Hostname: page-component-848d4c4894-hfldf Total loading time: 0 Render date: 2024-04-30T18:22:58.027Z Has data issue: false hasContentIssue false
  • English
  • Français

The Lorentz Transformation Group of the Special Theory of Relativity without Einstein's Isotropy Convention

Published online by Cambridge University Press:  01 April 2022

Abraham Ungar
Abraham Ungar*
Affiliation:
Department of Mathematics, North Dakota State University
Get access Rights & Permissions [Opens in a new window]

Abstract

Inertial frames and Lorentz transformations have a preferred status in the special theory of relativity (STR). Lorentz transformations, in turn, embody Einstein's convention that the velocity of light is isotropic, a convention that is necessary for the establishment of a standard signal synchrony. If the preferred status of Lorentz transformations in STR is not due to some particular bias introduced by a convention on signal synchronism, but to the fact that the Lorentz transformation group is the symmetry group of the theory, then the signal synchronism is not a matter of convention but rather a matter of fact. In order to explore the conventionalist thesis, that within the frame of STR isotropy in the velocity of light and, hence, signal synchronism is a matter of convention, we need a generalized Lorentz transformation group that does not embody Einstein's isotropy convention, and upon which STR can be based. We present here a new approach to the resulting search for a generalized STR, which is well suited for establishing some well-known results of Winnie as well as some new results.

Type
Research Article
Information
Philosophy of Science , Volume 53 , Issue 3 , September 1986 , pp. 395 - 402
Copyright
Copyright © The Philosophy of Science Association 1986

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Angel, R. B. (1980), Relativity: The Theory and its Philosophy, New York: Pergamon Press.Google Scholar
Einstein, A. (1952), “On the electrodynamics of moving bodies”, in The Principle of Relativity, A Collection of Original Memoires. New York: pp. 37–65 (Originally in Annalen der Physik, Ser. 4, 1905, 17: 891–921).Google Scholar
Giannoni, C. (1978), “Relativistic mechanics and electromagnetics without one-way velocity assumptions”, Philos. Sci. 45: 17–46.CrossRefGoogle Scholar
Giannoni, C. (1979), “Clock retardation, absolute space, and special relativity”, Found. Phys., 9: 426–44.CrossRefGoogle Scholar
Malament, D. (1977), “Causal theories of time and the conventionality of simultaneity”, Noûs 11: 293–300.CrossRefGoogle Scholar
Mittelstaedt, P. (1977), “Conventionalism in special relativity”, Foundations of Physics 7: 573–83.CrossRefGoogle Scholar
Reichenbach, H. (1958), The Philosophy of Space and Time. New York: Dover.Google Scholar
Torretti, R. (1983), Relativity and Geometry. New York: Pergamon Press.Google Scholar
Winnie, J. A. (1970), “Special relativity without one-way velocity assumptions”, Philosophy of Science 37: 81–99, 223–38.CrossRefGoogle Scholar
Winnie, J. A. (forthcoming), Invariants and Objectivity: A Theory with Applications to Relativity and Geometry. Colodny, R. (ed.). University of Pittsburgh Series in the Philosophy of Science, vol. 7. Pittsburgh: University of Pittsburgh Press.Google Scholar