S'. By exchanging the above signs and primes symmetrically, it follows that
1797:
2668:
1561:). So length contraction cannot be measured in the object's rest frame, but only in a frame in which the observed object is in motion. In addition, even in such a non-co-moving frame,
3643:
3415:{\displaystyle {\begin{aligned}\Delta x'&=\gamma \left(L_{0}-v\Delta t\right)&(1)\\\Delta t'&=\gamma \left(\Delta t-{\frac {vL_{0}}{c^{2}}}\right)=0&(2)\end{aligned}}}
4455:
4225:
3953:
3586:
542:
developed a model in which all forces are considered to be of electromagnetic origin, and length contraction appeared to be a direct consequence of this model. Yet it was shown by
4535:
in the direction of the boost than it was before the boost. In both cases, the transverse directions are unaffected and the three planes meeting at each corner of the cuboids are
4058:
3748:
5423:
3238:
447:
3512:
798:
759:
2276:
1318:. An observer at rest observing an object travelling very close to the speed of light would observe the length of the object in the direction of motion as very near zero.
2230:
2041:
1062:
618:
of the object can simply be determined by directly superposing a measuring rod. However, if the relative velocity is greater than zero, then one can proceed as follows:
3884:
5752:
4014:
4408:
4363:
4338:
4273:
4176:
3978:
3823:
3537:
2454:
1477:
1452:
1427:
556:(1905) is credited with removing the ad hoc character from the contraction hypothesis, by deriving this contraction from his postulates instead of experimental data.
3778:
3686:
1981:
1954:
1631:â and in fact, the results obtained from particle collisions can only be explained when the increased nucleon density due to length contraction is considered.
1311:
1031:
908:
848:
700:
616:
546:(1905) that electromagnetic forces alone cannot explain the electron's stability. So he had to introduce another ad hoc hypothesis: non-electric binding forces (
4383:
4313:
4293:
4248:
3904:
3843:
3798:
3706:
2001:
1497:
1402:
1382:
1284:
1184:
1162:
1002:
881:
821:
720:
663:
6373:
1667:. So, only with the aid of length contraction and the relativistic Doppler effect, the extremely small wavelength of undulator radiation can be explained.
6608:
6397:
6143:
1073:
440:
550:) that ensure the electron's stability, give a dynamical explanation for length contraction, and thus hide the motion of the stationary aether.
538:, because at this time there was no sufficient reason to assume that intermolecular forces behave the same way as electromagnetic ones. In 1897
6179:
6133:
402:
6317:
5655:
4869:
5801:
530:). Although both FitzGerald and Lorentz alluded to the fact that electrostatic fields in motion were deformed ("Heaviside-Ellipsoid" after
1820:
exists or not is misleading. It doesn't "really" exist, in so far as it doesn't exist for a comoving observer; though it "really" exists,
722:
as measured by clocks in the rod's rest frame. The length of the rod can be computed by multiplying its travel time by its velocity, thus
41:
4066:
433:
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5427:
6054:
5737:
61:
6059:
5700:
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5276:
5240:
5191:
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5133:
5107:
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1862:. However, those paradoxes can be solved by a correct application of the relativity of simultaneity. Another famous paradox is the
1643:
in frames in which the ionizing particles are moving, which increases their electrical field strength normal to the line of motion.
1582:
6379:
3120:
81:
1909:
and James
Terrell that moving objects generally do not appear length contracted on a photograph. This result was popularized by
1578:
523:
6092:
3056:
5690:
1639:
diminished; however, in relativity, the higher-than-expected ionization ability can be explained by length contraction of the
1627:
that are spherical when at rest should assume the form of "pancakes" or flat disks when traveling nearly at the speed of light
1558:
6195:
6273:
6336:
2182:{\displaystyle x'_{1}=\gamma \left(x_{1}-vt_{1}\right)\quad {\text{and}}\quad x'_{2}=\gamma \left(x_{2}-vt_{2}\right)\ \ .}
6626:
6368:
6203:
5449:
5232:
1516:
1355:), the length is still 99%. As the magnitude of the velocity approaches the speed of light, the effect becomes prominent.
509:
258:
5386:
Williams, E. J. (1931), "The Loss of Energy by ÎČ -Particles and Its
Distribution between Different Kinds of Collisions",
6190:
5002:
588:. If the relative velocity between an observer (or his measuring instruments) and the observed object is zero, then the
5950:
803:
In
Newtonian mechanics, simultaneity and time duration are absolute and therefore both methods lead to the equality of
138:
6645:
6231:
5965:
3431:
1664:
1551:
585:
420:
148:
86:
1859:
163:
1198:
927:
6518:
5960:
5913:
5717:
2366:
2281:
851:
666:
632:
The observer installs a row of clocks that either are synchronized a) by exchanging light signals according to the
143:
133:
6548:
6174:
5855:
1752:
515:
493:
325:
2544:
1620:. However, in the muon's frame, the effect is explained by the atmosphere being contracted, shortening the trip.
1542:
This effect also applies to magnetic particles without current, with current being replaced with electron spin.
6655:
6573:
6123:
5883:
5794:
2003:
is measured, according to the above conventions, by determining the simultaneous positions of its endpoints at
633:
560:
gave the geometrical interpretation of all relativistic effects by introducing his concept of four-dimensional
6302:
6224:
2464:
1892:
1526:
1577:
It was the negative result of a famous experiment, that required the introduction of length contraction: the
641:
the left end of the object was passing by, and a clock B at which the right end of the object was passing by
636:, or b) by "slow clock transport", that is, one clock is transported along the row of clocks in the limit of
5844:
5835:
1315:
277:
51:
6391:
6297:
2618:
576:
In special relativity, the observer measures events against an infinite latticework of synchronized clocks.
6528:
6255:
5929:
5893:
3714:
1875:
914:
519:
101:
96:
4946:
4590:
in euclidean geometry. Indeed, special relativity largely comes down to studying a kind of noneuclidean
3598:
6533:
6138:
6077:
4575:
4559:
4555:
1659:
3190:
1687:
4416:
4184:
3545:
1854:
Due to superficial application of the contraction formula, some paradoxes can occur. Examples are the
1824:
in such a way that it could be demonstrated in principle by physical means by a non-comoving observer.
6438:
6364:
6208:
5810:
5774:
5612:
5577:
5495:
Albert
Einstein's special theory of relativity. Emergence (1905) and early interpretation (1905â1911)
5395:
5352:
5313:
5264:
5017:
4903:
4738:
4571:
1897:
850:. Yet in relativity theory the constancy of light velocity in all inertial frames in connection with
547:
527:
222:
56:
5671:
764:
725:
6513:
6508:
6503:
6498:
6330:
6279:
6097:
6082:
5908:
5839:
5787:
5770:
5563:"Brightness and color of rapidly moving objects: The visual appearance of a large sphere revisited"
4563:
2235:
1804:
1651:
315:
272:
6402:
5562:
3708:). Time dilation was experimentally confirmed multiple times, and is represented by the relation:
572:
6578:
6478:
6260:
6241:
6235:
6186:
6128:
6037:
5873:
5850:
5818:
5628:
5368:
5342:
4927:
3909:
2195:
2006:
1681:
1503:, because the Lorentz transformation geometrically corresponds to a rotation in four-dimensional
637:
33:
5524:
Einstein, Albert (1911). "Zum
Ehrenfestschen Paradoxon. Eine Bemerkung zu V. VariÄaks Aufsatz".
5498:
5490:
4019:
1038:
5158:
3848:
3489:
6588:
6458:
6420:
6412:
6013:
5970:
5746:
5733:
5696:
5651:
5502:
5272:
5236:
5187:
5162:
5129:
5103:
4982:
4919:
4876:
4865:
4551:
3983:
1863:
1500:
557:
543:
535:
380:
345:
340:
310:
197:
168:
158:
153:
17:
4578:(preserve the origin). Lorentz transformations play the same role in Minkowski geometry (the
2439:
6553:
6493:
6483:
6430:
6407:
5985:
5620:
5585:
5403:
5360:
5025:
4911:
1910:
1887:
1640:
531:
350:
320:
3756:
3664:
1959:
1932:
1289:
1009:
913:
The deviation between the measurements in all inertial frames is given by the formulas for
886:
826:
678:
594:
6650:
6568:
6543:
6468:
6463:
6346:
6307:
6269:
6213:
6087:
6023:
1896:
Formula on a wall in Leiden, Netherlands. Lorentz was chair of theoretical physics at the
553:
534:, who derived this deformation from electromagnetic theory in 1888), it was considered an
489:
335:
330:
305:
282:
192:
6351:
1834:
Einstein also argued in that paper, that length contraction is not simply the product of
5616:
5581:
5399:
5356:
5268:
5021:
4907:
4473:
Additional geometrical considerations show that length contraction can be regarded as a
4388:
4343:
4318:
4253:
4156:
3958:
3803:
3517:
1457:
1432:
1407:
6593:
6265:
6249:
6245:
6148:
6118:
5975:
5878:
5721:
5151:
5123:
5096:
4728:
4567:
4368:
4298:
4278:
4233:
3889:
3828:
3783:
3691:
1986:
1855:
1535:
1482:
1387:
1367:
1269:
1169:
1147:
1066:
987:
866:
806:
705:
648:
497:
407:
375:
236:
91:
4523:
of a moving thin plate in
Minkowski spacetime (with one spatial dimension suppressed)
6639:
6583:
6563:
6558:
6473:
6341:
6169:
6113:
5945:
5898:
5207:
5070:
4945:
4579:
3655:
1906:
1871:
1617:
855:
589:
539:
473:
241:
123:
5632:
5473:
5372:
4931:
4890:
6603:
6523:
6488:
6018:
5980:
5725:
5036:
4972:
4591:
1676:
472:
is the phenomenon that a moving object's length is measured to be shorter than its
460:
370:
4915:
2610:
Thus an object at rest in S, when measured in S', will have the contracted length
2436:
Therefore the object's length, measured in the frame S, is contracted by a factor
621:
4859:
6387:
6356:
5903:
5603:
Weisskopf, Victor F. (1960). "The visual appearance of rapidly moving objects".
