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 Poincaré invariant equivalence relations in ℝ4 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. (shrink)

A new formulation of what may be called the “fundamental theorem of the theory of relativity” is presented and proved in -space-time, based on the full classification of special transformations and the corresponding velocity addition laws. A system of axioms is introduced and discussed leading to the result, and a study is made of several variants of that system. In particular the status of the group axiom is investigated with respect to the condition of the two-way isotropy of light. Several (...) issues which are ignored or misunderstood in the literature are emphasized. (shrink)

The concept of an objective spatial direction in special relativity is investigated and theories assuming light-speed isotropy while accepting the existence of a privileged spatial direction are classified, including so-called very special relativity. A natural generalization of the proper time principle is introduced which makes it possible to devise non-optical experimental tests of spatial isotropy. Several common misunderstandings in the relativistic literature concerning the role of spatial isotropy are clarified.