Lorentz Transformation and time dilatation
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Abstract
We consider two inertial frames S and and suppose that frame moves, for simplicity, in a single direction: the X -direction of frame S with a constant velocity v as measured in frame S.
Using homogeneity of space and time we derive a modified Lorentz Transformation (LT) between two inertial reference frames without using the second postulate of Einstein, i.e., we do not assume the invariant speed of light (in vacuum) under LT.
Roughly speaking we suppose: (H) Any clock which is at rest in its frame measures a small increment of time by some factor s=s(v). As a corollary of relativity theory (H) holds with Lorentz factor 1/γ. For s=1 we get the Galilean transformation of Newtonian physics, which assumes an absolute space and time. We also consider the relation between absolute space and Special Relativity Theory, thereafter STR.
It seems here that we need a physical explanation for (H).
We introduce Postulate 3. The two-way speed of light in x′ and z′ -directions of the frame S′ are c and outline derivation of (LT) in this setting. Note that Postulate 3 is a weaker assumption than Einstein's second postulate.
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Wigner EP. The unreasonable effectiveness of mathematics in the natural sciences. Richard Courant lecture in mathematical sciences delivered at New York University. May 11, 1959". Communications on Pure and Applied Mathematics. 1960; 13 (1): 1-14.
Kanda A, Prunescu M, Wong R. Logical Analysis of Relativity Theory. arXiv:2006.15289v1 [physics. hist-ph] 27 Jun 2020. Presented at Physics Beyond Relativity 2019 conference Prague. Czech Republic. October 20, 2019.
Reichenbach H. Axiomatization of the theory of relativity. 1969.
Sekerin VI. C28 The theory of relativity is a hoax of the 20th century. Novosibirsk: Publishing house "Art-Avenue". 2007; 128:ISBN 5-91220-011-X
Gift SJG. One-Way Speed of Light Relative to a Moving Observer. Applied Physics Research. January 2013; 5(1). DOI: 10.5539/apr.v5n1p135
Why is a debate about twin(s) paradox so bad? 2022. https://www.researchgate.net/post/Why_is_a_debate_about_twins_paradox_so_bad
Wu ETH. Special Relativity and Velocity Time Dilation - An Imagination or Just a Pure Mathematical Definition IOSR Journal Of Applied Physics (IOSR-JAP), e-ISSN: 2278-4861. 2021; 13: 2; 38-43.
F. Smarandache, Absolute Theory of Relativity (ATR) (January 30, 2016). Available at SSRN: https://ssrn.com/abstract=2724981 or http://dx.doi.org/10.2139/ssrn.2724981
Smarandache F. New Relativistic Paradoxes and Open Questions. Moroccan Society. 1983. https://fs.unm.edu/NewRelativisticParadoxes.pdf
de Abreu R, Guerra V. Relativity - Einstein's lost frame, extra]muros[, Lisboa. 2006.
Guerra V, de Abreu R. Special Relativity in Absolute Space: from a contradiction in terms to an obviousness. https://arxiv.org/ftp/physics/papers/0603/0603258.pdf
Ahlfors LV. Mobius Transformations in Several Dimensions, University of Minnesota. 1989.
Datta S. A Revisit to Lorentz Transformation without Light. 2022. ArXiv. /abs/2212.03706
Ignatowsky WV. Das relativit atsprinzip. Arch. Math. Phys. 1911; 3,1.
What is new about derivation of Lorentz transformation? ResearchGate. 2017, June 5. https://www.researchgate.net/post/What_is_new_about_derivation_of_Lorentz_transformation
Moylan P. Velocity reciprocity and the relativity principle. American Journal of Physics. 2022; 90:126. https://doi.org/10.1119/10.0009219.
Zeeman ECh. Causality implies the Lorentz group. Journal of Mathematical Physics. 1964; 5(4): 490-493, Bibcode:1964JMP.....5..490Z, doi:10.1063/1.1704140
Goldstein N. Inertiality Implies the Lorentz Group. Mathematical Physics Electronic Journal. 2007; 13:ISSN 1086-6655.
Levy J. The simplest derivation of the Lorentz transformation. 2006. ArXiv. /abs/physics/0606103
Minguzzi E. Differential aging from acceleration: An explicit formula. Am. J. Phys. 2005; 73: 876-880. arXiv:physics/0411233
Pal PB. Nothing but Relativity. 2003. ArXiv. https://doi.org/10.1088/0143-0807/24/3/312
Einstein A, Lorentz HA, Minkowski H, Weyl H. Arnold Sommerfeld. ed. The Principle of Relativity. Dover Publications: Mineola, NY. 1923; 38–49.
Walter SA. Poincaré on clocks in motion. Studies in History and Philosophy of Modern Physics. 2014; 47(1):131-141. doi 10.1016/j.shpsb.2014.01.003
Lambare J. Comment on "On the linearity of the generalized Lorentz transformation. July 2023. DOI: 10.32388/XEFX76, LicenseCC BY 4.0
Landau LD, Lifshitz EM. The Classical Theory of Fields. Butterworth-Heinemann. 1975; 2: ISBN 978-0-750-62768-9
Malament DB. The class of continuous timelike curves determines the topology of spacetime. Journal of Mathematical Physics. 1977; 18(7):1399–1404. https://doi.org/10.1063/1.523436
Landau LD, Lifšic iEM. Teoretičeskaja fizika III: Kvantovaya Mehanika, Moskva, Nauka. 1989.
Cuvaj C. Paul Langeyin and the Theory of Relativity. Japanese Studies in the History of Science. 1971; 10:113-142.
Bailey H. Measurements of relativistic time dilatation for positive and negative muons in a circular orbit. Nature. 1977; 268 (5618): 301–305.