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A constructive formulation of the one-way speed of light
1.A. Michelson and E. Morley, “On the relative motion of the Earth and the luminiferous Ether,” Am. J. Sci. 34(203), 333–345 (1887).
5.H. Ohanian, “Reply to Comment(s) on ‘The role of dynamics in the synchronization problem’ by A. Macdonald [Am. J. Phys. 73, 454 (2005)] and A. Martinez [Am. J. Phys. 73, 452 (2005),” Am. J. Phys. 73(5), 456–457 (2005).
6.A. S. Eddington, The Mathematical Theory of Relativity (Cambridge U. P., Cambridge, 1923).
7.H. Reichenbach, The Philosophy of Space and Time (Dover, New York, 1957)
7.[first published in German under the title Philosophie der Raum-Zeit-Lehre (Walter de Gruyter, Berlin, 1927)].
8.See particularly the references cited in the first two footnotes in Ref. 2.
9.A. Einstein, Relativity, The Special and General Theory (Three Rivers, New York, 1961).
11.The error in the method of slow separation of clocks is due to the directional dependence of the rate at which clocks run when moved at a specified speed in different directions in an anisotropic inertial frame. The error in synchronizing clocks by assuming the speed of light is constant in all directions is due to the invalidity of this assumption in an anisotropic inertial frame. In an isotropic inertial frame both methods are accurate and produce identical results. In an anisotropic inertial frame both methods are inaccurate but produce identical results.
12.D. Bohm, The Special Theory of Relativity (Benjamin, New York, 1965), Chap. 8.
13.H. A. Lorentz, “Simplified theory of electrical and optical phenomena in moving systems,” Proc. R. Acad. Sci. Amsterdam 1, 427–442 (1899).
14.H. A. Lorentz, “Electromagnetic phenomena in a system moving with any velocity smaller than that of light,” Proc. R. Acad. Sci. Amsterdam 6, 809–831 (1904).
15.Both Refs. 12 and 9 propose a time dilation function that does not contain any term in . The former is based on the conventional view of synchronization, and the latter on the relativistic view of synchronization. The analysis by the Lorentz theory of electrons (Ref. 12, Chap. 7) uses differential equations, and all functions are expected to be differentiable throughout the domain, which includes the point .
16.F. R. Tangherlini, “On energy-momentum tensor of gravitational field,” Nuovo Cimento, Suppl. 20, 1–19 (1961).
18.J. S. Bell, “How to teach special relativity,” Prog. Sci. Cult. 1, 67–80 (1976).
19.H. Minkowski, “Die grundgleichungen fur die elektromagnetischen vorgange in bewegten korpern,” Nachr. Ges. Wiss. Gottingen, Math.-Phys. Kl. 1908, 53–116, reprinted in
24.V. Guerra and R. de Abreu, “On the consistency between the assumption of a special system of reference and special relativity,” Found. Phys. 36(12), 1826–1845 (2006).
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