203:, i.e., the complete Lorentz transformation. PoincarĂ© obtained the full transformation earlier in 1905 but in the papers of that year he did not mention his synchronization procedure. This derivation was completely based on light speed invariance and the relativity principle, so Einstein noted that for the electrodynamics of moving bodies the aether is superfluous. Thus, the separation into "true" and "local" times of Lorentz and PoincarĂ© vanishes â all times are equally valid and therefore the relativity of length and time is a natural consequence.
193:). Therefore, if they synchronize their clocks by using light signals, they will only consider the transit time for the signals, but not their motion in respect to the aether. So the moving clocks are not synchronous and do not indicate the "true" time. Poincaré calculated that this synchronization error corresponds to Lorentz's local time. In 1904, Poincaré emphasized the connection between the principle of relativity, "local time", and light speed invariance; however, the reasoning in that paper was presented in a qualitative and conjectural manner.
300:
1580:
75:
83:
369:
361:
338:
330:
2433:
760:
919:) that might be referred to as the co-moving or "tangent free-float-frame" definition. This definition is naturally extrapolated to events in gravitationally-curved spacetimes, and to accelerated observers, through use of a radar-time/distance definition that (unlike the tangent free-float-frame definition for accelerated frames) assigns a unique time and position to any event.
189:
for observers in different states of motion. This was done in 1900, when
Poincaré derived local time by assuming that the speed of light is invariant within the aether. Due to the "principle of relative motion", moving observers within the aether also assume that they are at rest and that the speed of light is constant in all directions (only to first order in
25:
309:
along the axis of train movement (back and front of the train car). In the inertial frame of the standing observer, there are three events which are spatially dislocated, but simultaneous: standing observer facing the moving observer (i.e., the center of the train), lightning striking the front of the train car, and lightning striking the back of the car.
408:
In the second diagram, the two ends of the train moving to the right, are shown by parallel lines. The flash of light is given off at a point exactly halfway between the two ends of the train, and again form two 45° lines, expressing the constancy of the speed of light. In this picture, however, the
356:
For the observer standing on the platform, on the other hand, the rear of the traincar is moving (catching up) toward the point at which the flash was given off, and the front of the traincar is moving away from it. As the speed of light is finite and the same in all directions for all observers, the
145:
occur at the same time if those events are separated in space. If one reference frame assigns precisely the same time to two events that are at different points in space, a reference frame that is moving relative to the first will generally assign different times to the two events (the only exception
404:
In the first diagram, the two ends of the train are drawn as grey lines. Because the ends of the train are stationary with respect to the observer on the train, these lines are just vertical lines, showing their motion through time but not space. The flash of light is shown as the 45° red lines. The
352:
A flash of light is given off at the center of the traincar just as the two observers pass each other. For the observer on board the train, the front and back of the traincar are at fixed distances from the light source and as such, according to this observer, the light will reach the front and back
308:
Einstein's version of the experiment presumed that one observer was sitting midway inside a speeding traincar and another was standing on a platform as the train moved past. As measured by the standing observer, the train is struck by two bolts of lightning simultaneously, but at different positions
819:
Graphically, this can be represented on a spacetime diagram by the fact that a plot of the set of points regarded as simultaneous generates a line which depends on the observer. In the spacetime diagram, the dashed line represents a set of points considered to be simultaneous with the origin by an
188:
who already emphasized in 1898 the conventional nature of simultaneity and who argued that it is convenient to postulate the constancy of the speed of light in all directions. However, this paper did not contain any discussion of
Lorentz's theory or the possible difference in defining simultaneity
922:
The radar-time definition of extended-simultaneity further facilitates visualization of the way that acceleration curves spacetime for travelers in the absence of any gravitating objects. This is illustrated in the figure at right, which shows radar time/position isocontours for events in flat
149:
For example, a car crash in London and another in New York appearing to happen at the same time to an observer on Earth, will appear to have occurred at slightly different times to an observer on an airplane flying between London and New York. Furthermore, if the two events cannot be causally
150:
connected, depending on the state of motion, the crash in London may appear to occur first in a given frame, and the New York crash may appear to occur first in another. However, if the events can be causally connected, precedence order is preserved in all frames of reference.
