1671:
those two clock-synchronization schemes are important tests of relativity, they don't speak of "one-way speed of light" in connection with such measurements anymore, because of their consistency with non-standard synchronizations. Those experiments are consistent with all synchronizations using anisotropic one-way speeds on the basis of isotropic
109:(1977). Contrary to Robertson, Mansouri–Sexl not only added additional parameters to the Lorentz transformation, but also discussed different synchronization schemes. The Poincaré–Einstein synchronization is only used in the preferred frame, while in relatively moving frames they used "external synchronization",
1194:
1670:
between synchronization by slow clock transport and by light. They emphasize that the negative results of those tests are also consistent with aether theories in which moving bodies are subject to time dilation. However, even though many recent authors agree that measurements of the equivalence of
116:
Since the two-way speed of light in moving frames is anisotropic in both models, and only this speed is measurable without synchronization scheme in experimental tests, the models are experimentally equivalent and summarized as the "Robertson–Mansouri–Sexl test theory" (RMS). On the other hand, in
1642:
The combination of those three experiments, together with the
Poincaré–Einstein convention to synchronize the clocks in all inertial frames, is necessary to obtain the complete Lorentz transformation. Michelson–Morley only tested the combination between β and δ, while Kennedy–Thorndike tested the
791:
By giving the effects of time dilation and length contraction the exact relativistic value, this test theory is experimentally equivalent to special relativity, independent of the chosen synchronization. So
Mansouri and Sexl spoke about the "remarkable result that a theory maintaining absolute
2297:
Reinhardt, S.; Saathoff, G.; Buhr, H.; Carlson, L. A.; Wolf, A.; Schwalm, D.; Karpuk, S.; Novotny, C.; Huber, G.; Zimmermann, M.; Holzwarth, R.; Udem, T.; Hänsch, T. W.; Gwinner, G. (2007). "Test of relativistic time dilation with fast optical atomic clocks at different velocities".
2243:
Tobar, M. E.; Wolf, P.; Bize, S.; Santarelli, G.; Flambaum, V. (2010). "Testing local
Lorentz and position invariance and variation of fundamental constants by searching the derivative of the comparison frequency between a cryogenic sapphire oscillator and hydrogen maser".
1643:
combination between α and β. To obtain the individual values, it's necessary to measure one of these quantities directly. This was achieved by Ives–Stilwell who measured α. So β can be determined using
Kennedy–Thorndike, and subsequently δ using Michelson–Morley.
29:
An experiment to test the theory of relativity cannot assume the theory is true, and therefore needs some other framework of assumptions that are wider than those of relativity. For example, a test theory may have a different postulate about light concerning
2443:
MĂĽller, Holger; Stanwix, Paul Louis; Tobar, Michael Edmund; Ivanov, Eugene; Wolf, Peter; Herrmann, Sven; Senger, Alexander; Kovalchuk, Evgeny; Peters, Achim (2007). "Relativity tests by complementary rotating
Michelson–Morley experiments".
1038:
1478:
643:) to be measured by experiment, and to see how close the experimental values come to the values predicted by special relativity. (Notice that Newtonian physics, which has been conclusively excluded by experiment, results from
121:
the two-way speed of light is isotropic, therefore RMS gives different experimental predictions than special relativity. By evaluating the RMS parameters, this theory serves as a framework for assessing possible violations of
1342:
1637:
1701:
and others. Contrary to the
Robertson–Mansouri–Sexl (RMS) framework, which is kinematic in nature and restricted to special relativity, SME not only accounts for special relativity, but for dynamical effects of the
760:
clock synchronization like the
Poincaré–Einstein synchronization by using light signals, or synchronization by slow clock transport. Those synchronization schemes are in general not equivalent, except the case when
1729:
at 31°53'S 115°53E. A preferred background (leading to
Lorentz Violation) could never be at rest relative to both of them. A large number of other tests has been carried out in recent years, such as the
1556:
736:
529:
808:. Though Mansouri, Sexl, and the overwhelming majority of physicists prefer special relativity over such an aether theory, because the latter "destroys the internal symmetry of a physical theory".
1026:
888:
957:
113:, the clock indications of the preferred frame are employed in those frames. Therefore, not only the two-way speed of light but also the one-way speed is anisotropic in moving frames.
90:
the average speed from source to observer and back, is isotropic, while it is anisotropic in relatively moving frames due to the parameters employed. In addition, Robertson used the
625:
1382:
236:
1721:
For instance, a couple of SME parameters was tested in a 2007 study sensitive to 10. It employed two simultaneous interferometers over a year's observation: Optical in
1265:
1244:
568:
190:
2190:
Herrmann, S.; Senger, A.; Möhle, K.; Nagel, M.; Kovalchuk, E. V.; Peters, A. (2009). "Rotating optical cavity experiment testing
Lorentz invariance at the 10 level".