4733:
3659:
3592:
Likewise, the same method gives a symmetric result for an object at rest in S':
1812:
The author unjustifiably stated a difference of
Lorentz's view and that of mine
1647:
673:
355:
231:
1983:
denote the endpoints of an object in motion. In this frame the object's length
6598:
6164:
6008:
6003:
5364:
4060:. By inserting the time dilation formula, the ratio between those lengths is:
1867:
1635:
1612:
Given the thickness of the atmosphere as measured in Earth's reference frame,
477:
385:
365:
207:
202:
5030:
4519:
in the direction of the rotation than it was before the rotation. Right: the
5995:
5771:
Can You See the LorentzâFitzgerald Contraction? Or: Penrose-Terrell Rotation
1655:
1504:
561:
183:
5408:
4923:
4497:. In the latter case, however, we can interpret the boosted cuboid as the
1192:
Replacing the Lorentz factor in the original formula leads to the relation
5051:
6538:
5888:
5091:
4587:
3688:) is lower with respect to two synchronized "resting" clocks (indicating
3658:, according to which the rate of a single "moving" clock (indicating its
360:
5347:
910:
are not equal due to time dilation, resulting in different lengths too.
27:
Contraction of length in the direction of propagation in Minkowski space
1566:
extensions are too small to allow a direct measurement of contraction.
702:, which is traveling from one endpoint of the rod to the other in time
5624:
5292:
5226:
5184:
Understanding Relativity: a simplified approach to Einstein's theories
4558:
which can be characterized as the transformations between alternative
4489:(see left half figure at the right). This is the Euclidean analog of
1874:, and showing that for a co-rotating observer the geometry is in fact
1004:
is the length observed by an observer in motion relative to the object
6218:
4478:
5589:
5235:. Vol. 2 (Fourth ed.). Oxford UK: Butterworth-Heinemann.
4574:). Lorentz transformations are Poincaré transformations which are
4142:{\displaystyle {\frac {L'}{L_{0}}}={\frac {T'_{0}v}{Tv}}=1/\gamma }
1164:
is the relative velocity between the observer and the moving object
1135:{\displaystyle \gamma (v)\equiv {\frac {1}{\sqrt {1-v^{2}/c^{2}}}}}
4889:
1891:
1338:) contracted length is 99.9% of the length at rest; at a speed of
620:
571:
496:) and is usually only noticeable at a substantial fraction of the
459:
5157:(Reprint of 1968 ed.). Courier Dover Publications. pp.
1870:
is not compatible with relativity, reducing the applicability of
1033:
is the proper length (the length of the object in its rest frame)
6199:
5534:; Original: Der Verfasser hat mit Unrecht einen Unterschied der
5208:"The Feynman Lectures on Physics Vol. II Ch. 13: Magnetostatics"
4465:
1613:
5783:
4978:
Subtle is the Lord: The Science and the Life of Albert Einstein
5424:"What is SR, how is it generated and what are its properties?"
1624:
5779:
4594:
in Minkowski spacetime, as suggested by the following table:
4586:
of the self-isometries of the spacetime) which are played by
4230:
So since the clock's travel time across the rod is longer in
3166:
3148:
3102:
3084:
3180:{\displaystyle \Delta t'=t_{2}^{\prime }-t_{1}^{\prime }=0}
665:
of the moving object. Using this method, the definition of
1749:
are moving with 0.6c in opposite directions, resulting in
3110:{\displaystyle \Delta x'=x_{2}^{\prime }-x_{1}^{\prime }}
5450:"FLASH The Free-Electron Laser in Hamburg (PDF 7,8 MB)"
4947:"The Relative Motion of the Earth and the Aether"
4477:
phenomenon, with analogy to parallel slices through a
1573:
confirmations of this effect in a non-co-moving frame:
669:
is crucial for measuring the length of moving objects.
526:
and to rescue the hypothesis of the stationary aether (
5050:
476:, which is the length as measured in the object's own
5125:
Spacetime Physics: Introduction to Special Relativity
4419:
4391:
4371:
4346:
4321:
4301:
4281:
4256:
4236:
4187:
4159:
4069:
4022:
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3912:
3892:
3851:
3831:
3806:
3786:
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3717:
3694:
3667:
3601:
3548:
3520:
3492:
3434:
3249:
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3123:
3059:
2701:
2621:
2547:
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2369:
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2198:
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2009:
1989:
1962:
1935:
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1201:
1172:
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1012:
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889:
869:
863:
measured simultaneously. In the second method, times
829:
809:
767:
728:
708:
681:
651:
597:
5388:
Proceedings of the Royal Society of London. Series A
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6288:
6157:
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6068:
6047:
6036:
5994:
5938:
5922:
5864:
5828:
5817:
5692:
Classical Mechanics: Point Particles and Relativity
1921:Length contraction can be derived in several ways:
5186:. University of California Press. pp. 151ff.
5150:
5095:
4864:(2nd ed.). Academic Press. pp. 106â108.
4449:
4402:
4377:
4357:
4332:
4307:
4287:
4267:
4242:
4219:
4170:
4141:
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3947:
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3742:
3700:
3680:
3637:
3580:
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3506:
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3414:
3232:
3179:
3117:as well as assuming simultaneous time measurement
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2512:
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2412:
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2270:
2224:
2181:
2035:
1995:
1975:
1948:
1791:
1741:
1499:. This can be vividly illustrated using symmetric
1491:
1471:
1446:
1421:
1396:
1376:
1305:
1278:
1255:
1178:
1156:
1134:
1056:
1025:
996:
970:
902:
875:
842:
815:
792:
753:
714:
694:
657:
610:
5672:"Can You See the LorentzâFitzgerald Contraction?"
5333:Hands, Simon (2001). "The phase diagram of QCD".
645:. It's clear that distance AB is equal to length
5122:Edwin F. Taylor; John Archibald Wheeler (1992).
3486:which, when plugged into (1), demonstrates that
3476:{\displaystyle \Delta t={\frac {vL_{0}}{c^{2}}}}
1816:. The question as to whether length contraction
672:Another method is to use a clock indicating its
1810:
1684:on length contraction. Two rods of rest length
1654:, relativistic electrons were injected into an
1256:{\displaystyle L=L_{0}{\sqrt {1-v^{2}/c^{2}}}}
971:{\displaystyle L={\frac {1}{\gamma (v)}}L_{0}}
522:(1892) to explain the negative outcome of the
5795:
2413:{\displaystyle L_{0}^{'}=L\cdot \gamma \ \ .}
2351:{\displaystyle L_{0}^{'}=x_{2}^{'}-x_{1}^{'}}
441:
8:
5751:: CS1 maint: multiple names: authors list (
5519:
5517:
5069:Various English translations on Wikisource:
4891:"The Ether and the Earth's Atmosphere"
4858:Dalarsson, Mirjana; Dalarsson, Nils (2015).
4469:Cuboids in Euclidean and Minkowski spacetime
3654:Length contraction can also be derived from
5650:. London: Vintage Books. pp. 430â431.
1792:{\displaystyle A^{\ast }B^{\ast }<L_{0}}
6044:
5825:
5802:
5788:
5780:
5540:mit Bezug auf die physikalischen Tatsachen
4365:). Likewise, if the clock were at rest in
2587:{\displaystyle L_{0}=L'\cdot \gamma \ \ .}
448:
434:
29:
5407:
5346:
5259:Sexl, Roman; Schmidt, Herbert K. (1979),
5029:
4439:
4430:
4418:
4390:
4370:
4345:
4320:
4300:
4280:
4255:
4235:
4209:
4203:
4186:
4158:
4131:
4102:
4095:
4084:
4070:
4068:
4038:
4021:
3991:
3985:
3960:
3937:
3917:
3911:
3891:
3868:
3862:
3850:
3830:
3805:
3785:
3764:
3758:
3728:
3716:
3693:
3672:
3666:
3627:
3617:
3612:
3600:
3570:
3564:
3547:
3519:
3491:
3465:
3454:
3444:
3433:
3378:
3367:
3357:
3284:
3250:
3248:
3224:
3211:
3198:
3192:
3165:
3160:
3147:
3142:
3122:
3101:
3096:
3083:
3078:
3058:
3025:
3016:
3010:
2994:
2965:
2960:
2941:
2927:
2918:
2912:
2896:
2867:
2862:
2843:
2827:
2798:
2793:
2774:
2760:
2744:
2715:
2710:
2702:
2700:
2643:
2637:
2620:
2552:
2546:
2493:
2483:
2478:
2466:
2441:
2379:
2374:
2368:
2338:
2333:
2316:
2311:
2294:
2289:
2283:
2262:
2249:
2237:
2216:
2203:
2197:
2159:
2143:
2119:
2109:
2097:
2081:
2057:
2051:
2027:
2014:
2008:
1988:
1967:
1961:
1940:
1934:
1783:
1770:
1760:
1754:
1733:
1689:
1484:
1459:
1434:
1409:
1389:
1369:
1297:
1291:
1271:
1245:
1236:
1230:
1218:
1212:
1200:
1171:
1149:
1123:
1114:
1108:
1092:
1075:
1040:
1017:
1011:
989:
962:
937:
929:
894:
888:
868:
834:
828:
808:
778:
766:
733:
727:
707:
686:
680:
650:
602:
596:
528:LorentzâFitzGerald contraction hypothesis
5732:, John Wiley & Son, pp. 1032f,
4596:
4464:
2513:{\displaystyle L=L_{0}^{'}/\gamma \ \ .}
1675:
5730:Fundamentals of Physics, Chapters 33-37
5254:
5252:
4850:
4566:corresponding to alternative states of
3825:are moving along each other with speed
32:
5744:
5086:
5084:
5082:
4967:
4965:
4295:), the rod's length is also longer in
2358:, the proper length in S' is given by
1929:In an inertial reference frame S, let
5312:Manuel Calderon de la Barca Sanchez.
4981:, New York: Oxford University Press,
4511:in three-dimensional euclidean space
2663:{\displaystyle L'=L_{0}/\gamma \ \ .}
1680:Minkowski diagram of Einstein's 1911
514:Length contraction was postulated by
7:
5497:, Reading: AddisonâWesley, pp.