312:
Since the events are placed along the axis of train movement, their time coordinates become projected to different time coordinates in the moving train's inertial frame. Events which occurred at space coordinates in the direction of train movement happen
908:
67:
401:= 0, and is drawn horizontally. The statement that the speed of light is the same for all observers is represented by drawing a light ray as a 45° line, regardless of the speed of the source relative to the speed of the observer.
303:
Einstein imagined a stationary observer who witnessed two lightning bolts simultaneously striking both ends of a moving train. He concluded that an observer standing on the train would measure the bolts to strike at different
571:
763:
A spacetime diagram showing the set of points regarded as simultaneous by a stationary observer (horizontal dotted line) and the set of points regarded as simultaneous by an observer moving at v = 0.25c (dashed
654:
1305:
824:
of one-quarter of the speed of light. The dotted horizontal line represents the set of points regarded as simultaneous with the origin by a stationary observer. This diagram is drawn using the (
357:
light headed for the back of the train will have less distance to cover than the light headed for the front. Thus, the flashes of light will strike the ends of the traincar at different times.
2136:
1203:
832:) coordinates of the stationary observer, and is scaled so that the speed of light is one, i.e., so that a ray of light would be represented by a line with a 45° angle from the
317:
than events at coordinates opposite to the direction of train movement. In the moving train's inertial frame, this means that lightning will strike the front of the train car
86:
Events A, B, and C occur in different order depending on the motion of the observer. The white line represents a plane of simultaneity being moved from the past to the future.
1384:
472:. And suppose that the observers' coordinate axes are parallel and that they have the same origin. Then the Lorentz transformation expresses how the coordinates are related:
722:
688:
927:
roundtrip. One caveat of this approach is that the time and place of remote events are not fully defined until light from such an event is able to reach our traveler.
349:
in 1910 and
Einstein in 1917. It also consists of one observer midway inside a speeding traincar and another observer standing on a platform as the train moves past.
1366:
2183:
475:
2418:
2207:
1953:
46:
33:
575:
405:
points at which the two light flashes hit the ends of the train are at the same level in the diagram. This means that the events are simultaneous.
2465:
1989:
1943:
2127:
1417:
1165:
78:
Event B is simultaneous with A in the green reference frame, but it occurred before in the blue frame, and will occur later in the red frame.
1036:
1611:
429:, which relates the coordinates used by one observer to coordinates used by another in uniform relative motion with respect to the first.
748:
coordinate, so they will happen at different times in that frame. The term that accounts for the failure of absolute simultaneity is the
1427:
2235:
816:
constant. That is, the set of events which are regarded as simultaneous depends on the frame of reference used to make the comparison.
1864:
163:
1869:
1314:
1288:
1212:
1084:
946:
289:
2189:
1902:
2005:
2083:
2146:
261:. The book culminates in chapter 6, "The transition to the relativistic conception of simultaneity". Jammer indicates that
2436:
2178:
2013:
159:
114:
2000:
1228:
915:
The
Lorentz-transform calculation above uses a definition of extended-simultaneity (i.e. of when and where events occur
1760:
2460:
2455:
2041:
1775:
231:
732:. If two events happen at the same time in the frame of the first observer, they will have identical values of the
2328:
1723:
1035:
38:
2358:
1984:
1665:
345:
A popular picture for understanding this idea is provided by a thought experiment similar to those suggested by
299:
2383:
1933:
1693:
1604:
956:
896:
227:
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2034:
692:
658:
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110:
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1101:
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1739:
1703:
982:
951:
888:
426:
82:
2343:
1948:
1887:
346:
879:, and the set of simultaneous events for the second observer (at the origin) is described by the line
280:
can be expressed as the arbitrariness of which pair are taken to represent space and time in a plane.
2248:
2174:
2018:
1620:
1541:
1459:
1279:
Albert
Einstein's special theory of relativity. Emergence (1905) and early interpretation (1905â1911)
1243:
1145:
1001:
167:
1583:
2323:
2318:
2313:
2308:
2140:
2089:
1907:
1892:
1718:
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269:
181:
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1389:
184:
drift experiments. However, Lorentz gave no physical explanation of this effect. This was done by
2388:
2288:
2070:
2051:
2045:
1996:
1938:
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1765:
1683:
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1628:
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1531:
1483:
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991:
146:
being when motion is exactly perpendicular to the line connecting the locations of both events).