423:
382:
298:
267:
1218:
1189:{\displaystyle {\frac {c}{c'}}\sim 1+\left(\beta -\delta -{\frac {1}{2}}\right){\frac {v^{2}}{c^{2}}}\sin ^{2}\theta +(\alpha -\beta +1){\frac {v^{2}}{c^{2}}}}
2664:
1397:
1659:
1270:
1574:
1957:
Anderson, R.; Vetharaniam, I.; Stedman, G. E. (1998). "Conventionality of synchronisation, gauge dependence and test theories of relativity".
2831:
2878:
1267:
from the direction in which the frame is moving. To verify that special relativity is correct, the expected values of the parameters are
1718:. RMS is fully included in SME, though the latter has a much larger group of parameters that can indicate any Lorentz or CPT violation.
2795:
2697:
1485:, testing the dependence of the speed of light on the velocity of the apparatus with respect to a preferred frame. Precision in 2010:
2857:
2826:
2657:
2702:
1488:
2763:
1743:
646:
432:
2800:
2758:
2733:
1936:
1692:
784:
2873:
2650:
42:
in many different ways. Test theories predicting different experimental results from
Einstein's special relativity, are
2390:
KosteleckĂ˝, V. Alan; Mewes, Matthew (2009). "Electrodynamics with Lorentz-violating operators of arbitrary dimension".
2768:
2748:
2333:
964:
826:
895:
2707:
2692:
1482:
2810:
2687:
1821:
Mansouri R.; Sexl R.U. (1977). "A test theory of special relativity. I: Simultaneity and clock synchronization".
1391:
792:
simultaneity is equivalent to special relativity." They also noticed the similarity between this test theory and
1999:
Lämmerzahl, Claus; Braxmaier, Claus; Dittus, Hansjörg; Müller, Holger; Peters, Achim; Schiller, Stephan (2002).
787:) and using the clocks of this frame to synchronize the clocks in all other frames ("absolute" synchronization).
2753:
2717:
1394:, testing the direction dependence of the speed of light with respect to a preferred frame. Precision in 2009:
816:
RMS is currently used in the evaluation process of many modern tests of Lorentz invariance. To second order in
2805:
2790:
2743:
2738:
2041:
Giulini, Domenico; Straumann, Norbert (2005). "Einstein's impact on the physics of the twentieth century".
1731:
1560:
2925:
2673:
1564:
2631:
753:
and cannot be determined by experiment. Mansouri–Sexl discussed the following synchronization schemes:
573:
2442:
319:
are the Cartesian coordinates measured in a postulated preferred frame (in which the speed of light
2904:
1726:
1688:
1387:
The fundamental experiments to test those parameters, still repeated with increased accuracy, are:
91:
51:
2345:
Bluhm, Robert (2006). "Overview of the SME: Implications and Phenomenology of Lorentz Violation".
1771:
196:
1646:
In addition to those second order tests, Mansouri and Sexl described some experiments measuring
2894:
2147:
Mansouri R.; Sexl R.U. (1977). "A test theory of special relativity: III. Second-order tests".
2000:
1998:
1663:
1249:
534:
156:
95:
79:
75:
31:
1347:
2097:
Mansouri R.; Sexl R.U. (1977). "A test theory of special relativity: II. First order tests".
391:
350:
273:
242:
2593:
2528:
2463:
2409:
2307:
2263:
2209:
2156:
2106:
2060:
2015:
1966:
1880:
1830:
1786:
1666:". These are interpreted by them as tests of the equivalence of internal synchronizations,
793:
1223:
8:
1734:. A list of derived and already measured SME-values was given by KosteleckĂ˝ and Russell.
1202:
2597:
2532:
2467:
2413:
2311:
2267:
2213:
2160:
2110:
2064:
2019:
1970:
1884:
1834:
1790:
2782:
2609:
2583:
2551:
2518:
2506:
2487:
2453:
2425:
2399:
2372:
2354:
2279:
2253:
2225:
2199:
2172:
2122:
2076:
2050:
1921:
1896:
1846:
1711:
1707:
426:
123:
118:
59:
39:
23:
1978:
1698:
384:
is the factor by which the interval between ticks of a clock increases when it moves (
2847:
2712:
2556:
2479:
2429:
2283:
2229:
2176:
2126:
1932:
1900:
1473:{\displaystyle \left(\beta -\delta -{\tfrac {1}{2}}\right)=(4\pm 8)\times 10^{-12}\,}
134:
In the following, the notation of Mansouri–Sexl is used. They chose the coefficients
106:
2637:
2574:
KosteleckĂ˝, V. A.; Russell, N. (2011). "Data tables for Lorentz and CPT violation".