5003:"Zur Elektrodynamik bewegter Körper"
3743:{\displaystyle T=T_{0}\cdot \gamma }
2612:
2538:
2458:
2360:
6374:TolmanâOppenheimerâVolkoff equation
6327:FriedmannâLemaĂźtreâRobertsonâWalker
5314:"Relativistic heavy ion collisions"
4888:FitzGerald, George Francis (1889),
3638:{\displaystyle L=L_{0}^{'}/\gamma }
3187:, and by plugging in proper length
1866:, which proves that the concept of
5538:schen Auffassung von der meinigen
4861:Tensors, Relativity, and Cosmology
4153:Therefore, the length measured in
3493:
3435:
3348:
3322:
3296:
3254:
3124:
3060:
2948:
2945:
2942:
2781:
2778:
2775:
25:
6144:HamiltonâJacobiâEinstein equation
5225:E M Lifshitz, L D Landau (1980).
4410:, the above procedure would give
3233:{\displaystyle L_{0}=x_{2}-x_{1}}
1742:{\displaystyle A'B'=A''B''=L_{0}}
634:PoincarĂ©âEinstein synchronization
6622:
6621:
5291:Brookhaven National Laboratory.
4944:Lorentz, Hendrik Antoon (1892),
4450:{\displaystyle L=L'_{0}/\gamma }
4220:{\displaystyle L'=L_{0}/\gamma }
3581:{\displaystyle L'=L_{0}/\gamma }
1479:and its length is contracted in
1404:and its length is contracted in
415:
414:
401:
40:
5212:www.feynmanlectures.caltech.edu
5098:Einstein's Theory of Relativity
3753:Suppose a rod of proper length
2952:
2940:
2785:
2773:
2114:
2108:
918:
584:, that are at rest in the same
5951:Massâenergy equivalence (E=mc)
4660:Non-degenerate but indefinite
4543:at right, and in the sense of
3514:becomes the contracted length
3405:
3399:
3315:
3309:
1454:, it has its proper length in
1384:, it has its proper length in
1086:
1080:
1051:
1045:
952:
946:
793:{\displaystyle L=T_{0}\cdot v}
754:{\displaystyle L_{0}=T\cdot v}
486:LorentzâFitzGerald contraction
18:LorentzâFitzGerald contraction
1:
5542:statuiert. Die Frage, ob die
5233:Course of Theoretical Physics
5228:The classical theory of ields
4916:10.1126/science.ns-13.328.390
4570:(and different choices of an
2271:{\displaystyle L=x_{2}-x_{1}}
1814:concerning the physical facts
1672:Reality of length contraction
1517:Relativistic electromagnetism
1429:. However, if a rod rests in
510:History of special relativity
4952:Zittingsverlag Akad. V. Wet.
1583:KennedyâThorndike experiment
5966:Relativistic Doppler effect
5570:American Journal of Physics
5128:. New York: W. H. Freeman.
5049:Minkowski, Hermann (1909),
4598:Three plane trigonometries
4560:Cartesian coordinate charts
3948:{\displaystyle T'_{0}=L'/v}
2225:{\displaystyle t_{1}=t_{2}}
2036:{\displaystyle t_{1}=t_{2}}
1665:relativistic Doppler effect
1579:MichelsonâMorley experiment
1552:Tests of special relativity
800:in the clock's rest frame.
761:in the rod's rest frame or
586:inertial frame of reference
524:MichelsonâMorley experiment
149:Relativistic Doppler effect
87:Inertial frame of reference
6672:
6437:In computational physics:
5961:Relativity of simultaneity
5001:Einstein, Albert (1905a),
4461:Geometrical considerations
4053:{\displaystyle L'=T'_{0}v}
3053:Computing length interval
1885:
1559:TroutonâRankine experiment
1549:
1546:Experimental verifications
1514:
1057:{\displaystyle \gamma (v)}
852:relativity of simultaneity
507:
144:Relativity of simultaneity
6619:
6274:LenseâThirring precession
5856:Doubly special relativity
5526:Physikalische Zeitschrift
5365:10.1080/00107510110063843
5149:Albert Shadowitz (1988).
5057:Physikalische Zeitschrift
4759:Spacetime interpretation
3879:{\displaystyle T=L_{0}/v}
3507:{\displaystyle \Delta x'}
494:George Francis FitzGerald
6134:Post-Newtonian formalism
6124:Einstein field equations
6060:Mathematical formulation
5884:Hyperbolic orthogonality
5263:, Braunschweig: Vieweg,
5031:10.1002/andp.19053221004
4552:Poincaré transformations
4009:{\displaystyle L_{0}=Tv}
1860:Bell's spaceship paradox
164:Bell's spaceship paradox
5845:Galilean transformation
5836:Principle of relativity
5707:; Equations 31.4 â 31.6
5689:Walter Greiner (2006).
5646:Penrose, Roger (2005).
5478:– via Wikisource.
4550:In special relativity,
4531:. The cross section is
4515:. The cross section is
4340:(length contraction in
3800:and a clock at rest in
2449:{\displaystyle \gamma }
1332:(30 million mph, 0.0447
1316:Lorentz transformations
917:and time dilation (see
278:Galilean transformation
139:Massâenergy equivalence
52:Principle of relativity
5930:Lorentz transformation
5491:"VariÄak and Einstein"
5475:On Ehrenfest's Paradox
5409:10.1098/rspa.1931.0008
5102:, Dover Publications,
4576:linear transformations
4556:affine transformations
4470:
4451:
4404:
4379:
4359:
4334:
4309:
4289:
4269:
4244:
4221:
4172:
4143:
4054:
4010:
3974:
3949:
3900:
3880:
3839:
3819:
3794:
3774:
3744:
3702:
3682:
3639:
3582:
3533:
3508:
3477:
3416:
3234:
3181:
3111:
3044:
2664:
2588:
2514:
2450:
2414:
2352:
2272:
2226:
2183:
2037:
1997:
1977:
1950:
1901:
1832:
1800:
1793:
1743:
1493:
1473:
1448:
1423:
1398:
1378:
1349:(95 million mph, 0.141
1307:
1280:
1266:In this equation both
1257:
1180:
1158:
1136:
1058:
1027:
998:
972:
915:Lorentz transformation
904:
877:
844:
817:
794:
755:
716:
696:
659:
629:
612:
577:
520:Hendrik Antoon Lorentz
480:. It is also known as
466:
102:Lorentz transformation
6398:WeylâLewisâPapapetrou
6139:Raychaudhuri equation
6078:Equivalence principle
5775:The Barn and the Pole
5489:Miller, A.I. (1981),
5448:DESY photon science.
5422:DESY photon science.
5293:"The Physics of RHIC"
5261:Raum-Zeit-RelativitÀt
5052:"Raum und Zeit"
4739:Split-complex numbers
4468:
4452:
4405:
4380:
4360:
4335:
4310:
4290:
4270:
4245:
4222:
4173:
4144:
4055:
4011:
3975:
3950:
3901:
3881:
3840:
3820:
3795:
3775:
3773:{\displaystyle L_{0}}
3745:
3703:
3683:
3681:{\displaystyle T_{0}}
3640:
3583:
3534:
3509:
3478:
3417:
3235:
3182:
3112:
3045:
2665:
2589:
2515:
2451:
2415:
2353:
2273:
2227:
2184:
2038:
1998:
1978:
1976:{\displaystyle x_{2}}
1951:
1949:{\displaystyle x_{1}}
1895:
1829:Albert Einstein, 1911
1794:
1744:
1679:
1660:synchrotron radiation
1494:
1474:
1449:
1424:
1399:
1379:
1308:
1306:{\displaystyle L_{0}}
1281:
1258:
1186:is the speed of light
1181:
1159:
1137:
1059:
1028:
1026:{\displaystyle L_{0}}
999:
973:
905:
903:{\displaystyle T_{0}}
878:
845:
843:{\displaystyle L_{0}}
818:
795:
756:
717:
697:
695:{\displaystyle T_{0}}
660:
624:
613:
611:{\displaystyle L_{0}}
575:
463:
82:Einstein's postulates
6439:Numerical relativity
6280:pulsar timing arrays
5335:Contemporary Physics
5182:Leo Sartori (1996).
4768:Minkowski spacetime
4417:
4389:
4369:
4344:
4319:
4299:
4279:
4254:
4234:
4185:
4157:
4067:
4020:
3984:
3959:
3910:
3890:
3849:
3829:
3804:
3784:
3757:
3715:
3692:
3665:
3599:
3546:
3518:
3490:
3432:
3247:
3191:
3121:
3057:
2699:
2619:
2545:
2465:
2440:
2367:
2282:
2236:
2196:
2050:
2007:
1987:
1960:
1933:
1898:University of Leiden
1753:
1688:
1652:free-electron lasers
1581:(and later also the
1483:
1458:
1433:
1408:
1388:
1368:
1321:Then, at a speed of
1290:
1270:
1199:
1170:
1148:
1074:
1039:
1010:
988:
928:
887:
867:
827:
807:
765:
726:
706:
679:
649:
595:
57:Theory of relativity
6331:Friedmann equations
6225:HulseâTaylor binary
6187:Gravitational waves
6083:Riemannian geometry
5909:Proper acceleration
5894:Maxwell's equations
5840:Galilean relativity
5648:The Road to Reality
5617:1960PhT....13i..24W
5582:2000AmJPh..68...56K
5472:VariÄak, Vladimir.
5400:1931RSPSA.130..328W
5357:2001ConPh..42..209H
5269:1979raum.book.....S
5037:English translation
5022:1905AnP...322..891E
4908:1889Sci....13..390F
4877:Extract of page 106
4838:csch Ï = v (1 â v)
4810:sinh Ï = v (1 â v)
4765:Newtonian spacetime
4599:
4564:Minkowski spacetime
4537:mutually orthogonal
4501:of a moving plate.