142:
122:
2398:
2268:
2230:
2222:
1823:
1780:
1500:
Einstein's thought experiment used two light rays starting at both ends of the platform. See:
1475:
1413:
1310:
1284:
1208:
1161:
1080:
977:
936:
382:
207:
185:
118:
1424:
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2293:
2240:
2217:
1795:
1579:
1549:
1467:
1251:
1153:
1009:
941:
792:) coordinate system. From the above equations for the Lorentz transform it can be seen that
333:
The train-and-platform experiment from the reference frame of an observer on board the train
242:
74:
2378:
2353:
2278:
2273:
2156:
2117:
2079:
2023:
1897:
1833:
1522:
Dolby, Carl E.; Gull, Stephen F. (December 2001). "On radar time and the twin "paradox"".
1431:
1379:
784:= constant defines the "line of simultaneity" for the first (stationary) observer in the (
389:-axis is defined to be a point traced out in time by the origin of the spatial coordinate
368:
360:
249:, directly addressing the structure Minkowski had put in place for simultaneity. In 2006,
215:
196:
173:
134:
106:
2161:
341:
Reference frame of an observer standing on the platform (length contraction not depicted)
1545:
1504:
1463:
1247:
1149:
1005:
2403:
2075:
2059:
2055:
1958:
1928:
1785:
1688:
1277:
729:
1038:
Versuch einer
Theorie der electrischen und optischen Erscheinungen in bewegten Körpern
2449:
2393:
2373:
2368:
2283:
2151:
1979:
1923:
1755:
1708:
1561:
1348:
1021:
1487:
1446:
1442:
The thought experiment by
Comstock described two platforms in relative motion. See:
1182:
337:
329:
101:
2413:
2333:
2298:
1828:
1790:
1262:
1190:, vol. 1, Boston and New York: Houghton, Mifflin and Company, pp. 604â622
1116:
372:
The same diagram in the frame of an observer who sees the train moving to the right
268:
Naturally the mathematical notions preceded physical interpretation. For instance,
254:
759:
199:
used a similar method in 1905 to derive the time transformation for all orders in
1407:
2197:
2166:
1713:
1471:
2408:
1974:
1818:
1813:
1013:
907:
262:
250:
235:
230:
of spatial directions to the worldline associated to the rapidity. Then every
211:
66:
1256:
1100:
464:. Now suppose that the first observer sees the second observer moving in the
1805:
1157:
864:
1479:
780:) coordinate system for the second (moving) observer, just as the equation
24:
1331:
923:
spacetime as experienced by a traveler (red trajectory) taking a constant
895:
of the worldline and simultaneous events, in accord with the principle of
2348:
1698:
223:
219:
1130:
91:
1553:
1536:
2028:
566:{\displaystyle t'={\frac {t-{v\,x/c^{2}}}{\sqrt {1-v^{2}/c^{2}}}}\,,}
1503:
1188:
Congress of arts and science, universal exposition, St. Louis, 1904
996:
906:
892:
758:
367:
359:
336:
328:
298:
81:
73:
65:
1056:
105: â whether two spatially separated events occur at the same
2009:
1445:
1181:
409:
points at which the light flashes hit the ends of the train are
1593:
1306:
Subtle is the Lord: The
Science and the Life of Albert Einstein
397:-axis is defined as the set of all points in space at the time
364:
The spacetime diagram in the frame of the observer on the train
259:
Concepts of
Simultaneity: from antiquity to Einstein and beyond
226:, and the ordinary sense of simultaneity becomes dependent on
18:
16:
Concept that simultaneity depends on choice of reference frame
1589:
649:{\displaystyle x'={\frac {x-v\,t}{\sqrt {1-v^{2}/c^{2}}}}\,,}
425:
The relativity of simultaneity can be demonstrated using the
736:-coordinate. However, if they have different values of the
133:
According to the special theory of relativity introduced by
1204:
Thematic
Origins of Scientific Thought: Kepler to Einstein
1107:
Archives NĂ©erlandaises des Sciences Exactes et Naturelles
812:
constant are different from the set of points that makes
1102:"La théorie de Lorentz et le principe de réaction"
856:= 0, the equation of the dotted line of simultaneity is
844:= 1, the equation of the dashed line of simultaneity is
432:
Assume that the first observer uses coordinates labeled
265:
demythologized the absolute time of Newtonian physics.
1330:
1388:(1 ed.). Dublin: Longman, Green and Co. p.