2491:
2376:
1850:
805:
627:
then the Lorentz transformation follows. The purpose of the test theory is to allow
2613:
2601:
2546:
2536:
2471:
2417:
2364:
2315:
2271:
2217:
2164:
2114:
2080:
2068:
2023:
1974:
1928:
1888:
1838:
1794:
2475:
797:
750:
83:
35:
2072:
50:
which is equivalent to Robertson's theory. Another, more extensive model is the
2421:
2296:
2275:
2221:
1703:
55:
2642:
2027:
1799:
2919:
2852:
2778:
2605:
1568:
1337:{\displaystyle \alpha =-{\tfrac {1}{2}},\ \beta ={\tfrac {1}{2}},\ \delta =0}
801:
425:
is factor by which the length of a measuring rod is shortened when it moves (
385:
102:
22:
give a mathematical framework for analyzing results of experiments to verify
2368:
1632:{\displaystyle \left|\alpha +{\tfrac {1}{2}}\right|\leq 8.4\times 10^{-8}\,}
2560:
2483:
1715:
2242:
783:
clock synchronization by choosing a "preferred" reference frame (like the
1956:
17:
2541:
2189:
2055:
1697:
Another, more extensive, model is the Standard Model Extension (SME) by
2359:
2168:
2118:
1892:
1842:
2523:
1032:
Deviations from the two-way (round-trip) speed of light are given by:
2319:
2040:
2588:
2458:
2404:
2258:
2204:
1772:"Postulate versus Observation in the Special Theory of Relativity"
2389:
1871:
Zhang, Yuan Zhong (1995). "Test theories of special relativity".
1722:
1710:
as well. It investigates possible spontaneous breaking of both
1246:
is the speed of light measured in the moving frame at an angle
820:, the parameters of the RMS framework have the following form:
2573:
1551:{\displaystyle (\alpha -\beta +1)=-4.8(3.7)\times 10^{-8}\,}
343:
direction (with the same origin and parallel axes) at speed
150:
of the following transformation between reference frames:
731:{\displaystyle a(v)=b(v)=d(v)=1,{\text{ and }}e(v)=0\,.}
524:{\displaystyle 1/a(v)=b(v)=1/{\sqrt {1-v^{2}/c^{2}}}\,,}
339:
are the coordinates measured in a frame moving in the +
1590:
1419:
1308:
1284:
2632:
What is the experimental basis of special relativity?
1577:
1491:
1400:
1350:
1273:
1252:
1226:
1205:
1041:
967:
898:
829:
649:
576:
537:
435:
394:
353:
276:
245:
199:
159:
2146:
2096:
1820:
65:
2638:
Background information on Lorentz and CPT violation
2043:
Studies in History and Philosophy of Modern Physics
1923:
Special Relativity and Its Experimental Foundations
86:of reference, in which the two-way speed of light,
2001:"Kinematical Test Theories for Special Relativity"
1920:
1631:
1550:
1472:
1376:
1336:
1259:
1238:
1220:is the speed of light in the preferred frame, and
1212:
1188:
1020:
951:
882:
730:
619:
562:
523:
417:
376:
292:
261:
230:
184:
1918:
1870:
1028:, length perpendicular to the direction of motion
2917:
2504:
1769:
2672:
1021:{\displaystyle d(v)\sim 1+\delta v^{2}/c^{2}\,}
883:{\displaystyle a(v)\sim 1+\alpha v^{2}/c^{2}\,}
347:relative to the preferred frame. And therefore
952:{\displaystyle b(v)\sim 1+\beta v^{2}/c^{2}\,}
82:by adding additional parameters. He assumed a
2658:
2344:
1682:
1660:Rømer's determination of the speed of light
2665:
2651:
1952:
1950:
1948:
34:vs. two-way speed of light, it may have a
2827:Tests of relativistic energy and momentum
2630:Roberts, Schleif (2006); Relativity FAQ:
2587:
2550:
2540:
2522:
2457:
2403:
2358:
2332:Roberts, Schleif (2006): Relativity FAQ,
2257:
2203:
2054:
2008:International Journal of Modern Physics D
1798:
1628:
1547:
1469:
1373:
1256:
1235:
1209:
1017:
948:
879:
724:
613:
556:
517:
289:
258:
227:
181:
1914:
1912:
1910:
2764:Lorentz-violating neutrino oscillations
2142:
2140:
2138:
2136:
2092:
2090:
1945:
1866:
1864:
1862:
1860:
811:
2918:
1816:
1814:
1812:
1810:
1744:Parameterized post-Newtonian formalism
777:) have their exact relativistic value.
