Abstract.
Relativistic twin paradox can have important implications for Mach’s principle. It has been recently argued that the behavior of the time asynchrony (different aging of twins) between two flying clocks along closed loops can be attributed to the existence of an absolute spacetime, which makes Mach’s principle unfeasible. In this paper, we shall revisit, and support, this argument from a different viewpoint using the Sagnac delay. This is possible since the above time asynchrony is known to be exactly the same as the Sagnac delay between two circumnavigating light rays re-uniting at the orbiting source/receiver. We shall calculate the effect of mass M and cosmological constant \( \Lambda\) on the delay in the general case of Kerr-de Sitter spacetime. It follows that, in the independent limits \( M\rightarrow 0\), spin \( a\rightarrow 0\) and \( \Lambda \rightarrow 0\), while the Kerr-dS metric reduces to Minkowski metric, the clocks need not tick in consonance since there will still appear a non-zero observable Sagnac delay. While we do not measure spacetime itself, we do measure the Sagnac effect, which signifies an absolute substantive Minkowski spacetime instead of a void. We shall demonstrate a completely different limiting behavior of Sagnac delay, heretofore unknown, between the case of non-geodesic and geodesic source/observer motion.
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References
H.I.M. Lichtenegger, L. Iorio, Eur. Phys. J. Plus 126, 129 (2011)
R. Schlegel, Nature (London) 242, 180 (1973)
J.C. Hafele, R.E. Keating, Science 177, 166 (1972)
J.C. Hafele, R.E. Keating, Science 177, 168 (1972)
G. Sagnac, C. R. Acad. Sci. Paris 157, 708 (1913)
A. Bhadra, T.B. Nayak, K.K. Nandi, Phys. Lett. A 295, 1 (2002)
K.K. Nandi, P.M. Alsing, J.C. Evans, T.B. Nayak, Phys. Rev. D 63, 084027 (2001)
A. Ashtekar, A. Magnon, J. Math. Phys. 16, 343 (1975)
A. Tartaglia, Phys. Rev. D 58, 064009 (1998)
J.M. Cohen, B. Mashhoon, Phys. Lett. A 181, 353 (1993)
A. Einstein, The Meaning of Relativity (Princeton U.P., Princeton, NJ, 1955) pp. 55--63
B.F. Schutz, A First Course in General Relativity (Cambridge U.P., New York, 1985) p. 298
T.A. Weber, Am. J. Phys. 65, 486 (1997)
L.D. Landau, E.M. Lifshitz, The Classical Theory of Fields, 4th ed. (Pergamon, New York, 1975) pp. 234--237
B. Carter, in Les Astres Occlus, edited by C. DeWitt, B. DeWitt (Gordon & Breach, New York, 1973)
J.A.R. Cembranos, A. de la Cruz-Dombriz, P. Jimeno Romero, Int. J. Geom. Methods Mod. Phys. 11, 1450001 (2014)
D. Pérez, G.E. Romero, S.E. Perez Bergliaffa, Astron. Astrophys. 551, A4 (2013)
Y. Aharonov, D. Bohm, Phys. Rev. 115, 485 (1959)
M.D. Semon, Found. Phys. 12, 49 (1982)
M.L. Ruggiero, Nuovo Cimento B 119, 893 (2004)
J.J. Sakurai, Phys. Rev. D 21, 2993 (1980)
K.K. Nandi, Y.-Z. Zhang, Phys. Rev. D 66, 063005 (2002)
P.M. Alsing, J.C. Evans, K.K. Nandi, Gen. Rel. Grav. 33, 1459 (2001)
L. Iorio, M.L. Ruggiero, JCAP 03, 024 (2009)
W. Rindler, M. Ishak, Phys. Rev. D 76, 043006 (2007)
A. Bhattacharya, G.M. Garipova, E. Laserra, A. Bhadra, K.K. Nandi, JCAP 02, 028 (2011)
A. Bhattacharya, A. Panchenko, M. Scalia, C. Cattani, K.K. Nandi, JCAP 09, 004 (2010)
C. Cattani, M. Scalia, E. Laserra, I. Bochicchio, K.K. Nandi, Phys. Rev. D 87, 047503 (2013)
M. Sereno, P. Jetzer, Phys. Rev. D 73, 063004 (2006)
V. Kagramanova, J. Kunz, C. Lämmerzahl, Phys. Lett. B 634, 465 (2006)
C. Chakraborty, P. Majumdar, Class. Quantum Grav. 31, 075006 (2014)
V. Kagramanova, J. Kunz, E. Hackmann, C. Lämmerzahl, Phys. Rev. D 81, 124044 (2010)
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Karimov, R.K., Izmailov, R.N., Garipova, G.M. et al. Sagnac delay in the Kerr-dS spacetime: Implications for Mach’s principle. Eur. Phys. J. Plus 133, 44 (2018). https://doi.org/10.1140/epjp/i2018-11919-x
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DOI: https://doi.org/10.1140/epjp/i2018-11919-x