695:
661:
578:
478:
448:, while the second observer uses coordinates labeled
121:
in 1900, and thereafter became a central idea in the
867:
in the spacetime of the first observer described by
772:= constant defines a "line of simultaneity" in the (
744:-direction), they will have different values of the
381:
It may be helpful to visualize this situation using
2261:
2126:
2098:
1967:
1916:
1878:
1857:
1846:
1804:
1748:
1732:
1674:
1638:
1627:
1385:
A History of the Theories of Aether and Electricity
1077:
Einstein's Clocks, Poincaré's Maps: Empires of Time
978:"Simultaneity as an invariant equivalence relation"
1401:
1399:
1276:
716:
682:
648:
565:
70:On spaceships, map-clocks may look unsynchronized.
214:of a particle in his model of the cosmos called
176:used a mathematical method called "local time"
117:. This possibility was raised by mathematician
1183:"The Principles of Mathematical Physics"
836:axis. From our previous analysis, given that
1605:
1367:Bulletin of the American Mathematical Society
1055:
808:= constant. Thus the set of points that make
8:
1347:Various English translations on Wikisource:
863:In general the second observer traces out a
1412:, Samaira Book Publishers, pp. 30â33,
1409:Relativity - The Special and General Theory
1064:, New York: Science Press, pp. 222â234
321:the two observers align (face each other).
218:. In Minkowski's view, the naĂŻve notion of
1854:
1635:
1612:
1598:
1590:
1506:Relativity: The Special and General Theory
1535:
1255:
1131:"The Genesis of the theory of relativity"
995:
710:
694:
676:
660:
642:
633:
624:
618:
602:
590:
577:
559:
550:
541:
535:
516:
507:
503:
499:
490:
477:
740:-coordinate (different positions in the
49:of all important aspects of the article.
968:
45:Please consider expanding the lead to
1309:, New York: Oxford University Press,
7:
1363:Orthogonality and Spacetime Geometry
1229:"Zur Elektrodynamik bewegter Körper"
247:Orthogonality and Spacetime Geometry
2184:TolmanâOppenheimerâVolkoff equation
2137:FriedmannâLemaĂźtreâRobertsonâWalker
1447:"The principle of relativity"
276:are related as space and time. The
353:of the traincar at the same time.
164:History of Lorentz transformations
14:
1954:HamiltonâJacobiâEinstein equation
2432:
2431:
1578:
1361:A.D. Taimanov (1989) "Review of
1034:Lorentz, Hendrik Antoon (1895),
911:Roundtrip radar-time isocontours
820:observer moving with a velocity
393:, and is drawn vertically. The
137:, it is impossible to say in an
23:
37:may be too short to adequately
2466:Thought experiments in physics
1761:Massâenergy equivalence (E=mc)
947:Einstein's thought experiments
290:Einstein's thought experiments
47:provide an accessible overview
1:
1180:PoincarĂ©, Henri (1904â1906),
1054:PoincarĂ©, Henri (1898â1913),
976:Mamone-Capria, Marco (2012),
917:at which you were not present
385:. For a given observer, the
160:History of special relativity
1207:, Harvard University Press,
413:at the same level; they are
210:introduced the concept of a
180:for explaining the negative
123:special theory of relativity
1776:Relativistic Doppler effect
1524:American Journal of Physics
1329:Minkowski, Hermann (1909),
1283:, Reading: AddisonâWesley,
1057:"The Measure of Time"
796:is constant if and only if
232:inertial frame of reference
2482:
2247:In computational physics:
1771:Relativity of simultaneity
1472:10.1126/science.31.803.767
1275:Miller, Arthur I. (1981),
1129:Darrigol, Olivier (2005),
1062:The foundations of science
287:
157:
115:observer's reference frame
96:relativity of simultaneity
2429:
2084:LenseâThirring precession
1666:Doubly special relativity
1406:Einstein, Albert (2017),
1337:Physikalische Zeitschrift
1227:Einstein, Albert (1905),
1079:, New York: W.W. Norton,
1014:10.1007/s10701-012-9674-4
468:-direction at a velocity
1944:Post-Newtonian formalism
1934:Einstein field equations
1870:Mathematical formulation