749:) depends only on the choice of clock
2832:Kaufmann–Bucherer–Neumann experiments
2801:Experimental testing of time dilation
2759:Antimatter tests of Lorentz violation
2734:Modern searches for Lorentz violation
2646:
2334:One-Way Tests of Light-Speed Isotropy
1994:
1992:
1990:
1988:
1907:
1765:
1763:
1761:
1759:
1693:Modern searches for Lorentz violation
2507:"Modern Tests of Lorentz Invariance"
2133:
2087:
1857:
1725:at 52°31'N 13°20'E and microwave in
2900:Test theories of special relativity
2326:
1807:
959:, length in the direction of motion
70:
13:
2034:
1985:
1873:General Relativity and Gravitation
1756:
101:A similar model was introduced by
14:
2937:
2858:Michelson–Gale–Pearson experiment
2769:Lorentz-violating electrodynamics
2749:Experiments of Rayleigh and Brace
2624:
92:Poincaré–Einstein synchronization
66:Robertson–Mansouri–Sexl framework
2811:Length contraction confirmations
2708:de Sitter double star experiment
1679:time dilation of moving bodies.
1662:) as being "measurements of the
620:{\displaystyle e(v)=-v/c^{2}\,,}
2567:
2498:
2436:
2383:
2338:
2290:
2236:
2183:
2879:Refutations of emission theory
2718:Measurements of neutrino speed
1528:
1522:
1510:
1492:
1450:
1438:
1159:
1141:
977:
971:
908:
902:
839:
833:
715:
709:
689:
683:
674:
668:
659:
653:
586:
580:
547:
541:
468:
462:
453:
447:
412:
406:
371:
365:
224:
209:
44:Robertson's test theory (1949)
38:of reference, and may violate
1:
2476:10.1103/PhysRevLett.99.050401
1979:10.1016/S0370-1573(97)00051-3
1749:
2874:Refutations of aether theory
2796:Moessbauer rotor experiments
2698:Moessbauer rotor experiments
2693:Kennedy–Thorndike experiment
1567:, and thus the relativistic
1483:Kennedy–Thorndike experiment
7:
2688:Michelson–Morley experiment
2674:Tests of special relativity
2073:10.1016/j.shpsb.2005.09.004
1737:
1565:relativistic Doppler effect
1392:Michelson–Morley experiment
231:{\displaystyle x=b(X-vT)\,}
48:Mansouri–Sexl theory (1977)
10:
2942:
2754:Trouton–Rankine experiment
2422:10.1103/PhysRevD.80.015020
2276:10.1103/PhysRevD.81.022003
2222:10.1103/PhysRevD.80.105011
1919:Zhang, Yuan Zhong (1997).
1686:
98:isotropic in all of them.
94:in all frames, making the
54:, which also includes the
2887:
2866:
2840:
2819:
2806:Hafele–Keating experiment
2777:
2726:
2680:
2576:Reviews of Modern Physics
2505:Mattingly, David (2005).
2028:10.1142/S021827180200261X
1800:10.1103/RevModPhys.21.378
1779:Reviews of Modern Physics
1770:Robertson, H. P. (1949).
1732:Hughes–Drever experiments
1260:{\displaystyle \theta \,}
563:{\displaystyle d(v)=1\,,}
185:{\displaystyle t=aT+ex\,}
129:
2905:Standard-Model Extension
2791:Ives–Stilwell experiment
2744:Trouton–Noble experiment
2739:Hughes–Drever experiment
2606:10.1103/RevModPhys.83.11
1689:Standard-Model Extension
1683:Standard Model Extension
1561:Ives–Stilwell experiment
1377:{\displaystyle c/c'=1\,}
52:Standard-Model Extension
2369:10.1007/3-540-34523-X_8
2895:One-way speed of light
1664:one-way speed of light
1633:
1552:
1474:
1378:
1338:
1261:
1240:
1214:
1190:
1022:
953:
884:
732:
621:
564:
525:
419:
418:{\displaystyle 1/b(v)}
378:
377:{\displaystyle 1/a(v)}
294:
293:{\displaystyle z=dZ\,}
263:
262:{\displaystyle y=dY\,}
232:
186:
96:one-way speed of light
80:Lorentz transformation
76:Howard Percy Robertson
32:one-way speed of light
2703:Resonator experiments
1634:
1571:. Precision in 2007:
1553:
1475:
1379:
1339:
1262:
1241:
1215:
1191:
1023:
954:
885:
733:
622:
565:
526:
420:
379:
295:
264:
233:
187:
78:(1949) extended the
20:of special relativity
1575:
1489:
1398:
1348:
1271:
1250:
1239:{\displaystyle c'\,}
1224:
1203:
1039:
965:
896:
827:
812:Experiments with RMS
794:Lorentz ether theory
647:
574:
535:
433:
392:
351:
274:
243:
197:
157:
2820:Relativistic energy
2598:2011RvMP...83...11K
2542:10.12942/lrr-2005-5
2533:2005LRR.....8....5M
2511:Living Rev. Relativ
2468:2007PhRvL..99e0401M
2414:2009PhRvD..80a5020K
2312:2007NatPh...3..861R
2268:2010PhRvD..81b2003T
2214:2009PhRvD..80j5011H
2161:1977GReGr...8..809M
2111:1977GReGr...8..515M
