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Test theories of special relativity

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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
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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
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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
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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
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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".
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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".
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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.
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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
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Müller, 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".
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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
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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
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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
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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
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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
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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
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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".
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Anderson, R.; Vetharaniam, I.; Stedman, G. E. (1998). "Conventionality of synchronisation, gauge dependence and test theories of relativity".
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from the direction in which the frame is moving. To verify that special relativity is correct, the expected values of the parameters are
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in many different ways. Test theories predicting different experimental results from Einstein's special relativity, are
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KosteleckĂ˝, V. Alan; Mewes, Matthew (2009). "Electrodynamics with Lorentz-violating operators of arbitrary dimension".
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Mansouri R.; Sexl R.U. (1977). "A test theory of special relativity. I: Simultaneity and clock synchronization".
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simultaneity is equivalent to special relativity." They also noticed the similarity between this test theory and
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Lämmerzahl, Claus; Braxmaier, Claus; Dittus, Hansjörg; Müller, Holger; Peters, Achim; Schiller, Stephan (2002).
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RMS is currently used in the evaluation process of many modern tests of Lorentz invariance. To second order in
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Giulini, Domenico; Straumann, Norbert (2005). "Einstein's impact on the physics of the twentieth century".
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and cannot be determined by experiment. Mansouri–Sexl discussed the following synchronization schemes:
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are the Cartesian coordinates measured in a postulated preferred frame (in which the speed of light
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The fundamental experiments to test those parameters, still repeated with increased accuracy, are:
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Bluhm, Robert (2006). "Overview of the SME: Implications and Phenomenology of Lorentz Violation".
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In addition to those second order tests, Mansouri and Sexl described some experiments measuring
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Mansouri R.; Sexl R.U. (1977). "A test theory of special relativity: III. Second-order tests".
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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 (
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In the following, the notation of Mansouri–Sexl is used. They chose the coefficients
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KosteleckĂ˝, V. A.; Russell, N. (2011). "Data tables for Lorentz and CPT violation".
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then the Lorentz transformation follows. The purpose of the test theory is to allow
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which is equivalent to Robertson's theory. Another, more extensive model is the
