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Optical Axiomatization of Minkowski Space-Time Geometry

Published online by Cambridge University Press:  01 April 2022

Brent Mundy
Brent Mundy*
Affiliation:
Department of Philosophy, University of Oklahoma
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Abstract

Minkowski geometry is axiomatized in terms of the asymmetric binary relation of optical connectibility, using ten first-order axioms and the second-order continuity axiom. An axiom system in terms of the symmetric binary optical connection relation is also presented. The present development is much simpler than the corresponding work of Robb, upon which it is modeled.

Type
Research Article
Information
Philosophy of Science , Volume 53 , Issue 1 , March 1986 , pp. 1 - 30
Copyright
Copyright © The Philosophy of Science Association 1986

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Footnotes

†

This work was supported by a grant from the National Endowment for the Humanities.

References

Borsuk, K., and Szmielew, W. (1960), Foundations of Geometry. Amsterdam: North-Holland.Google Scholar
Busemann, H. (1955), The Geometry of Geodesics. New York: Academic Press.Google Scholar
Dorling, J. (forthcoming), “Special Relativity out of Euclidean Geometry”, in HPS IV (Proceedings of IUHPS Blacksburg conference, 1982), J. Pitt (ed.).Google Scholar
Earman, J.; Glymour, C.; and Stachel, J. (eds.) (1977), Foundations of Space-Time Theories. Minnesota Studies in the Philosophy of Science, vol. 8, Minneapolis: University of Minnesota Press.Google Scholar
Krantz, D.; Luce, R.; Suppes, P.; and Tversky, A. (1971), Foundations of Measurement. Vol. 1. New York: Academic Press.Google Scholar
Latzer, R. (1973), “Nondirected Light Signals and the Structure of Time”, in Space, Time, and Geometry, Suppes, Patrick (ed.). Dordrecht: D. Reidel, pp. 321–65.Google Scholar
Malament, D. (1977), “Causal Theories of Time and the Conventionality of Simultaneity”, Noûs 11: 293–300.CrossRefGoogle Scholar
Mehlberg, H. [1935] (1980), Essay on the Causal Theory of Time. Reprinted edition, with additions. Time, Causality and the Quantum Theory, vol. 1. Dordrecht: D. Reidel.Google Scholar
Mundy, B. (1982), Synthetic Affine Space-Time Geometry. Ph.D. dissertation, Stanford University.Google Scholar
Mundy, B. (forthcoming), “The Physical Content of Minkowski Geometry”, British Journal for the Philosophy of Science.Google Scholar
Reichenbach, H. [1924] (1969), Axiomatization of the Theory of Relativity. Berkeley and Los Angeles: University of California Press.Google Scholar
Robb, A. A. (1914), A Theory of Time and Space. Cambridge.Google Scholar
Robb, A. A. (1921), The Absolute Relations of Time and Space. Cambridge.Google Scholar
Robb, A. A. (1936), Geometry of Time and Space. Cambridge.Google Scholar
Schutz, J. (1973), Foundations of Special Relativity: Kinematic Axioms for Minkowski Space-Time. Lecture Notes in Mathematics, vol. 361, Berlin: Springer.CrossRefGoogle Scholar
Schutz, J. (1981), “An Axiomatic System for Minkowski Space-Time”, Journal of Mathematical Physics 22: 293–302.CrossRefGoogle Scholar
Sklar, L. (1977), “Facts, Conventions, and Assumptions in the Theory of Space-Time”, in Earman et al., pp. 206–74.Google Scholar
Stachel, J. (1983), “Special Relativity from Measuring Rods”, in Physics, Philosophy and Psychoanalysis, Cohen, R. S. and Laudan, L., (eds.). Dordrecht: D. Reidel, pp. 255–72.Google Scholar
Stein, H. (1977), “On Space-Time Ontology: Extracts from a Letter to Adolf Grünbaum”, in Earman et al., pp. 374–402.Google Scholar
Suppes, P. (1968), “The Desirability of Formalization in Science”, Journal of Philosophy 65: 651–64.CrossRefGoogle Scholar
Walker, A. G. (1948), “Foundations of Relativity: Parts I and II”, Proceedings of the Royal Society of Edinburgh A62:319–35.CrossRefGoogle Scholar
Winnie, J. A. (1977), “The Causal Theory of Space-Time”, in Earman et al., pp. 134–205.Google Scholar