2065:2006SHPMP..37..115G
2020:2002IJMPD..11.1109L
1971:1998PhR...295...93A
1885:1995GReGr..27..475Z
1835:1977GReGr...8..497M
1791:1949RvMP...21..378R
1675:speed of light and
1213:{\displaystyle c\,}
323:is isotropic), and
2926:Special relativity
2783:Length contraction
2727:Lorentz invariance
2169:10.1007/BF00759585
2119:10.1007/BF00762635
1893:10.1007/BF02105074
1843:10.1007/BF00762634
1712:Lorentz invariance
1708:general relativity
1629:
1599:
1548:
1470:
1428:
1374:
1334:
1317:
1293:
1257:
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1210:
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1018:
949:
880:
728:
617:
560:
521:
427:length contraction
415:
374:
290:
259:
228:
182:
124:Lorentz invariance
119:special relativity
60:general relativity
40:Lorentz invariance
24:special relativity
2913:
2912:
2853:Sagnac experiment
2848:Fizeau experiment
2713:Hammar experiment
2392:Physical Review D
2246:Physical Review D
2192:Physical Review D
1938:978-981-02-2749-4
1650:order effects in
1598:
1427:
1324:
1316:
1300:
1292:
1184:
1120:
1091:
1055:
704:
515:
107:Roman Ulrich Sexl
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2347:Lect. Notes Phys
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2320:10.1038/nphys778
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2240:
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2149:Gen. Rel. Gravit
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2099:Gen. Rel. Gravit
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2085:
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2031:
2014:(7): 1109–1136.
2005:
1996:
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1982:
1954:
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1929:World Scientific
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1823:Gen. Rel. Gravit
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191:
189:
188:
183:
71:Basic principles
2941:
2940:
2936:
2935:
2934:
2932:
2931:
2930:
2916:
2915:
2914:
2909:
2883:
2862:
2836:
2815:
2781:
2773:
2722:
2676:
2671:
2627:
2622:
2621:
2572:
2568:
2503:
2499:
2446:Phys. Rev. Lett
2441:
2437:
2388:
2384:
2343:
2339:
2331:
2327:
2306:(12): 861–864.
2295:
2291:
2241:
2237:
2198:(100): 105011.
2188:
2184:
2155:(10): 809–814.
2145:
2134:
2095:
2088:
2056:physics/0507107
2039:
2035:
2003:
1997:
1986:
1965:(3–4): 93–180.
1959:Physics Reports
1955:
1946:
1939:
1917:
1908:
1869:
1858:
1819:
1808:
1774:
1768:
1757:
1752:
1740:
1699:Alan KosteleckĂ˝
1695:
1687:Main articles:
1685:
1619:
1615:
1589:
1582:
1578:
1576:
1573:
1572:
1538:
1534:
1490:
1487:
1486:
1460:
1456:
1418:
1405:
1401:
1399:
1396:
1395:
1359:
1354:
1349:
1346:
1345:
1307:
1283:
1272:
1269:
1268:
1251:
1248:
1247:
1227:
1225:
1222:
1221:
1204:
1201:
1200:
1178:
1174:
1168:
1164:
1162:
1126:
1122:
1114:
1110:
1104:
1100:
1098:
1083:
1070:
1066:
1047:
1042:
1040:
1037:
1036:
1011:
1007:
1002:
996:
992:
966:
963:
962:
942:
938:
933:
927:
923:
897:
894:
893:
890:, time dilation
873:
869:
864:
858:
854:
828:
825:
824:
814:
798:Hendrik Lorentz
751:synchronization
703: and
701:
648:
645:
644:
607:
603:
598:
575:
572:
571:
536:
533:
532:
509:
505:
500:
494:
490:
482:
477:
439:
434:
431:
430:
398:
393:
390:
389:
357:
352:
349:
348:
275:
272:
271:
244:
241:
240:
198:
195:
194:
158:
155:
154:
132:
84:preferred frame
73:
68:
36:preferred frame
12:
11:
5:
2939:
2929:
2928:
2911:
2910:
2908:
2907:
2902:
2897:
2891:
2889:
2885:
2884:
2882:
2881:
2876:
2870:
2868:
2864:
2863:
2861:
2860:
2855:
2850:
2844:
2842:
2838:
2837:
2835:
2834:
2829:
2823:
2821:
2817:
2816:
2814:
2813:
2808:
2803:
2798:
2793:
2787:
2785:
2775:
2774:
2772:
2771:
2766:
2761:
2756:
2751:
2746:
2741:
2736:
2730:
2728:
2724:
2723:
2721:
2720:
2715:
2710:
2705:
2700:
2695:
2690:
2684:
2682:
2681:Speed/isotropy
2678:
2677:
2670:
2669:
2662:
2655:
2647:
2641:
2640:
2634:
2626:
2625:External links
2623:
2620:
2619:
2566:
2497:
2435:
2382:
2360:hep-ph/0506054
2337:
2325:
2300:Nature Physics
2289:
2235:
2182:
2132:
2105:(7): 515–524.