4481:before and after a
4438:
4110:
4046:
3925:
3650:Using time dilation
3626:
3425:Equation (2) gives
3170:
3152:
3106:
3088:
2974:
2876:
2807:
2724:
2687:Known proper length
2492:
2388:
2347:
2325:
2303:
2127:
2065:
1925:Known moving length
1569:However, there are
568:Basis in relativity
482:Lorentz contraction
273:Galilean relativity
193:Minkowski spacetime
97:Maxwell's equations
6646:Special relativity
6380:ReissnerâNordström
6298:BransâDicke theory
6129:Linearized gravity
5956:Length contraction
5874:Frame of reference
5851:Special relativity
5561:Kraus, U. (2000).
5153:Special relativity
5010:Annalen der Physik
4617:Kleinian Geometry
4597:
4471:
4447:
4426:
4403:{\displaystyle S'}
4400:
4375:
4358:{\displaystyle S'}
4355:
4333:{\displaystyle S'}
4330:
4305:
4285:
4275:(time dilation in
4268:{\displaystyle S'}
4265:
4240:
4217:
4171:{\displaystyle S'}
4168:
4139:
4098:
4050:
4034:
4006:
3973:{\displaystyle S'}
3970:
3945:
3913:
3896:
3876:
3835:
3818:{\displaystyle S'}
3815:
3790:
3770:
3740:
3698:
3678:
3635:
3608:
3578:
3532:{\displaystyle L'}
3529:
3504:
3473:
3412:
3410:
3230:
3177:
3156:
3138:
3107:
3092:
3074:
3040:
3038:
2956:
2858:
2789:
2706:
2660:
2584:
2510:
2474:
2446:
2410:
2370:
2348:
2329:
2307:
2285:
2268:
2222:
2179:
2115:
2053:
2033:
1993:
1973:
1946:
1902:
1801:
1789:
1739:
1682:thought experiment
1527:André-Marie AmpÚre
1501:Minkowski diagrams
1489:
1472:{\displaystyle S'}
1469:
1447:{\displaystyle S'}
1444:
1422:{\displaystyle S'}
1419:
1394:
1374:
1303:
1276:
1253:
1176:
1154:
1132:
1054:
1023:
994:
968:
900:
873:
840:
813:
790:
751:
712:
692:
655:
630:
626:Length contraction
608:
578:
470:Length contraction
467:
408:Physics portal
129:Length contraction
34:Special relativity
6633:
6632:
6447:
6446:
6426:OzsvĂĄthâSchĂŒcking
6032:
6031:
6014:Minkowski diagram
5971:Thomas precession
5914:Relativistic mass
5657:978-0-09-944068-0
5625:10.1063/1.3057105
4871:978-0-12-803401-9
4842:
4841:
4832:csc Ï = m (1 + m)
4824:sech Ï = (1 â v)
4804:sin Ï = m (1 + m)
4796:cosh Ï = (1 â v)
4711:Type of isotropy
4654:Positive definite
4539:(in the sense of
4378:{\displaystyle S}
4308:{\displaystyle S}
4288:{\displaystyle S}
4243:{\displaystyle S}
4123:
4090:
3899:{\displaystyle S}
3838:{\displaystyle v}
3793:{\displaystyle S}
3701:{\displaystyle T}
3471:
3384:
2684:
2683:
2656:
2653:
2608:
2607:
2580:
2577:
2534:
2533:
2506:
2503:
2434:
2433:
2406:
2403:
2232:, and by setting
2175:
2172:
2112:
1996:{\displaystyle L}
1864:Ehrenfest paradox
1492:{\displaystyle S}
1397:{\displaystyle S}
1377:{\displaystyle S}
1279:{\displaystyle L}
1251:
1179:{\displaystyle c}
1157:{\displaystyle v}
1130:
1129:
997:{\displaystyle L}
956:
876:{\displaystyle T}
816:{\displaystyle L}
715:{\displaystyle T}
658:{\displaystyle L}
558:Hermann Minkowski
548:Poincaré stresses
536:ad hoc hypothesis
516:George FitzGerald
458:
457:
198:Spacetime diagram
169:Ehrenfest paradox
159:Relativistic disk
154:Thomas precession
134:Relativistic mass
16:(Redirected from
6663:
6625:
6624:
6408:van Stockum dust
6180:Two-body problem
6098:Mach's principle
6045:
5986:Terrell rotation
5826:
5804:
5797:
5790:
5781:
5757:
5756:
5750:
5742:
5714:
5708:
5706:
5686:
5680:
5679:
5668:
5662:
5661:
5643:
5637:
5636:
5600:
5594:
5593:
5567:
5558:
5552:
5533:
5521:
5512:
5511:
5486:
5480:
5479:
5469:
5463:
5462:
5460:
5459:
5454:
5445:
5439:
5438:
5436:
5435:
5426:. Archived from
5419:
5413:
5412:
5411:
5394:(813): 328â346,
5383:
5377:
5376:
5350:
5330:
5324:
5323:
5321:
5320:
5309:
5303:
5302:
5300:
5299:
5288:
5282:
5281:
5256:
5247:
5246:
5222:
5216:
5215:
5204:
5198:
5197:
5179:
5173:
5172:
5156:
5146:
5140:
5139:
5119:
5113:
5112:
5101:
5088:
5077:
5064:
5054:
5046:
5040:
5034:
5033:
5007:
4998:
4992:
4991:
4969:
4960:
4959:
4949:
4941:
4935:
4934:
4893:
4885:
4879:
4875:
4855:
4626:Minkowski plane
4600:
4456:
4454:
4453:
4448:
4443:
4434:
4409:
4407:
4406:
4401:
4399:
4384:
4382:
4381:
4376:
4364:
4362:
4361:
4356:
4354:
4339:
4337:
4336:
4331:
4329:
4314:
4312:
4311:
4306:
4294:
4292:
4291:
4286:
4274:
4272:
4271:
4266:
4264:
4249:
4247:
4246:
4241:
4226:
4224:
4223:
4218:
4213:
4208:
4207:
4195:
4177:
4175:
4174:
4169:
4167:
4148:
4146:
4145:
4140:
4135:
4124:
4122:
4114:
4106:
4096:
4091:
4089:
4088:
4079:
4071:
4059:
4057:
4056:
4051:
4042:
4030:
4015:
4013:
4012:
4007:
3996:
3995:
3979:
3977:
3976:
3971:
3969:
3954:
3952:
3951:
3946:
3941:
3936:
3921:
3905:
3903:
3902:
3897:
3885:
3883:
3882:
3877:
3872:
3867:
3866:
3844:
3842:
3841:
3836:
3824:
3822:
3821:
3816:
3814:
3799:
3797:
3796:
3791:
3779:
3777:
3776:
3771:
3769:
3768:
3749:
3747:
3746:
3741:
3733:
3732:
3707:
3705:
3704:
3699:
3687:
3685:
3684:
3679:
3677:
3676:
3644:
3642:
3641:
3636:
3631:
3625:
3624:
3616:
3587:
3585:
3584:
3579:
3574:
3569:
3568:
3556:
3538:
3536:
3535:
3530:
3528:
3513:
3511:
3510:
3505:
3503:
3482:
3480:
3479:
3474:
3472:
3470:
3469:
3460:
3459:
3458:
3445:
3421:
3419:
3418:
3413:
3411:
3390:
3386:
3385:
3383:
3382:
3373:
3372:
3371:
3358:
3332:
3306:
3302:
3289:
3288:
3264:
3239:
3237:
3236:
3231:
3229:
3228:
3216:
3215:
3203:
3202:
3186:
3184:
3183:
3178:
3169:
3164:
3151:
3146:
3134:
3116:
3114:
3113:
3108:
3105:
3100:
3087:
3082:
3070:
3049:
3047:
3046:
3041:
3039:
3035:
3031:
3030:
3029:
3020:
3015:
3014:
2999:
2998:
2973:
2972:
2964:
2954:
2951:
2937:
2933:
2932:
2931:
2922:
2917:
2916:
2901:
2900:
2875:
2874:
2866:
2853:
2849:
2848:
2847:
2832:
2831:
2806:
2805:
2797:
2787:
2784:
2770:
2766:
2765:
2764:
2749:
2748:
2723:
2722:
2714:
2678:
2669:
2667:
2666:
2661:
2654:
2651:
2647:
2642:
2641:
2629:
2613:
2602:
2593:
2591:
2590:
2585:
2578:
2575:
2568:
2557:
2556:
2539:
2528:
2519:
2517:
2516:
2511:
2504:
2501:
2497:
2491:
2490:
2482:
2459:
2455:
2453:
2452:
2447:
2428:
2419:
2417:
2416:
2411:
2404:
2401:
2387:
2386:
2378:
2361:
2357:
2355:
2354:
2349:
2346:
2345:
2337:
2324:
2323:
2315:
2302:
2301:
2293:
2277:
2275:
2274:
2269:
2267:
2266:
2254:
2253:
2231:
2229:
2228:
2223:
2221:
2220:
2208:
2207:
2188:
2186:
2185:
2180:
2173:
2170:
2169:
2165:
2164:
2163:
2148:
2147:
2123:
2113:
2110:
2107:
2103:
2102:
2101:
2086:
2085:
2061:
2042:
2040:
2039:
2034:
2032:
2031:
2019:
2018:
2002:
2000:
1999:
1994:
1982:
1980:
1979:
1974:
1972:
1971:
1955:
1953:
1952:
1947:
1945:
1944:
1911:Victor Weisskopf
1888:Terrell rotation
