Simultaneity as an Invariant Equivalence Relation
Abstract
This paper deals with the concept of simultaneity in classical and relativistic physics as construed in terms of groupinvariant equivalence relations. A full examination of Newton, Galilei and Poincaré 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 interesting for its own sake, does not cut in the debate concerning the conventionality of simultaneity in special relativity.
 Publication:

Foundations of Physics
 Pub Date:
 November 2012
 DOI:
 10.1007/s1070101296744
 arXiv:
 arXiv:1202.6578
 Bibcode:
 2012FoPh...42.1365M
 Keywords:

 Special relativity;
 Simultaneity;
 Invariant equivalence relations;
 Malament's theorem;
 Mathematical Physics;
 General Relativity and Quantum Cosmology;
 Physics  History and Philosophy of Physics
 EPrint:
 Some corrections, mostly of misprints. Keywords: special relativity, simultaneity, invariant equivalence relations, Malament's theorem