2086:
2049:(1): 115–173.
2033:
1984:
1944:
1937:
1906:
1879:(5): 475–493.
1856:
1829:(7): 497–513.
1806:
1785:(3): 378–382.
1754:
1753:
1751:
1748:
1747:
1746:
1739:
1736:
1704:standard model
1684:
1681:
1640:
1639:
1625:
1622:
1618:
1614:
1611:
1608:
1604:
1597:
1594:
1588:
1585:
1581:
1563:, testing the
1558:
1544:
1541:
1537:
1533:
1530:
1527:
1524:
1521:
1518:
1515:
1512:
1509:
1506:
1503:
1500:
1497:
1494:
1480:
1466:
1463:
1459:
1455:
1452:
1449:
1446:
1443:
1440:
1437:
1433:
1426:
1423:
1417:
1414:
1411:
1408:
1404:
1372:
1369:
1365:
1362:
1357:
1353:
1333:
1330:
1327:
1321:
1315:
1312:
1306:
1303:
1297:
1291:
1288:
1282:
1279:
1276:
1255:
1233:
1230:
1208:
1197:
1196:
1181:
1177:
1171:
1167:
1161:
1158:
1155:
1152:
1149:
1146:
1143:
1140:
1137:
1134:
1129:
1125:
1117:
1113:
1107:
1103:
1096:
1090:
1087:
1082:
1079:
1076:
1073:
1069:
1065:
1062:
1059:
1053:
1050:
1046:
1030:
1029:
1014:
1010:
1005:
999:
995:
991:
988:
985:
982:
979:
976:
973:
970:
960:
945:
941:
936:
930:
926:
922:
919:
916:
913:
910:
907:
904:
901:
891:
876:
872:
867:
861:
857:
853:
850:
847:
844:
841:
838:
835:
832:
813:
810:
806:Henri Poincaré
789:
788:
778:
727:
723:
720:
717:
714:
711:
708:
700:
697:
694:
691:
688:
685:
682:
679:
676:
673:
670:
667:
664:
661:
658:
655:
652:
616:
610:
606:
601:
597:
594:
591:
588:
585:
582:
579:
559:
555:
552:
549:
546:
543:
540:
520:
512:
508:
503:
497:
493:
489:
486:
480:
476:
473:
470:
467:
464:
461:
458:
455:
452:
449:
446:
442:
438:
414:
411:
408:
405:
401:
397:
373:
370:
367:
364:
360:
356:
301:
300:
288:
285:
282:
279:
269:
257:
254:
251:
248:
238:
226:
223:
220:
217:
214:
211:
208:
205:
202:
192:
180:
177:
174:
171:
168:
165:
162:
131:
128:
72:
69:
67:
64:
56:standard model
9:
6:
4:
3:
2:
2938:
2927:
2924:
2923:
2921:
2906:
2903:
2901:
2898:
2896:
2893:
2892:
2890:
2886:
2880:
2877:
2875:
2872:
2871:
2869:
2865:
2859:
2856:
2854:
2851:
2849:
2846:
2845:
2843:
2841:Fizeau/Sagnac
2839:
2833:
2830:
2828:
2825:
2824:
2822:
2818:
2812:
2809:
2807:
2804:
2802:
2799:
2797:
2794:
2792:
2789:
2788:
2786:
2784:
2780:
2779:Time dilation
2776:
2770:
2767:
2765:
2762:
2760:
2757:
2755:
2752:
2750:
2747:
2745:
2742:
2740:
2737:
2735:
2732:
2731:
2729:
2725:
2719:
2716:
2714:
2711:
2709:
2706:
2704:
2701:
2699:
2696:
2694:
2691:
2689:
2686:
2685:
2683:
2679:
2675:
2668:
2663:
2661:
2656:
2654:
2649:
2648:
2645:
2639:
2635:
2633:
2629:
2628:
2615:
2611:
2607:
2603:
2599:
2595:
2590:
2585:
2581:
2577:
2570:
2562:
2558:
2553:
2548:
2543:
2538:
2534:
2530:
2525:
2524:gr-qc/0502097
2520:
2516:
2512:
2508:
2501:
2493:
2489:
2485:
2481:
2477:
2473:
2469:
2465:
2460:
2455:
2452:(5): 050401.
