Uniqueness of simultaneity


Abstract
We consider the problem of uniqueness of certain simultaneity structures in flat spacetime. Absolute simultaneity is specifiled to be a non-trivial equivalence relation which is invariant under the automorphism group Aut of spacetime. Aut is taken to be the identity-component of either the inhomogeneous Galilei group or the inhomogeneous Lorentz group. Uniqueness of standard simultaneity in the first, and absence of any absolute simultaneity in the second case are demonstrated and related to certain group theoretic properties. Relative simultaneity with respect to an additional structure X on spacetime is specified to be a non-trivial equivalence relation which is invariant under the subgroup in Aut that stabilises X. Uniqueness of standard Einstein simultaneity is proven in the Lorentzian case when X is an inertial frame. We end by discussing the relation to previous work of others.
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Reprint years 2000, 2001
DOI 10.1093/bjps/52.4.651
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References found in this work BETA

Relativity and Geometry.Michael Friedman - 1984 - Noûs 18 (4):653-664.
Relativity and Geometry.R. Torretti - 1985 - British Journal for the Philosophy of Science 36 (1):100-104.
Simultaneity and Conventionality.Allen I. Janis - 1983 - In R. Cohen & L. Laudan (eds.), Physics, Philosophy, and Psychoanalysis. D. Reidel. pp. 101--110.

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Citations of this work BETA

Time in Classical and Relativistic Physics.Gordon Belot - 2013 - In Adrian Bardon & Heather Dyke (eds.), A Companion to the Philosophy of Time. Blackwell. pp. 185-200.
Dust, Time and Symmetry.Gordon Belot - 2005 - British Journal for the Philosophy of Science 56 (2):255-291.
Causality and Temporal Order in Special Relativity.Hanoch Ben-Yami - 2006 - British Journal for the Philosophy of Science 57 (3):459-479.
Simultaneity as an Invariant Equivalence Relation.Marco Mamone-Capria - 2012 - Foundations of Physics 42 (11):1365-1383.
A Note on Dolby and Gull on Radar Time and the Twin 'Paradox'.Antony Eagle - 2005 - American Journal of Physics 73 (10):976–979.

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