Simultaneity as an Invariant Equivalence relation

Details Simultaneity as an Invariant Equivalence relation Simultaneity as an Invariant Equivalence relation

2012-02-29

arxiv.org/abs/1202.6578v1

Physics

Mathematical Physics

Scientific paper

This paper deals with the concept of simultaneity in classical and relativistic physics as construed in terms of group-invariant equivalence relations. A full examination of Newton, Galilei and Poincar\'e invariant equivalence relations in $\R^4$ is presented, which provides alternative proofs, additions and occasionally corrections of results in the literature, including Malament's theorem and some of its variants. It is argued that the interpretation of simultaneity as an invariant equivalence relation, although mathematically interesting, does not cut in the debate concerning the conventionality of simultaneity in special relativity.

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