1694:Hyperbolic orthogonality
1257:10.1002/andp.19053221004
1099:Poincaré, Henri (1900),
957:Einstein synchronisation
897:hyperbolic orthogonality
228:hyperbolic orthogonality
141:sense that two distinct
1655:Galilean transformation
1646:Principle of relativity
1444:Comstock, D.F. (1910),
1201:Holton, Gerald (1988),
1158:10.1007/3-7643-7436-5_1
1075:Galison, Peter (2003),
717:{\displaystyle z'=z\,,}
683:{\displaystyle y'=y\,,}
278:principle of relativity
236:simultaneous hyperplane
1740:Lorentz transformation
1303:Pais, Abraham (1982),
983:Foundations of Physics
912:
889:multiplicative inverse
765:
718:
684:
650:
567:
427:Lorentz transformation
421:Lorentz transformation
373:
365:
342:
334:
325:The train-and-platform
305:
87:
79:
71:
2208:WeylâLewisâPapapetrou
1949:Raychaudhuri equation
1888:Equivalence principle
1332:"Raum und Zeit"
910:
903:Accelerated observers
762:
719:
685:
651:
568:
371:
363:
347:Daniel Frost Comstock
340:
332:
302:
294:
234:has a rapidity and a
113:, but depends on the
85:
77:
69:
2249:Numerical relativity
2090:pulsar timing arrays
1502:Einstein A. (1917),
1043:, Leiden: E.J. Brill
693:
659:
576:
476:
274:conjugate hyperbolas
168:Lorentz ether theory
98:is the concept that
2141:Friedmann equations
2035:HulseâTaylor binary
1997:Gravitational waves
1893:Riemannian geometry
1719:Proper acceleration
1704:Maxwell's equations
1650:Galilean relativity
1546:2001AmJPh..69.1257D
1464:1910Sci....31..767C
1263:English translation
1248:1905AnP...322..891E
1150:2006eins.book....1D
1117:English translation
1006:2012FoPh...42.1365M
952:Ehrenfest's paradox
925:proper-acceleration
284:Thought experiments
270:conjugate diameters
2461:History of physics
2456:Special relativity
2190:ReissnerâNordström
2108:BransâDicke theory
1939:Linearized gravity
1766:Length contraction
1684:Frame of reference
1661:Special relativity
1584:Special relativity
1430:2020-10-12 at the
1236:Annalen der Physik
1138:Séminaire Poincaré
913:
766:
714:
680:
646:
563:
383:spacetime diagrams
377:Spacetime diagrams
374:
366:
343:
335:
306:
172:In 1892 and 1895,
88:
80:
72:
2443:
2442:
2257:
2256:
2236:OzsvĂĄthâSchĂŒcking
1842:
1841:
1824:Minkowski diagram
1781:Thomas precession
1724:Relativistic mass
1554:10.1119/1.1407254
1530:(12): 1257â1261.
1419:978-81-935401-7-6
1167:978-3-7643-7435-8
990:(11): 1365â1383,
937:Andromeda paradox
640:
639:
557:
556:
222:is replaced with
208:Hermann Minkowski
64:
63:
2473:
2435:
2434:
2218:van Stockum dust
1990:Two-body problem
1908:Mach's principle
1855:
1796:Terrell rotation
1636:
1614:
1607:
1600:
1591:
1582:
1566:
1565:
1539:
1519:
1513:
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1510:
1498:
1492:
1490:
1458:(803): 767â772,
1449:
1440:
1434:
1422:
1403:
1394:
1393:
1376:
1370:
1359:
1353:
1344:
1334:
1326:
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1300:
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1177:
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1126:
1120:
1114:
1104:
1096:
1090:
1089:
1072:
1066:
1065:
1059:
1051:
1045:
1044:
1042:
1031:
1025:
1024:
999:
973:
942:Causal structure
891:relation of the
723:
721:
720:
715:
703:
689:
687:
686:
681:
669:
655:
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558:
555:
554:
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523:
522:
521:
520:
511:
491:
486:
295:Einstein's train
243:Robert Goldblatt
59:
56:
50:
27:
19:
2481:
2480:
2476:
2475:
2474:
2472:
2471:
2470:
2446:
2445:
2444:
2439:
2425:
2253:
2157:BKL singularity
2147:LemaĂźtreâTolman
2122:
2118:Quantum gravity
2100:
2094:
2080:geodetic effect
2054:(together with
2024:LISA Pathfinder
1963:
1912:
1898:Penrose diagram
1880:
1874:
1849:
1838:
1834:Minkowski space
1800:
1744:
1728:
1676:
1670:
1630:
1623:
1618:
1575:
1570:
1569:
1521:
1520:
1516:
1501:
1499:
1495:
1443:
1441:
1437:
1432:Wayback Machine
1420:
1405:
1404:
1397:
1380:Whittaker, E.T.
