Spatial Directions, Anisotropy and Special Relativity

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. A natural generalization of the proper time principle is introduced which makes it possible to devise experimental tests of spatial isotropy. Several common misunderstandings in the relativistic literature concerning the role of spatial isotropy are clarified.Comment: 24 pages, 2 figures. Final enlarged and slightly corrected version. Keywords: relativity, very special relativity, spatial isotropy, reciprocity, differential aging; Foundations of Physics, 201

On Selleri's "Weak Relativity''

F. Selleri's main arguments for the restoration of absolute simultaneity in physics are analysed and shown to be faulty. In particular both the classical Sagnac effect and the recent so-called linear Sagnac effect can be dealt with within special relativity in a natural way. The appeal to the conventionality of simultaneity thesis is also shown to be ineffectual. Other arguments, such as the two spaceships' argument and the block universe argument are briefly examined. Notwithstanding a negative overall assessment, the importance of keeping alive the research on the foundations of relativity is emphasized and Selleri's role in this undertaking appreciated.Comment: 27 pages, 8 figure

Simultaneity as an Invariant Equivalence Relation

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 interesting for its own sake, does not cut in the debate concerning the conventionality of simultaneity in special relativity.Comment: Some corrections, mostly of misprints. Keywords: special relativity, simultaneity, invariant equivalence relations, Malament's theore