2451:
2447:
2439:
2431:
2427:
2423:
2419:
2415:
2411:
2406:
2401:
2398:(1): 015020.
2397:
2393:
2386:
2378:
2374:
2370:
2366:
2361:
2356:
2352:
2348:
2341:
2335:
2329:
2321:
2317:
2313:
2309:
2305:
2301:
2293:
2285:
2281:
2277:
2273:
2269:
2265:
2260:
2255:
2252:(2): 022003.
2251:
2247:
2239:
2231:
2227:
2223:
2219:
2215:
2211:
2206:
2201:
2197:
2193:
2186:
2178:
2174:
2170:
2166:
2162:
2158:
2154:
2150:
2143:
2141:
2139:
2137:
2128:
2124:
2120:
2116:
2112:
2108:
2104:
2100:
2093:
2091:
2082:
2078:
2074:
2070:
2066:
2062:
2057:
2052:
2048:
2044:
2037:
2029:
2025:
2021:
2017:
2013:
2009:
2002:
1995:
1993:
1991:
1989:
1980:
1976:
1972:
1968:
1964:
1960:
1953:
1951:
1949:
1940:
1934:
1930:
1925:
1924:
1915:
1913:
1911:
1902:
1898:
1894:
1890:
1886:
1882:
1878:
1874:
1867:
1865:
1863:
1861:
1852:
1848:
1844:
1840:
1836:
1832:
1828:
1824:
1817:
1815:
1813:
1811:
1801:
1796:
1792:
1788:
1784:
1780:
1773:
1766:
1764:
1762:
1760:
1755:
1745:
1742:
1741:
1735:
1733:
1728:
1724:
1719:
1717:
1713:
1709:
1705:
1700:
1694:
1690:
1680:
1678:
1674:
1669:
1665:
1661:
1657:
1653:
1649:
1644:
1623:
1620:
1616:
1612:
1609:
1606:
1602:
1595:
1592:
1586:
1583:
1579:
1570:
1569:time dilation
1566:
1562:
1559:
1542:
1539:
1535:
1531:
1525:
1519:
1516:
1513:
1507:
1504:
1501:
1498:
1495:
1484:
1481:
1464:
1461:
1457:
1453:
1447:
1444:
1441:
1435:
1431:
1424:
1421:
1415:
1412:
1409:
1406:
1402:
1393:
1390:
1389:
1388:
1385:
1370:
1367:
1363:
1360:
1355:
1351:
1331:
1328:
1325:
1319:
1313:
1310:
1304:
1301:
1295:
1289:
1286:
1280:
1277:
1274:
1253:
1231:
1228:
1206:
1179:
1175:
1169:
1165:
1156:
1153:
1150:
1147:
1144:
1138:
1135:
1132:
1127:
1123:
1115:
1111:
1105:
1101:
1094:
1088:
1085:
1080:
1077:
1074:
1071:
1067:
1063:
1060:
1057:
1051:
1048:
1044:
1035:
1034:
1033:
1012:
1008:
1003:
997:
993:
989:
986:
983:
980:
974:
968:
961:
943:
939:
934:
928:
924:
920:
917:
914:
911:
905:
899:
892:
874:
870:
865:
859:
855:
851:
848:
845:
842:
836:
830:
823:
822:
821:
819:
809:
807:
803:
802:Joseph Larmor
799:
795:
786:
782:
779:
776:
772:
768:
764:
759:
756:
755:
754:
752:
748:
744:
741:The value of
739:
725:
721:
718:
712:
706:
698:
695:
692:
686:
680:
677:
671:
665:
662:
656:
650:
642:
638:
634:
630:
614:
608:
604:
599:
595:
592:
589:
583:
577:
557:
553:
550:
544:
538:
518:
510:
506:
501:
495:
491:
487:
484:
478:
474:
471:
465:
459:
456:
450:
444:
440:
436:
428:
409:
403:
399:
395:
387:
386:time dilation
368:
362:
358:
354:
346:
342:
338:
334:
330:
326:
322:
318:
314:
310:
306:
286:
283:
280:
277:
270:
255:
252:
249:
246:
239:
221:
218:
215:
212:
206:
203:
200:
193:
178:
175:
172:
169:
166:
163:
160:
153:
152:
151:
149:
145:
141:
137:
127:
125:
120:
114:
112:
108:
104:
103:Reza Mansouri
99:
97:
93:
89:
85:
81:
77:
63:
61:
57:
53:
49:
45:
41:
37:
33:
27:
25:
21:
19:
18:Test theories
2899:
2867:Alternatives
2636:KosteleckĂ˝:
2582:(1): 11–32.