1378:
1377:
1373:
1360:
1356:
1328:
1327:
1323:
1317:
1302:
1301:
1297:
1291:
1274:
1273:
1269:
1242:(10): 891â921,
1231:
1226:
1225:
1221:
1215:
1200:
1199:
1195:
1179:
1178:
1174:
1168:
1133:
1128:
1127:
1123:
1115:. See also the
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1097:
1093:
1087:
1074:
1073:
1069:
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297:
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216:Minkowski space
197:Albert Einstein
174:Hendrik Lorentz
170:
158:Main articles:
156:
135:Albert Einstein
131:
109: â is not
60:
54:
51:
44:
32:This article's
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17:
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2196:Axisymmetric:
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2159:
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2135:Cosmological:
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2123:
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2120:
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2110:
2104:
2102:
2096:
2095:
2093:
2092:
2087:
2076:frame-dragging
2073:
2068:
2063:
2060:Einstein rings
2056:Einstein cross
2049:
2038:
2037:
2032:
2026:
2021:
2016:
2003:
1993:
1992:
1987:
1982:
1977:
1971:
1969:
1965:
1964:
1962:
1961:
1959:Ernst equation
1956:
1951:
1946:
1941:
1936:
1931:
1929:BSSN formalism
1926:
1920:
1918:
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1911:
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1786:Ladder paradox
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1689:Speed of light
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1573:External links
1571:
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1349:Space and Time
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417:simultaneous.
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186:Henri Poincaré
178:t' = t â v x/c
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119:Henri Poincaré
62:
61:
41:the key points
31:
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22:
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2175:Schwarzschild
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2014:collaboration
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1924:ADM formalism
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1709:Proper length
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1537:gr-qc/0104077
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1316:0-19-520438-7
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1214:0-674-87747-0
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1163:
1159:
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1086:0-393-32604-7
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890:
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874:
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866:
861:
859:
855:
852:= 0 and with
851:
847:
843:
839:
835:
831:
827:
823:
817:
815:
811:
807:
803:
799:
795:
791:
787:
783:
779:
775:
771:
768:The equation
761:
757:
755:
751:
747:
743:
739:
735:
731:
727:
711:
707:
704:
700:
697:
677:
673:
670:
666:
663:
643:
634:
630:
625:
619:
615:
611:
608:
603:
599:
596:
593:
587:
583:
580:
560:
551:
547:
542:
536:
532:
528:
525:
517:
513:
508:
504:
500:
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493:
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483:
480:
471:
467:
463:
459:
455:
451:
447:
443:
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435:
430:
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420:
418:
416:
412:
406:
402:
400:
396:
392:
388:
384:
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362:
358:
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350:
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339:
331:
324:
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320:
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84:
76:
68:
58:
48:
42:
40:
35:
30:
26:
21:
20:
2419:
2113:KaluzaâKlein
1865:Introduction
1791:Twin paradox
1770:
1586:at Wikibooks
1527:
1523:
1517:
1505:
1496:
1455:
1451:
1438:
1408:
1383:
1374:
1362:
1357:
1340:
1336:
1324:
1304:
1298:
1278:
1270:
1261:. See also:
1239:
1235:
1222:
1202:
1196:
1187:
1175:
1141:
1137:
1124:
1110:
1106:
1094:
1076:
1070:
1061:
1049:
1037:
1029:
987:
981:
971:
921:
916:
914:
884:
880:
876:
872:
868:
862:
857:
853:
849:
845:
841:
837:
833:
829:
825:
821:
818:
813:
809:
805:
801:
797:
793:
789:
785:
781:
777:
773:
769:
767:
753:
749:
745:
741:
737:
733:
725:
469:
465:
461:
457:
453:
449:
445:
441:
437:
433:
431:
424:
414:
410:
407:
403:
398:
394:
390:
386:
380:
355:
351:
344:
318:
314:
311:
307:
267:
258:
257:, published
255:Project MUSE
246:
240:
205:
200:
195:
190:
177:
171:
148:
138:
132:
102:simultaneity
99:
95:
89:
55:October 2022
52:
36:
34:lead section
2202:KerrâNewman
2173:Spherical:
2042:Other tests
1985:Singularity
1917:Formulation
1879:Fundamental
1733:Formulation
1714:Proper time
1675:Fundamental
887:. Note the
840:= 0.25 and
129:Description
2450:Categories
2354:Zel'dovich
2262:Scientists
2241:Alcubierre
2048:of Mercury
2046:precession
1975:Black hole
1858:Background
1850:relativity
1819:World line
1814:Light cone
1639:Background
1631:relativity
1621:Relativity
1511:, Springer
1425:Chapter IX
963:References
288:See also:
263:Ernst Mach
253:, through
251:Max Jammer
212:world line
2324:Robertson
2309:Friedmann
2304:Eddington
2294:de Sitter
2128:Solutions
2006:detectors
2001:astronomy
1968:Phenomena
1903:Geodesics
1806:Spacetime
1749:Phenomena
1562:119067219
1113:: 252â278
1022:254513121
997:1202.6578
865:worldline
612:−
597:−
529:−
497:−
241:In 1990,
206:In 1908,
39:summarize
2437:Category
2314:LemaĂźtre
2279:Einstein
2269:Poincaré
2229:Others:
2213:TaubâNUT
2179:interior
2101:theories
2099:Advanced
2066:redshift
1881:concepts
1699:Rapidity
1677:concepts
1488:33246058
1480:17758464
1428:Archived
1382:(1910).
1144:: 1â22,
931:See also
778:t′
774:x′
770:t′
701:′
667:′
584:′
484:′
462:z′
458:y′
454:x′
450:t′
224:rapidity
220:velocity
139:absolute
111:absolute
100:distant
2379:Hawking
2374:Penrose
2359:Novikov
2339:Wheeler
2284:Hilbert
2274:Lorentz
2231:pp-wave
2052:lensing
1848:General
1629:Special
1542:Bibcode
1460:Bibcode
1452:Science
1343:: 75â88
1244:Bibcode
1146:Bibcode
1002:Bibcode
728:is the
315:earlier
154:History
92:physics
2420:others
2409:Thorne
2399:Misner
2384:Taylor
2369:Geroch
2364:Ehlers
2334:Zwicky
2152:Kasner
1560:
1508:
1486:
1478:
1416:
1313:
1287:
1211:
1164:
1083:
1040:
1020:
893:slopes
848:â 0.25
724:where
460:, and
444:, and
319:before
304:times.
245:wrote
182:aether
166:, and
143:events
94:, the
2414:Weiss
2394:Bondi
2389:Hulse
2319:Milne
2223:discs
2167:Milne
2162:Gödel
2019:Virgo
1558:S2CID
1532:arXiv
1484:S2CID
1369:21(1)
1232:(PDF)
1134:(PDF)
1018:S2CID
992:arXiv
860:= 0.
764:line)
272:of a
2349:Kerr
2299:Weyl
2198:Kerr
2058:and
2012:and
2010:LIGO
1476:PMID
1414:ISBN
1311:ISBN
1285:ISBN
1209:ISBN
1162:ISBN
1081:ISBN
107:time
2404:Yau
2029:GEO
1550:doi
1468:doi
1390:441
1365:",
1252:doi
1240:322
1154:doi
1010:doi
814:t'
415:not
411:not
201:v/c
191:v/c
90:In
2452::
2078:/
2044::
1999::
1556:.
1548:.
1540:.
1528:69
1526:.
1482:,
1474:,
1466:,
1456:31
1454:,
1450:,
1423:,
1398:^
1341:10
1339:,
1335:,
1250:,
1238:,
1234:,
1186:,
1160:,
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1136:,
1109:,
1105:,
1060:,
1016:,
1008:,
1000:,
988:42
986:,
980:,
899:.
885:vx
883:=
871:=
828:,
802:vx
800:â
794:t'
788:,
776:,
756:.
750:vx
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452:,
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2177:(
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2082:(
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2008:(
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1648:(
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1470::
1462::
1392:.
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1254::
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1156::
1148::
1142:1
1119:.
1111:5
1012::
1004::
994::
881:t
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875:/
873:x
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804:/
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790:t
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752:/
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705:=
698:z
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674:y
671:=
664:y
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626:/
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588:=
581:x
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505:x
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488:=
481:t
470:v
466:x
446:z
442:y
438:x
434:t
399:t
395:x
391:x
387:t
57:)
53:(
43:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