1830:
1805:Vladimir VariÄak
1798:
1796:
1795:
1790:
1788:
1787:
1775:
1774:
1765:
1764:
1748:
1746:
1745:
1740:
1738:
1737:
1725:
1717:
1706:
1698:
1630:
1498:
1496:
1495:
1490:
1478:
1476:
1475:
1470:
1468:
1453:
1451:
1450:
1445:
1443:
1428:
1426:
1425:
1420:
1418:
1403:
1401:
1400:
1395:
1383:
1381:
1380:
1375:
1354:
1348:
1346:
1343:
1337:
1331:
1329:
1326:
1312:
1310:
1309:
1304:
1302:
1301:
1285:
1283:
1282:
1277:
1262:
1260:
1259:
1254:
1252:
1250:
1249:
1240:
1235:
1234:
1219:
1217:
1216:
1185:
1183:
1182:
1177:
1163:
1161:
1160:
1155:
1141:
1139:
1138:
1133:
1131:
1128:
1127:
1118:
1113:
1112:
1097:
1093:
1063:
1061:
1060:
1055:
1032:
1030:
1029:
1024:
1022:
1021:
1003:
1001:
1000:
995:
977:
975:
974:
969:
967:
966:
957:
955:
938:
909:
907:
906:
901:
899:
898:
882:
880:
879:
874:
849:
847:
846:
841:
839:
838:
822:
820:
819:
814:
799:
797:
796:
791:
783:
782:
760:
758:
757:
752:
738:
737:
721:
719:
718:
713:
701:
699:
698:
693:
691:
690:
664:
662:
661:
656:
643:at the same time
617:
615:
614:
609:
607:
606:
532:Oliver Heaviside
450:
443:
436:
423:
418:
417:
410:
406:
405:
298:
225:
186:
117:
75:
44:
30:
21:
6671:
6670:
6666:
6665:
6664:
6662:
6661:
6660:
6656:Hendrik Lorentz
6636:
6635:
6634:
6629:
6615:
6443:
6347:BKL singularity
6337:LemaĂźtreâTolman
6312:
6308:Quantum gravity
6290:
6284:
6270:geodetic effect
6244:(together with
6214:LISA Pathfinder
6153:
6102:
6088:Penrose diagram
6070:
6064:
6039:
6028:
6024:Minkowski space
5990:
5934:
5918:
5866:
5860:
5820:
5813:
5808:
5766:
5761:
5760:
5743:
5740:
5716:
5715:
5711:
5703:
5688:
5687:
5683:
5670:
5669:
5665:
5658:
5645:
5644:
5640:
5602:
5601:
5597:
5590:10.1119/1.19373
5565:
5560:
5559:
5555:
5523:
5522:
5515:
5509:
5488:
5487:
5483:
5471:
5470:
5466:
5457:
5455:
5452:
5447:
5446:
5442:
5433:
5431:
5421:
5420:
5416:
5385:
5384:
5380:
5348:physics/0105022
5332:
5331:
5327:
5318:
5316:
5311:
5310:
5306:
5297:
5295:
5290:
5289:
5285:
5279:
5258:
5257:
5250:
5243:
5224:
5223:
5219:
5206:
5205:
5201:
5194:
5181:
5180:
5176:
5169:
5148:
5147:
5143:
5136:
5121:
5120:
5116:
5110:
5090:
5089:
5080:
5048:
5047:
5043:
5016:(10): 891â921,
5005:
5000:
4999:
4995:
4989:
4971:
4970:
4963:
4943:
4942:
4938:
4887:
4886:
4882:
4872:
4857:
4856:
4852:
4847:
4818:sec Ï = (1 + m)
4790:cos Ï = (1 + m)
4729:Complex numbers
4725:Algebra over R
4688:Isotropy group
4665:Isometry group
4651:Quadratic form
4620:Euclidean plane
4568:inertial motion
4554:are a class of
4463:
4415:
4414:
4392:
4387:
4386:
4385:and the rod in
4367:
4366:
4347:
4342:
4341:
4322:
4317:
4316:
4297:
4296:
4277:
4276:
4257:
4252:
4251:
4232:
4231:
4199:
4188:
4183:
4182:
4160:
4155:
4154:
4115:
4097:
4080:
4072:
4065:
4064:
4023:
4018:
4017:
3987:
3982:
3981:
3962:
3957:
3956:
3929:
3908:
3907:
3888:
3887:
3858:
3847:
3846:
3827:
3826:
3807:
3802:
3801:
3782:
3781:
3760:
3755:
3754:
3724:
3713:
3712:
3690:
3689:
3668:
3663:
3662:
3652:
3618:
3597:
3596:
3560:
3549:
3544:
3543:
3521:
3516:
3515:
3496:
3488:
3487:
3461:
3450:
3446:
3430:
3429:
3409:
3408:
3397:
3374:
3363:
3359:
3347:
3343:
3333:
3325:
3319:
3318:
3307:
3280:
3279:
3275:
3265:
3257:
3245:
3244:
3220:
3207:
3194:
3189:
3188:
3127:
3119:
3118:
3063:
3055:
3054:
3037:
3036:
3021:
3006:
2990:
2989:
2985:
2975:
2966:
2953:
2938:
2923:
2908:
2892:
2891:
2887:
2877:
2868:
2855:
2854:
2839:
2823:
2822:
2818:
2808:
2799:
2786:
2771:
2756:
2740:
2739:
2735:
2725:
2716:
2697:
2696:
2689:
2676:
2633:
2622:
2617:
2616:
2600:
2561:
2548:
2543:
2542:
2526:
2484:
2463:
2462:
2438:
2437:
2426:
2380:
2365:
2364:
2339:
2317:
2295:
2280:
2279:
2258:
2245:
2234:
2233:
2212:
2199:
2194:
2193:
2155:
2139:
2138:
2134:
2093:
2077:
2076:
2072:
2048:
2047:
2023:
2010:
2005:
2004:
1985:
1984:
1963:
1958:
1957:
1936:
1931:
1930:
1927:
1919:
1890:
1884:
1852:
1845:
1831:
1828:
1779:
1766:
1756:
1751:
1750:
1729:
1718:
1710:
1699:
1691:
1686:
1685:
1674:
1628:
1554:
1548:
1519:
1513:
1511:Magnetic forces
1481:
1480:
1461:
1456:
1455:
1436:
1431:
1430:
1411:
1406:
1405:
1386:
1385:
1366:
1365:
1361:
1350:
1344:
1341:
1339:
1333:
1327:
1324:
1322:
1293:
1288:
1287:
1268:
1267:
1241:
1226:
1208:
1197:
1196:
1168:
1167:
1146:
1145:
1119:
1104:
1072:
1071:
1037:
1036:
1013:
1008:
1007:
986:
985:
958:
942:
926:
925:
890:
885:
884:
865:
864:
830:
825:
824:
805:
804:
774:
763:
762:
729:
724:
723:
704:
703:
682:
677:
676:
647:
646:
598:
593:
592:
570:
554:Albert Einstein
512:
506:
490:Hendrik Lorentz
454:
413:
400:
399:
392:
391:
390:
300:
299:
296:
288:
287:
283:Aether theories
268:
267:
266:
247:
246:
227:
226:
221:
213:
212:
188:
187:
182:
174:
173:
119:
118:
115:
107:
106:
77:
76:
73:
28:
23:
22:
15:
12:
11:
5:
6669:
6667:
6659:
6658:
6653:
6648:
6638:
6637:
6631:
6630:
6620:
6617:
6616:
6614:
6613:
6606:
6601:
6596:
6591:
6586:
6581:
6576:
6571:
6566:
6561:
6556:
6551:
6546:
6541:
6536:
6534:Choquet-Bruhat
6531:
6526:
6521:
6516:
6511:
6506:
6501:
6496:
6491:
6486:
6481:
6476:
6471:
6466:
6461:
6455:
6453:
6449:
6448:
6445:
6444:
6442:
6441:
6434:
6433:
6428:
6423:
6416:
6415:
6410:
6405:
6400:
6395:
6386:Axisymmetric:
6383:
6382:
6377:
6371:
6360:
6359:
6354:
6349:
6344:
6339:
6334:
6325:Cosmological:
6322:
6320:
6314:
6313:
6311:
6310:
6305:
6300:
6294:
6292:
6286:
6285:
6283:
6282:
6277:
6266:frame-dragging
6263:
6258:
6253:
6250:Einstein rings
6246:Einstein cross
6239:
6228:
6227:
6222:
6216:
6211:
6206:
6193:
6183:
6182:
6177:
6172:
6167:
6161:
6159:
6155:
6154:
6152:
6151:
6149:Ernst equation
6146:
6141:
6136:
6131:
6126:
6121:
6119:BSSN formalism
6116:
6110:
6108:
6104:
6103:
6101:
6100:
6095:
6090:
6085:
6080:
6074:
6072:
6066:
6065:
6063:
6062:
6057:
6051:
6049:
6042:
6034:
6033:
6030:
6029:
6027:
6026:
6021:
6016:
6011:
6006:
6000:
5998:
5992:
5991:
5989:
5988:
5983:
5978:
5976:Ladder paradox
5973:
5968:
5963:
5958:
5953:
5948:
5942:
5940:
5936:
5935:
5933:
5932:
5926:
5924:
5920:
5919:
5917:
5916:
5911:
5906:
5901:
5896:
5891:
5886:
5881:
5879:Speed of light
5876:
5870:
5868:
5862:
5861:
5859:
5858:
5853:
5848:
5842:
5832:
5830:
5823:
5815:
5814:
5809:
5807:
5806:
5799:
5792:
5784:
5778:
5777:
5765:
5764:External links
5762:
5759:
5758:
5739:978-0470547946
5738:
5722:Robert Resnick
5718:David Halliday
5709:
5701:
5681:
5663:
5656:
5638:
5595:
5553:
5513:
5507:
5481:
5464:
5440:
5414:
5378:
5341:(4): 209â225.