2579:
2575:
2569:
2514:
2510:
2500:
2449:
2445:
2438:
2395:
2391:
2385:
2350:
2346:
2340:
2328:
2303:
2299:
2292:
2249:
2245:
2238:
2195:
2191:
2185:
2152:
2148:
2102:
2098:
2046:
2042:
2036:
2011:
2007:
1962:
1958:
1922:
1876:
1872:
1826:
1822:
1782:
1778:
1720:
1716:CPT symmetry
1696:
1676:
1672:
1667:
1655:
1651:
1647:
1645:
1641:
1386:
1198:
1031:
817:
815:
790:
780:
774:
770:
766:
762:
757:
746:
742:
740:
640:
636:
632:
628:
344:
340:
336:
332:
328:
324:
320:
316:
312:
308:
304:
302:
147:
143:
139:
135:
133:
115:
110:
100:
87:
74:
47:
43:
28:
16:
15:
2353:: 191–226.
1344:, and thus
1750:References
46:, and the
2589:0801.0287
2459:0706.2031
2430:119241509
2405:0905.0031
2284:119262822
2259:0912.2803
2230:118346408
2205:1002.1284
2177:121834946
2127:121525782
1901:121455464
1658:(such as
1621:−
1613:×
1607:≤
1584:α
1540:−
1532:×
1517:−
1502:β
1499:−
1496:α
1462:−
1454:×
1445:±
1416:−
1413:δ
1410:−
1407:β
1326:δ
1302:β
1281:−
1275:α
1254:θ
1151:β
1148:−
1145:α
1136:θ
1133:
1081:−
1078:δ
1075:−
1072:β
1058:∼
990:δ
981:∼
921:β
912:∼
852:α
843:∼
593:−
488:−
216:−
2920:Category
2561:28163649
2517:(5): 5.
2492:33003084
2484:17930733
2377:15898253
1851:67852594
1738:See also
1364:′
1232:′
1052:′
781:External
758:Internal
2888:General
2614:3236027
2594:Bibcode
2552:5253993
2529:Bibcode
2464:Bibcode
2410:Bibcode
2308:Bibcode
2264:Bibcode
2210:Bibcode
2157:Bibcode
2107:Bibcode
2081:2062237
2061:Bibcode
2016:Bibcode
1967:Bibcode
1881:Bibcode
1831:Bibcode
1787:Bibcode
1677:two-way
1673:two-way
2612:
2559:
2549:
2490:
2482:
2428:
2375:
2282:
2228:
2175:
2125:
2079:
1935:
1899:
1849:
1723:Berlin
1323:
1299:
1199:where
769:) and
635:) and
429:). If
388:) and
303:where
130:Theory
2610:S2CID
2584:arXiv
2519:arXiv
2488:S2CID
2454:arXiv
2426:S2CID
2400:arXiv
2373:S2CID
2355:arXiv
2280:S2CID
2254:arXiv
2226:S2CID
2200:arXiv
2173:S2CID
2123:S2CID
2077:S2CID
2051:arXiv
2004:(PDF)
1897:S2CID
1847:S2CID
1775:(PDF)
1727:Perth
1648:first
2557:PMID
2480:PMID
1933:ISBN
1714:and
1706:and
1691:and
1668:i.e.
804:and
570:and
531:and
111:i.e.
105:and
88:i.e.
58:and
2602:doi
2547:PMC
2537:doi
2472:doi
2418:doi
2365:doi
2351:702
2316:doi
2272:doi
2218:doi
2165:doi
2115:doi
2069:doi
2024:doi
1975:doi
1963:295
1889:doi
1839:doi
1795:doi
1610:8.4
1526:3.7
1520:4.8
1124:sin
818:v/c
796:of
785:CMB
2922::
2608:.
2600:.
2592:.
2580:83
2578:.
2555:.
2545:.
2535:.
2527:.
2513:.
2509:.
2486:.
2478:.
2470:.
2462:.
2450:99
2448:.
2424:.
2416:.
2408:.
2396:80
2394:.
2371:.
2363:.
2349:.
2314:.
2302:.
2278:.
2270:.
2262:.
2250:81
2248:.
2224:.
2216:.
2208:.
2196:80
2194:.
2171:.
2163:.
2151:.
2135:^
2121:.
2113:.
2101:.
2089:^
2075:.
2067:.
2059:.
2047:37
2045:.
2022:.
2012:11
2010:.
2006:.
1987:^
1973:.
1961:.
1947:^
1931:.
1927:.
1909:^
1895:.
1887:.
1877:27
1875:.
1859:^
1845:.
1837:.
1825:.
1809:^
1793:.
1783:21
1781:.
1777:.
1758:^
1617:10
1536:10
1465:12
1458:10
1384:.
800:,
738:)
335:,
331:,
327:,
315:,
311:,
307:,
146:,
142:,
138:,
126:.
62:.
26:.
2666:e
2659:t
2652:v
2616:.
2604::
2596::
2586::
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