Abstract
In this chapter we begin to develop the consequences of Einstein’s “first postulate,” the relativity principle (RP)—a principle of venerable standing in mechanics, now newly extended to all of physics. Einstein chose to ignite it with a spark from electromagnetic theory: his “second postulate,” according to which light travels rectilinearly with constant speed c in vacuum in every inertial frame. After the blaze, the old relativity principle showed its new mathematical core: the Lorentz transformation (LT). Previously “common sense” had shown that the core “must” be the Galilean transformation (GT).
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References
J. G. Fox, Am. J. Phys. 30, 297 (1962).
See T. A. Filippas and J. G. Fox, Phys. Rev. 135, B1071 (1964), where further references can be found.
However, in some modern areas such as the quantum theory of interacting systems, there still remain fundamental difficulties with the relativistic formulation.
As Einstein wrote in 1952: “There is, of course, no logical way to the establishment of a theory . . .” (cf. p. 35 of R. S. Shankland, Am. J. Phys. 32, 16 (1964)). See also pp. 11, 12 of Einstein’s Autobiographical Notes in Albert Einstein: Philosopher-Scientist (ed. P. A. Schilpp), 1949.
See p. 35 of R. S. Shankland, Am. J. Phys. 32, 16 (1964).
Cf. RSR (1960).
See, for example, V. Fock, The Theory of Space Time and Gravitation, Pergamon Press, 1959, Appendix A.
The same limitation results from the demand that uniformly moving bodies transform into uniformly moving bodies (conservation of parallelism). Another argument for linearity can be made from the constancy of the speed of light—see, for example, RSR, page 17.
The following remarks to the end of the present paragraph are intended to be suggestive only, and no very accurate understanding is called for at this stage.
We are here violating our resolve to work in strict inertial frames only! The conscientious reader may replace the force of gravity acting down the hole by a sandblast from the top—the result will be the same. For a fuller discussion of this paradox, see W. Rindler, Am. J. Phys. 29, 365 (1961).
D. H. Perkins, Introduction to High Energy Physics, Addison-Wesley Pub. Co. (1972), p. 192.
J. C. Hafele and R. Keating, Science 177, 166 (1972). The flights were made in easterly and westerly directions, respectively, which allowed a separation of the velocity effect from the “gravitational time dilation” effect mentioned in Section 1.21.
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© 1977 Wolfgang Rindler
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Rindler, W. (1977). Einsteinian Kinematics. In: Essential Relativity. Text and Monographs in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-86650-0_2
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DOI: https://doi.org/10.1007/978-3-642-86650-0_2
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