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is factor by which the length of a measuring rod is shortened when it moves (
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give a mathematical framework for analyzing results of experiments to verify
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clock synchronization by choosing a "preferred" reference frame (like the
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Another, more extensive, model is the Standard Model Extension (SME) by
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Deviations from the two-way (round-trip) speed of light are given by:
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Zhang, Yuan Zhong (1995). "Test theories of special relativity".
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as well. It investigates possible spontaneous breaking of both
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is the speed of light measured in the moving frame at an angle
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direction (with the same origin and parallel axes) at speed
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of the following transformation between reference frames:
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are the coordinates measured in a frame moving in the +
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What is the experimental basis of special relativity?
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Background information on Lorentz and CPT violation
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Studies in History and Philosophy of Modern Physics
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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: 1236: 1210: 1186: 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 2933: 2667: 2660: 2653: 2644: 2643: 2618: 2617: 2591: 2571: 2565: 2564: 2554: 2544: 2526: 2502: 2496: 2495: 2461: 2440: 2434: 2433: 2407: 2387: 2381: 2380: 2362: 2347:Lect. Notes Phys 2342: 2336: 2330: 2324: 2323: 2320:10.1038/nphys778 2294: 2288: 2287: 2261: 2240: 2234: 2233: 2207: 2187: 2181: 2180: 2149:Gen. Rel. Gravit 2144: 2131: 2130: 2099:Gen. Rel. Gravit 2094: 2085: 2084: 2058: 2038: 2032: 2031: 2014:(7): 1109–1136. 2005: 1996: 1983: 1982: 1954: 1943: 1942: 1929:World Scientific 1926: 1916: 1905: 1904: 1868: 1855: 1854: 1823:Gen. Rel. 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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 PoincarĂ© 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:: 2563:. 2539:: 2531:: 2521:: 2515:8 2494:. 2474:: 2466:: 2456:: 2432:. 2420:: 2412:: 2402:: 2379:. 2367:: 2357:: 2322:. 2318:: 2310:: 2304:3 2286:. 2274:: 2266:: 2256:: 2232:. 2220:: 2212:: 2202:: 2179:. 2167:: 2159:: 2153:8 2129:. 2117:: 2109:: 2103:8 2083:. 2071:: 2063:: 2053:: 2030:. 2026:: 2018:: 1981:. 1977:: 1969:: 1941:. 1903:. 1891:: 1883:: 1853:. 1841:: 1833:: 1827:8 1803:. 1797:: 1789:: 1656:c 1654:/ 1652:v 1624:8 1603:| 1596:2 1593:1 1587:+ 1580:| 1543:8 1529:) 1523:( 1514:= 1511:) 1508:1 1505:+ 1493:( 1451:) 1448:8 1442:4 1439:( 1436:= 1432:) 1425:2 1422:1 1403:( 1371:1 1368:= 1361:c 1356:/ 1352:c 1332:0 1329:= 1320:, 1314:2 1311:1 1305:= 1296:, 1290:2 1287:1 1278:= 1229:c 1207:c 1180:2 1176:c 1170:2 1166:v 1160:) 1157:1 1154:+ 1142:( 1139:+ 1128:2 1116:2 1112:c 1106:2 1102:v 1095:) 1089:2 1086:1 1068:( 1064:+ 1061:1 1049:c 1045:c 1013:2 1009:c 1004:/ 998:2 994:v 987:+ 984:1 978:) 975:v 972:( 969:d 944:2 940:c 935:/ 929:2 925:v 918:+ 915:1 909:) 906:v 903:( 900:b 875:2 871:c 866:/ 860:2 856:v 849:+ 846:1 840:) 837:v 834:( 831:a 775:v 773:( 771:b 767:v 765:( 763:a 747:v 745:( 743:e 726:. 722:0 719:= 716:) 713:v 710:( 707:e 699:, 696:1 693:= 690:) 687:v 684:( 681:d 678:= 675:) 672:v 669:( 666:b 663:= 660:) 657:v 654:( 651:a 641:v 639:( 637:b 633:v 631:( 629:a 615:, 609:2 605:c 600:/ 596:v 590:= 587:) 584:v 581:( 578:e 558:, 554:1 551:= 548:) 545:v 542:( 539:d 519:, 511:2 507:c 502:/ 496:2 492:v 485:1 479:/ 475:1 472:= 469:) 466:v 463:( 460:b 457:= 454:) 451:v 448:( 445:a 441:/ 437:1 413:) 410:v 407:( 404:b 400:/ 396:1 372:) 369:v 366:( 363:a 359:/ 355:1 345:v 341:X 337:z 333:y 329:x 325:t 321:c 317:Z 313:Y 309:X 305:T 287:Z 284:d 281:= 278:z 256:Y 253:d 250:= 247:y 225:) 222:T 219:v 213:X 210:( 207:b 204:= 201:x 179:x 176:e 173:+ 170:T 167:a 164:= 161:t 148:e 144:d 140:b 136:a

Index

Test theories
special relativity
one-way speed of light
preferred frame
Lorentz invariance
Standard-Model Extension
standard model
general relativity
Howard Percy Robertson
Lorentz transformation
preferred frame
Poincaré–Einstein synchronization
one-way speed of light
Reza Mansouri
Roman Ulrich Sexl
special relativity
Lorentz invariance
time dilation
length contraction
synchronization
CMB
Lorentz ether theory
Hendrik Lorentz
Joseph Larmor
Henri Poincaré
Michelson–Morley experiment
Kennedy–Thorndike experiment
Ives–Stilwell experiment
relativistic Doppler effect
time dilation

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