5325:
5304:
5283:
5277:
5248:
5241:
5217:
5199:
5192:
5174:
5167:
5141:
5134:
5114:
5108:
5078:
5076:
5075:
5074:
5073:
5071:Space and Time
5041:
4993:
4987:
4961:
4936:
4880:
4870:
4849:
4848:
4846:
4843:
4840:
4839:
4836:
4833:
4830:
4826:
4825:
4822:
4819:
4816:
4812:
4811:
4808:
4805:
4802:
4798:
4797:
4794:
4791:
4788:
4784:
4783:
4780:
4777:
4774:
4770:
4769:
4766:
4763:
4760:
4756:
4755:
4752:
4749:
4746:
4742:
4741:
4736:
4731:
4726:
4722:
4721:
4718:
4715:
4712:
4708:
4707:
4701:
4695:
4689:
4685:
4684:
4678:
4672:
4666:
4662:
4661:
4658:
4655:
4652:
4648:
4647:
4642:
4637:
4632:
4628:
4627:
4624:
4623:Galilean plane
4621:
4618:
4614:
4613:
4610:
4607:
4604:
4584:isotropy group
4529:boosted cuboid
4509:rotated cuboid
4462:
4459:
4458:
4457:
4446:
4442:
4437:
4433:
4429:
4425:
4422:
4398:
4395:
4374:
4353:
4350:
4328:
4325:
4304:
4284:
4263:
4260:
4239:
4228:
4227:
4216:
4212:
4206:
4202:
4198:
4194:
4191:
4166:
4163:
4151:
4150:
4138:
4134:
4130:
4127:
4121:
4118:
4113:
4109:
4105:
4101:
4094:
4087:
4083:
4078:
4075:
4049:
4045:
4041:
4037:
4033:
4029:
4026:
4005:
4002:
3999:
3994:
3990:
3968:
3965:
3944:
3940:
3935:
3932:
3928:
3924:
3920:
3916:
3895:
3875:
3871:
3865:
3861:
3857:
3854:
3834:
3813:
3810:
3789:
3767:
3763:
3751:
3750:
3739:
3736:
3731:
3727:
3723:
3720:
3697:
3675:
3671:
3651:
3648:
3647:
3646:
3634:
3630:
3623:
3620:
3615:
3611:
3607:
3604:
3590:
3589:
3577:
3573:
3567:
3563:
3559:
3555:
3552:
3527:
3524:
3502:
3499:
3495:
3484:
3483:
3468:
3464:
3457:
3453:
3449:
3443:
3440:
3437:
3423:
3422:
3407:
3404:
3401:
3398:
3396:
3393:
3389:
3381:
3377:
3370:
3366:
3362:
3356:
3353:
3350:
3346:
3342:
3339:
3336:
3334:
3331:
3328:
3324:
3321:
3320:
3317:
3314:
3311:
3308:
3305:
3301:
3298:
3295:
3292:
3287:
3283:
3278:
3274:
3271:
3268:
3266:
3263:
3260:
3256:
3253:
3252:
3240:, it follows:
3227:
3223:
3219:
3214:
3210:
3206:
3201:
3197:
3176:
3173:
3168:
3163:
3159:
3155:
3150:
3145:
3141:
3137:
3133:
3130:
3126:
3104:
3099:
3095:
3091:
3086:
3081:
3077:
3073:
3069:
3066:
3062:
3051:
3050:
3034:
3028:
3024:
3019:
3013:
3009:
3005:
3002:
2997:
2993:
2988:
2984:
2981:
2978:
2976:
2971:
2968:
2963:
2959:
2955:
2950:
2947:
2944:
2939:
2936:
2930:
2926:
2921:
2915:
2911:
2907:
2904:
2899:
2895:
2890:
2886:
2883:
2880:
2878:
2873:
2870:
2865:
2861:
2857:
2856:
2852:
2846:
2842:
2838:
2835:
2830:
2826:
2821:
2817:
2814:
2811:
2809:
2804:
2801:
2796:
2792:
2788:
2783:
2780:
2777:
2772:
2769:
2763:
2759:
2755:
2752:
2747:
2743:
2738:
2734:
2731:
2728:
2726:
2721:
2718:
2713:
2709:
2705:
2704:
2688:
2685:
2682:
2681:
2672:
2670:
2659:
2650:
2646:
2640:
2636:
2632:
2628:
2625:
2606:
2605:
2596:
2594:
2583:
2574:
2571:
2567:
2564:
2560:
2555:
2551:
2532:
2531:
2522:
2520:
2509:
2500:
2496:
2489:
2486:
2481:
2477:
2473:
2470:
2445:
2432:
2431:
2422:
2420:
2409:
2400:
2397:
2394:
2391:
2385:
2382:
2377:
2373:
2344:
2341:
2336:
2332:
2328:
2322:
2319:
2314:
2310:
2306:
2300:
2297:
2292:
2288:
2265:
2261:
2257:
2252:
2248:
2244:
2241:
2219:
2215:
2211:
2206:
2202:
2190:
2189:
2178:
2168:
2162:
2158:
2154:
2151:
2146:
2142:
2137:
2133:
2130:
2126:
2122:
2118:
2106:
2100:
2096:
2092:
2089:
2084:
2080:
2075:
2071:
2068:
2064:
2060:
2056:
2030:
2026:
2022:
2017:
2013:
1992:
1970:
1966:
1943:
1939:
1926:
1923:
1918:
1915:
1886:Main article:
1883:
1882:Visual effects
1880:
1856:ladder paradox
1851:
1848:
1843:
1826:
1786:
1782:
1778:
1773:
1769:
1763:
1759:
1736:
1732:
1728:
1724:
1721:
1716:
1713:
1709:
1705:
1702:
1697:
1694:
1673:
1670:
1669:
1668:
1644:
1632:
1621:
1610:
1547:
1544:
1536:drift velocity
1515:Main article:
1512:
1509:
1488:
1467:
1464:
1442:
1439:
1417:
1414:
1393:
1373:
1360:
1357:
1300:
1296:
1275:
1264:
1263:
1248:
1244:
1239:
1233:
1229:
1225:
1222:
1215:
1211:
1207:
1204:
1190:
1189:
1188:
1187:
1175:
1165:
1153:
1126:
1122:
1117:
1111:
1107:
1103:
1100:
1096:
1091:
1088:
1085:
1082:
1079:
1070:, defined as
1067:Lorentz factor
1053:
1050:
1047:
1044:
1034:
1020:
1016:
1005:
993:
979:
978:
965:
961:
954:
951:
948:
945:
941:
936:
933:
897:
893:
872:
837:
833:
812:
789:
786:
781:
777:
773:
770:
750:
747:
744:
741:
736:
732:
711:
689:
685:
654:
605:
601:
569:
566:
544:Henri Poincaré
508:Main article:
505:
502:
498:speed of light
456:
455:
453:
452:
445:
438:
430:
427:
426:
425:
424:
411:
394:
393:
389:
388:
383:
378:
373:
368:
363:
358:
353:
348:
343:
338:
333:
328:
323:
318:
313:
308:
302:
301:
295:
294:
293:
290:
289:
286:
285:
280:
275:
269:
265:
264:
261:
255:
254:
253:
252:
249:
248:
245:
244:
239:
234:
228:
220:
219:
218:
215:
214:
211:
210:
205:
200:
195:
189:
181:
180:
179:
176:
175:
172:
171:
166:
161:
156:
151:
146:
141:
136:
131:
126:
120:
114:
113:
112:
109:
108:
105:
104:
99:
94:
92:Speed of light
89:
84:
78:
72:
71:
70:
67:
66:
65:
64:
59:
54:
46:
45:
37:
36:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
6668:
6657:
6654:
6652:
6649:
6647:
6644:
6643:
6641:
6628:
6618:
6612:
6611:
6607:
6605:
6602:
6600:
6597:
6595:
6592:
6590:
6587:
6585:
6582:
6580:
6577:
6575:
6572:
6570:
6567:
6565:
6562:
6560:
6557:
6555:
6552:
6550:
6547:
6545:
6542:
6540:
6537:
6535:
6532:
6530:
6527:
6525:
6522:
6520:
6519:Chandrasekhar
6517:
6515:
6512:
6510:
6507:
6505:
6502:
6500:
6497:
6495:
6492:
6490:
6487:
6485:
6482:
6480:
6479:Schwarzschild
6477:
6475:
6472:
6470:
6467:
6465:
6462:
6460:
6457:
6456:
6454:
6450:
6440:
6436:
6435:
6432:
6429:
6427:
6424:
6422:
6418:
6417:
6414:
6411:
6409:
6406:
6404:
6401:
6399:
6396:
6393:
6389:
6385:
6384:
6381:
6378:
6375:
6372:
6370:
6366:
6365:Schwarzschild
6362:
6361:
6358:
6355:
6353:
6350:
6348:
6345:
6343:
6340:
6338:
6335:
6332:
6328:
6324:
6323:
6321:
6319:
6315:
6309:
6306:
6304:
6301:
6299:
6296:
6295:
6293:
6287:
6281:
6278:
6275:
6271:
6267:
6264:
6262:
6261:Shapiro delay
6259:
6257:
6254:
6251:
6247:
6243:
6240:
6237:
6233:
6230:
6229:
6226:
6223:
6220:
6217:
6215:
6212:
6210:
6207:
6205:
6204:collaboration
6201:
6197:
6194:
6192:
6188:
6185:
6184:
6181:
6178:
6176:
6173:
6171:
6170:Event horizon
6168:
6166:
6163:
6162:
6160:
6156:
6150:
6147:
6145:
6142:
6140:
6137:
6135:
6132:
6130:
6127:
6125:
6122:
6120:
6117:
6115:
6114:ADM formalism
6112:
6111:
6109:
6105:
6099:
6096:
6094:
6091:
6089:
6086:
6084:
6081:
6079:
6076:
6075:
6073:
6067:
6061:
6058:
6056:
6053:
6052:
6050:
6046:
6043:
6041:
6035:
6025:
6022:
6020:
6019:Biquaternions
6017:
6015:
6012:
6010:
6007:
6005:
6002:
6001:
5999:
5997:
5993:
5987:
5984:
5982:
5979:
5977:
5974:
5972:
5969:
5967:
5964:
5962:
5959:
5957:
5954:
5952:
5949:
5947:
5946:Time dilation
5944:
5943:
5941:
5937:
5931:
5928:
5927:
5925:
5921:
5915:
5912:
5910:
5907:
5905:
5902:
5900:
5899:Proper length
5897:
5895:
5892:
5890:
5887:
5885:
5882:
5880:
5877:
5875:
5872:
5871:
5869:
5863:
5857:
5854:
5852:
5849:
5846:
5843:
5841:
5837:
5834:
5833:
5831:
5827:
5824:
5822:
5816:
5812:
5805:
5800:
5798:
5793:
5791:
5786:
5785:
5782:
5776:
5772:
5769:Physics FAQ:
5768:
