Absolute simultaneity and invariant lengths: Special Relativity without light signals or synchronised clocks

Abstract

It is demonstrated that the measured spatial separation of two objects, at rest in some inertial frame, is invariant under space-time transformations. This result holds in both Galilean and Special Relativity. A corollary is that there are no `length contraction' or associated 'relativity of simultaneity' effects in the latter theory. A thought experiment employing four unsynchronised clocks and a single measuring rod reveals that the physical basis of the time dilatation effect is a relative velocity transformation law, not `length contraction'. Time dilatation, which is universal and translation invariant for all synchronised clocks at rest in any inertial frame, is the unique space-time phenomenon discriminating Special from Galilean Relativity.