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.

After discussing in the first five sections the meaning and the difficulties of the principle of relativity we present a new sel of spacetime transformations between inertial systems (“inertial” transformations), based on three assumptions: (1) The two-way velocity of light is c in all inertial systems and in all directions; (2) Time dilation effects take place with the usual relativistic factor; (3) Clocks are synchronized in the way chosen by nature itself, e.g., in the Sagnac effect. We show that our (...) new transformation laws can explain the available experimental evidence in spite of the implied noninvariance of the one-way velocity of light. (shrink)

In this paper the classical topic of “conventionality” in defining the simultaneity (or synchrony) of distant events is tackled again, and the validity of Reichenbach's view is carefully circumscribed. In particular, the role of “one-way” assumptions in the foundations of special relativity is emphasized. The restriction by the round-trip isotropy condition on the admissible distance functions in inertial frames is studied, and its relevance to several issues (absolute simultaneity, the interpretation of Michelson–Morley type experiments, the self-measured speed of a clock) (...) is shown. Two “clock transport” synchronizations in an inertial frame, using self-measured speed and “proper distance,” are presented in detail, and the agreement of the synchronies so established with standard synchrony is proven to be non- circular. By assuming a reasonable concept of “convention” this result is shown to dissolve several objections by supporters of a strong version of conventionalism. Throughout, a number of common misapprehensions in the literature are pointed out. (shrink)

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)