5767:
5763:
5754:
5748:
5741:
5735:
5731:
5727:
5723:
5719:
5713:
5710:
5704:
5702:9780387218519
5698:
5694:
5693:
5685:
5682:
5677:
5673:
5667:
5664:
5659:
5653:
5649:
5642:
5639:
5634:
5630:
5626:
5622:
5618:
5614:
5610:
5606:
5605:Physics Today
5599:
5596:
5591:
5587:
5583:
5579:
5575:
5571:
5564:
5557:
5554:
5549:
5545:
5541:
5537:
5531:
5527:
5520:
5518:
5514:
5510:
5508:0-201-04679-2
5504:
5500:
5496:
5492:
5485:
5482:
5477:
5476:
5468:
5465:
5451:
5444:
5441:
5430:on 2016-06-03
5429:
5425:
5418:
5415:
5410:
5405:
5401:
5397:
5393:
5389:
5382:
5379:
5374:
5370:
5366:
5362:
5358:
5354:
5349:
5344:
5340:
5336:
5329:
5326:
5315:
5308:
5305:
5294:
5287:
5284:
5280:
5278:3-528-17236-3
5274:
5270:
5266:
5262:
5255:
5253:
5249:
5244:
5242:0-7506-2768-9
5238:
5234:
5230:
5229:
5221:
5218:
5213:
5209:
5203:
5200:
5195:
5193:0-520-20029-2
5189:
5185:
5178:
5175:
5170:
5168:0-486-65743-4
5164:
5160:
5155:
5154:
5145:
5142:
5137:
5135:0-7167-2327-1
5131:
5127:
5126:
5118:
5115:
5111:
5109:0-486-60769-0
5105:
5100:
5099:
5093:
5087:
5085:
5083:
5079:
5072:
5068:
5067:
5066:
5065:
5062:
5058:
5053:
5045:
5042:
5038:
5032:
5027:
5023:
5019:
5015:
5011:
5004:
4997:
4994:
4990:
4988:0-19-520438-7
4984:
4980:
4979:
4974:
4973:Pais, Abraham
4968:
4966:
4962:
4957:
4953:
4948:
4940:
4937:
4933:
4929:
4925:
4921:
4917:
4913:
4909:
4905:
4901:
4897:
4892:
4884:
4881:
4878:
4873:
4867:
4863:
4862:
4854:
4851:
4844:
4837:
4834:
4831:
4828:
4827:
4823:
4820:
4817:
4814:
4813:
4809:
4806:
4803:
4800:
4799:
4795:
4792:
4789:
4786:
4785:
4781:
4778:
4775:
4772:
4771:
4767:
4764:
4761:
4758:
4757:
4753:
4750:
4747:
4744:
4743:
4740:
4737:
4735:
4732:
4730:
4727:
4724:
4723:
4719:
4716:
4713:
4710:
4709:
4705:
4702:
4699:
4696:
4693:
4690:
4687:
4686:
4682:
4679:
4676:
4673:
4670:
4667:
4664:
4663:
4659:
4656:
4653:
4650:
4649:
4646:
4643:
4641:
4638:
4636:
4633:
4630:
4629:
4625:
4622:
4619:
4616:
4615:
4611:
4608:
4605:
4603:Trigonometry
4602:
4601:
4595:
4593:
4589:
4585:
4581:
4580:Lorentz group
4577:
4573:
4569:
4565:
4561:
4557:
4553:
4548:
4546:
4542:
4538:
4534:
4530:
4527:, which is a
4526:
4522:
4518:
4514:
4510:
4506:
4502:
4500:
4496:
4492:
4488:
4484:
4480:
4476:
4475:trigonometric
4467:
4460:
4444:
4440:
4435:
4431:
4427:
4423:
4420:
4413:
4412:
4411:
4396:
4393:
4372:
4351:
4348:
4326:
4323:
4302:
4282:
4261:
4258:
4237:
4214:
4210:
4204:
4200:
4196:
4192:
4189:
4181:
4180:
4179:
4164:
4161:
4136:
4132:
4128:
4125:
4119:
4116:
4111:
4107:
4103:
4099:
4092:
4085:
4081:
4076:
4073:
4063:
4062:
4061:
4047:
4043:
4039:
4035:
4031:
4027:
4024:
4003:
4000:
3997:
3992:
3988:
3966:
3963:
3942:
3938:
3933:
3930:
3926:
3922:
3918:
3914:
3893:
3873:
3869:
3863:
3859:
3855:
3852:
3832:
3811:
3808:
3787:
3765:
3761:
3737:
3734:
3729:
3725:
3721:
3718:
3711:
3710:
3709:
3695:
3673:
3669:
3661:
3657:
3656:time dilation
3649:
3632:
3628:
3621:
3619:
3613:
3609:
3605:
3602:
3595:
3594:
3593:
3575:
3571:
3565:
3561:
3557:
3553:
3550:
3542:
3541:
3540:
3525:
3522:
3500:
3497:
3466:
3462:
3455:
3451:
3447:
3441:
3438:
3428:
3427:
3426:
3402:
3394:
3391:
3387:
3379:
3375:
3368:
3364:
3360:
3354:
3351:
3344:
3340:
3337:
3335:
3329:
3326:
3312:
3303:
3299:
3293:
3290:
3285:
3281:
3276:
3272:
3269:
3267:
3261:
3258:
3243:
3242:
3241:
3225:
3221:
3217:
3212:
3208:
3204:
3199:
3195:
3174:
3171:
3161:
3157:
3153:
3143:
3139:
3135:
3131:
3128:
3097:
3093:
3089:
3079:
3075:
3071:
3067:
3064:
3032:
3026:
3022:
3017:
3011:
3007:
3003:
3000:
2995:
2991:
2986:
2982:
2979:
2977:
2969:
2967:
2961:
2957:
2934:
2928:
2924:
2919:
2913:
2909:
2905:
2902:
2897:
2893:
2888:
2884:
2881:
2879:
2871:
2869:
2863:
2859:
2850:
2844:
2840:
2836:
2833:
2828:
2824:
2819:
2815:
2812:
2810:
2802:
2800:
2794:
2790:
2767:
2761:
2757:
2753:
2750:
2745:
2741:
2736:
2732:
2729:
2727:
2719:
2717:
2711:
2707:
2695:
2694:
2693:
2686:
2680:
2673:
2671:
2657:
2648:
2644:
2638:
2634:
2630:
2626:
2623:
2615:
2614:
2611:
2604:
2597:
2595:
2581:
2572:
2569:
2565:
2562:
2558:
2553:
2549:
2541:
2540:
2537:
2530:
2523:
2521:
2507:
2498:
2494:
2487:
2485:
2479:
2475:
2471:
2468:
2461:
2460:
2457:
2443:
2430:
2423:
2421:
2407:
2398:
2395:
2392:
2389:
2383:
2381:
2375:
2371:
2363:
2362:
2359:
2342:
2340:
2334:
2330:
2326:
2320:
2318:
2312:
2308:
2304:
2298:
2296:
2290:
2286:
2263:
2259:
2255:
2250:
2246:
2242:
2239:
2217:
2213:
2209:
2204:
2200:
2176:
2166:
2160:
2156:
2152:
2149:
2144:
2140:
2135:
2131:
2128:
2124:
2120:
2116:
2104:
2098:
2094:
2090:
2087:
2082:
2078:
2073:
2069:
2066:
2062:
2058:
2054:
2046:
2045:
2044:
2028:
2024:
2020:
2015:
2011:
1990:
1968:
1964:
1941:
1937:
1924:
1922:
1916:
1914:
1912:
1908:
1907:Roger Penrose
1899:
1894:
1889:
1881:
1879:
1877:
1876:non-Euclidean
1873:
1872:Born rigidity
1869:
1865:
1861:
1857:
1849:
1847:
1842:
1837:
1825:
1823:
1819:
1815:
1809:
1806:
1784:
1780:
1776:
1771:
1767:
1761:
1757:
1734:
1730:
1726:
1722:
1719:
1714:
1711:
1707:
1703:
1700:
1695:
1692:
1683:
1678:
1671:
1666:
1661:
1657:
1653:
1649:
1645:
1642:
1641:Coulomb field
1637:
1633:
1626:
1622:
1619:
1618:time dilation
1615:
1611:
1608:
1604:
1600:
1596:
1592:
1588:
1584:
1580:
1576:
1575:
1574:
1572:
1567:
1564:
1560:
1553:
1545:
1543:
1540:
1537:
1533:
1528:
1523:
1518:
1510:
1508:
1506:
1502:
1486:
1465:
1462:
1440:
1437:
1415:
1412:
1391:
1371:
1358:
1356:
1353:
1336:
1319:
1317:
1298:
1294:
1273:
1246:
1242:
1237:
1231:
1227:
1223:
1220:
1213:
1209:
1205:
1202:
1195:
1194:
1193:
1173:
1166:
1151:
1144:
1143:
1124:
1120:
1115:
1109:
1105:
1101:
1098:
1094:
1089:
1083:
1077:
1069:
1068:
1048:
1042:
1035:
1018:
1014:
1006:
991:
984:
983:
982:
963:
959:
949:
943:
939:
934:
931:
924:
923:
922:
920:
916:
911:
895:
891:
870:
862:
857:
856:time dilation
853:
835:
831:
810:
801:
787:
784:
779:
775:
771:
768:
748:
745:
742:
739:
734:
730:
709:
687:
683:
675:
670:
668:
652:
644:
639:
635:
627:
623:
619:
603:
599:
591:
590:proper length
587:
583:
574:
567:
565:
563:
559:
555:
551:
549:
545:
541:
540:Joseph Larmor
537:
533:
529:
525:
521:
517:
511:
503:
501:
499:
495:
491:
487:
483:
479:
475:
474:proper length
471:
462:
451:
446:
444:
439:
437:
432:
431:
429:
428:
422:
412:
409:
404:
398:
397:
396:
395:
387:
384:
382:
379:
377:
374:
372:
369:
367:
364:
362:
359:
357:
354:
352:
349:
347:
344:
342:
339:
337:
334:
332:
329:
327:
324:
322:
319:
317:
314:
312:
309:
307:
304:
303:
292:
291:
284:
281:
279:
276:
274:
271:
270:
262:
260:
257:
256:
251:
250:
243:
242:Four-momentum
240:
238:
235:
233:
230:
229:
224:
217:
216:
209:
206:
204:
201:
199:
196:
194:
191:
190:
185:
178:
177:
170:
167:
165:
162:
160:
157:
155:
152:
150:
147:
145:
142:
140:
137:
135:
132:
130:
127:
125:
124:Time dilation
122:
121:
111:
110:
103:
100:
98:
95:
93:
90:
88:
85:
83:
80:
79:
69:
68:
63:
60:
58:
55:
53:
50:
49:
48:
47:
43:
39:
38:
35:
31:
19:
6609:
6303:KaluzaâKlein
6055:Introduction
5981:Twin paradox
5955:
5729:
5726:Jearl Walker
5712:
5695:. Springer.
