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A Universal Axiomatization of Kinematical Theories

Published online by Cambridge University Press:  28 February 2022

Carlo Giannoni
Carlo Giannoni*
Affiliation:
Rice University
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Extract

By a kinematical theory we mean a theory of space, time, and light signals as measured by rigid rods and clocks. In this paper we shall construct an axiomatization of possible kinematical theories which has two especially interesting properties: it is universal in the sense that it presents a threefold continuum of kinematical theories ranging from Special Relativity (STR) on one extreme to Classical Aether Theory on the other; and it is synchronization independent, that is, it does not assume any particular synchronization for clocks. Reichenbach's axiomatization has the threefold continuum implicitly in it, but he does not explicitly present it as a universal axiomatization and he does not give it a synchrony free formulation. On the other hand, the synchrony free axiomatization of STR by Winnie is not universal and it masks an important distinction within the light principle. However, both of these axiomatizations were central to developing the present axiomatization.

Type
Part II. Philosophy of Physics
Information
PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association , Volume 1978 , Issue 1: Volume One: Contributed Papers 1978 , 1978 , pp. 60 - 70
Copyright
Copyright © 1978 by the Philosophy of Science Association

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References

Giannoni, Carlo. “Clock Retardation, Absolute Space, and Special Relativity.” Foundations of Physics. Forthcoming.Google Scholar
Giannoni, Carlo. “Relativistic Mechanics and Electrodynamics Without One-Way Velocity Assumptions.” Philosophy of Science 45(1978): 17–46.CrossRefGoogle Scholar
Reichenbach, Hans. Axiomatization of the Theory of Relativity. Berkeley and Los Angeles: University of California Press, 1969. (Translation of Axiomatik der relativistischen Raum-Zeit-Lehre. Braunschweig: Friedrich Vieweg, 1924.)Google Scholar
Robertson, H.P. “Postulate versus Observation in the Special Theory of Relativity.” Reviews of Modern Physics 21(1949): 378–382.CrossRefGoogle Scholar
Winnie, John. “Special Relativity Without One-Way Velocity Assumptions.” Philosophy of Science 37(1970): 81–99 and 223-238.CrossRefGoogle Scholar