Abstract
In this note I briefly discuss some aspects of relative geometric simultaneity in special relativity. After saying a few words about the status and nature of Minkowski spacetime in special relativity, I recall a uniqueness result due to David Malament concerning simultaneity relative to an inertial worldline and an extension of it due to Mark Hogarth and I prove an extension of it for simultaneity relative to an inertial frame in time-oriented spacetimes. Then I point out that the uniqueness results do not generalise to definitions of simultaneity relative to the rotating disk. Finally, I evaluate some recent claims of Selleri in the light of the results. Whilst some of his claims are supported by the approach taken here, the conclusion he draws from these claims, that special relativity harbours a discontinuity and so stands in need of replacement, does not follow and is rejected.
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REFERENCES
Budden, T. (1997a), “A star in the Minkowskian sky: Anisotropic special relativity,” Stud. Hist. Phil. Mod. Phys. 28(3), 325–361.
Budden, T. (1997b), “Galileo's ship and spacetime symmetry,” Brit. J. Phil. Sci. 48, 483–516.
Budden, T. (1997c), “Numbers and locality,” preprint.
Earman, J. (1989), World Enough and Space-Time (MIT Press, Boston).
Field, H. (1980), Science Without Numbers (Blackwell, Oxford).
Hogarth, M. (1993), “Standard simultaneity is unique in metrical Minkowski spacetime: A generalisation of Malament's theorem,” unpublished manuscript.
Malament, D. (1975), “Does the Causal Structure of Space-Time Determine its Geometry?,” Ph.D. thesis, Rockefeller University.
Malament, D. (1977), “Causal theories of time and the conventionality of simultaneity,” Noûs 11, 293–300.
Norton, J. (1984), “What was Einstein's principle of equivalence?,” Stud. Hist. Phil. Sci 16(3), 203–246.
Robb, A. A. (1914), A Theory of Space and Time (Cambridge University Press, Cambridge).
Selleri, F. (1997), “Noninvariant one-way speed of light and locally equivalent reference frames,” Found. Phys. Lett. 10(1), 73–83.
Spirtes, P. (1981), “Conventionalism in the Philosophy of Henri Poincará,” Ph.D. thesis, University of Pittsburgh.
Stein, H. (1991), “On relativity theory and openness of the future,” Phil. Sci. 58, 147–167.
Winnie, J. (1977), “The causal theory of space-time,” in J. Earman, ed., Foundations of Space-Time Theories (Minnesota Studies in the Philosophy of Science, Vol. VIII) (University of Minnesota Press, Minneapolis), pp. 134–205.
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Budden, T. Geometric Simultaneity and the Continuity of Special Relativity. Found Phys Lett 11, 343–357 (1998). https://doi.org/10.1023/A:1022176907790
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DOI: https://doi.org/10.1023/A:1022176907790