5691:
5684:
5676:math.ucr.edu
5675:
5666:
5647:
5641:
5611:(9): 24â27.
5608:
5604:
5598:
5576:(1): 56â60.
5573:
5569:
5556:
5547:
5546:-VerkĂŒrzung
5543:
5539:
5535:
5529:
5525:
5494:
5484:
5474:
5467:
5456:. Retrieved
5443:
5432:. Retrieved
5428:the original
5417:
5391:
5387:
5381:
5338:
5334:
5328:
5317:. Retrieved
5307:
5296:. Retrieved
5286:
5260:
5227:
5220:
5211:
5202:
5183:
5177:
5152:
5144:
5124:
5117:
5097:
5060:
5056:
5044:
5035:. See also:
5013:
5009:
4996:
4976:
4955:
4951:
4939:
4902:(328): 390,
4899:
4895:
4883:
4860:
4853:
4734:Dual numbers
4703:
4697:
4691:
4680:
4674:
4668:
4644:
4639:
4634:
4592:trigonometry
4583:
4549:
4544:
4540:
4536:
4532:
4528:
4524:
4520:
4516:
4512:
4508:
4504:
4503:
4498:
4494:
4493:a cuboid in
4490:
4486:
4482:
4474:
4472:
4229:
4178:is given by
4152:
3752:
3653:
3591:
3485:
3424:
3052:
2690:
2674:
2609:
2598:
2535:
2524:
2435:
2424:
2191:
1928:
1920:
1903:
1900:(1877-1910).
1868:rigid bodies
1853:
1840:
1835:
1833:
1821:
1817:
1813:
1811:
1802:
1648:synchrotrons
1606:
1602:
1598:
1594:
1590:
1586:
1570:
1568:
1562:
1555:
1541:
1531:
1524:
1520:
1362:
1351:
1334:
1320:
1265:
1191:
1065:
980:
912:
860:
802:
671:
667:simultaneity
642:
631:
625:
581:
579:
552:
513:
485:
481:
469:
468:
128:
116:Consequences
62:Formulations
6392:KerrâNewman
6363:Spherical:
6232:Other tests
6175:Singularity
6107:Formulation
6069:Fundamental
5923:Formulation
5904:Proper time
5865:Fundamental
5551:Beobachter.
4829:"cosecant"
4782:tanh Ï = v
4612:Hyperbolic
3780:at rest in
3660:proper time
674:proper time
518:(1889) and
237:Proper mass
232:Proper time
74:Foundations
6640:Categories
6544:Zel'dovich
6452:Scientists
6431:Alcubierre
6238:of Mercury
6236:precession
6165:Black hole
6048:Background
6040:relativity
6009:World line
6004:Light cone
5829:Background
5821:relativity
5811:Relativity
5532:: 509â510.
5458:2013-01-01
5434:2013-01-01
5319:2013-01-01
5298:2013-01-01
4845:References
4835:cscp Ï = u
4821:secp Ï = 1
4807:sinp Ï = u
4793:cosp Ï = 1
4779:tanp Ï = u
4657:Degenerate
4582:forms the
4547:at left).
4521:world slab
4507:: Left: a
4499:world slab
1917:Derivation
1658:, so that
1636:ionization
1550:See also:
919:Derivation
478:rest frame
326:FitzGerald
311:Sommerfeld
263:Precursors
208:Light cone
203:World line
6514:Robertson
6499:Friedmann
6494:Eddington
6484:de Sitter
6318:Solutions
6196:detectors
6191:astronomy
6158:Phenomena
6093:Geodesics
5996:Spacetime
5939:Phenomena
5092:Born, Max
4815:"secant"
4787:"cosine"
4776:tan Ï = m
4714:Rotations
4609:Parabolic
4588:rotations
4445:γ
4215:γ
4137:γ
3738:γ
3735:⋅
3633:γ
3576:γ
3494:Δ
3436:Δ
3355:−
3349:Δ
3341:γ
3323:Δ
3297:Δ
3291:−
3273:γ
3255:Δ
3218:−
3167:′
3154:−
3149:′
3125:Δ
3103:′
3090:−
3085:′
3061:Δ
3001:−
2983:γ
2903:−
2885:γ
2834:−
2816:γ
2751:−
2733:γ
2649:γ
2573:γ
2570:⋅
2499:γ
2444:γ
2399:γ
2396:⋅
2327:−
2256:−
2150:−
2132:γ
2088:−
2070:γ
1850:Paradoxes
1836:arbitrary
1772:∗
1762:∗
1656:undulator
1525:In 1820,
1505:spacetime
1347: m/s
1330: m/s
1224:−
1102:−
1090:≡
1078:γ
1043:γ
944:γ
785:⋅
746:⋅
638:vanishing
562:spacetime
376:Ehrenfest
346:Minkowski
316:Michelson
184:Spacetime
6627:Category
6504:LemaĂźtre
6469:Einstein
6459:Poincaré
6419:Others:
6403:TaubâNUT
6369:interior
6291:theories
6289:Advanced
6256:redshift
6071:concepts
5889:Rapidity
5867:concepts
5747:citation
5728:(2010),
5633:36707809
5548:wirklich
5373:16835076
5094:(1964),
4975:(1982),
4932:43610293
4924:17819387
4606:Circular
4491:boosting
4483:rotation
4436:′
4397:′
4352:′
4327:′
4315:than in
4262:′
4250:than in
4193:′
4165:′
4108:′
4077:′
4044:′
4028:′
3967:′
3934:′
3923:′
3812:′
3622:′
3554:′
3526:′
3501:′
3330:′
3262:′
3132:′
3068:′
2970:′
2872:′
2803:′
2720:′
2627:′
2566:′
2488:′
2384:′
2343:′
2321:′
2299:′
2125:′
2063:′
1827:â
1803:In 1911
1723:″
1715:″
1704:′
1696:′
1571:indirect
1466:′
1441:′
1416:′
1359:Symmetry
421:Category
371:von Laue
341:Poincaré
331:Herglotz
306:Einstein
223:Dynamics
6569:Hawking
6564:Penrose
6549:Novikov
6529:Wheeler
6474:Hilbert
6464:Lorentz
6421:pp-wave
6242:lensing
6038:General
5819:Special
5613:Bibcode
5578:Bibcode
5544:Lorentz
5536:Lorentz
5499:249â253
5396:Bibcode
5353:Bibcode
5265:Bibcode
5063:: 75â88
5018:Bibcode
4958:: 74â79
4904:Bibcode
4896:Science
4801:"sine"
4720:Boosts
4631:Symbol
4533:thinner
3980:, thus
1629:
1064:is the
504:History
488:(after
356:Abraham
336:Lorentz
259:History
6651:Length
6610:others
6599:Thorne
6589:Misner
6574:Taylor
6559:Geroch
6554:Ehlers
6524:Zwicky
6342:Kasner
5736:
5699:
5654:
5631:
5505:
5371:
5275:
5239:
5190:
5165:
5132:
5106:
4985:
4930:
4922:
4868:
4773:Slope
4717:Shears
4706:(1,1)
4683:(1,1)
4572:origin
4517:longer
4479:cuboid
2655:
2652:
2579:
2576:
2505:
2502:
2405:
2402:
2192:Since
2174:
2171:
1818:really
1623:Heavy
1597:) and
1563:direct
1532:denser
1142:where
981:where
419:
381:Tolman
366:Planck
351:Fizeau
321:Morley
297:People
6604:Weiss
6584:Bondi
6579:Hulse
6509:Milne
6413:discs
6357:Milne
6352:Gödel
6209:Virgo
5629:S2CID
5566:(PDF)
5453:(PDF)
5369:S2CID
5343:arXiv
5159:20â22
5006:(PDF)
4928:S2CID
4700:(0,1)
4677:(0,1)
4505:Image
1614:muons
386:Dirac
6539:Kerr
6489:Weyl
6388:Kerr
6248:and
6202:and
6200:LIGO
5753:link
5734:ISBN
5697:ISBN
5652:ISBN
5503:ISBN
5273:ISBN
5237:ISBN
5188:ISBN
5163:ISBN
5130:ISBN
5104:ISBN
4983:ISBN
4920:PMID
4866:ISBN
4762:None
4016:and
3906:and
2278:and
1956:and
1858:and
1822:i.e.
1777:<
1650:and
1634:The
1625:ions
1286:and
883:and
854:and
823:and
582:i.e.
492:and
361:Born
6594:Yau
6219:GEO
5621:doi
5586:doi
5404:doi
5392:130
5361:doi
5026:doi
5014:322
4912:doi
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4671:(2)
4562:on
4485:in
3955:in
3886:in
2111:and
1646:In
1345:000
1342:300
1328:000
1325:400
861:not
484:or
6642::
6268:/
6234::
6189::
5773:;
5749:}}
5745:{{
5724:,
5720:,
5674:.
5627:.
5619:.
5609:13
5607:.
5584:.
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5516:^
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5493:,
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5251:^
5231:.
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5081:^
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4954:,
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4692:SO
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6394:)
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4441:/
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2305:=
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2264:1
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2243:=
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2177:.
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1206:=
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740:=
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710:T
688:0
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653:L
604:0
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442:t
435:v
20:)
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