. ge n - ph ] 2 5 A ug 2 00 8 Absolute simultaneity and invariant lengths : Special Relativity without light signals or synchronised clocks

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. PACS 03.30.+p In the conventional presentation of Special Relativity Theory (SRT), following the approach of Einstein's seminal paper on the subject [1], light signals and clock synchro-nisation play a crucial role in the development of predictions of space-time geometrical effects on the basis of the Lorentz transformation (LT). However, as early as 1910 [2], it was realised that Einstein's methodology is not the only, and not the most economical, way (in terms both of the number of postulates and their simplicity) to formulate the foundations of SRT. In a previous paper by the present author [3], using a similar approach to Ref. [2], it was shown that only two weak, and, from a naive point-of-view, 'evident' postulates, unrelated to classical electrodynamics or any other dynamical theory, suffice to derive the LT. This is true for events lying along the common x, x ′ axis of two frames S and S' in which the latter frame moves with constant velocity along the x-axis in S. The symbol t is used to denote the recorded time (epoch) of a clock a rest in S, and t ′ to denote the epoch of a clock a rest in S'. An event in S is specified by (x,t), one in S' by (x ′ ,t ′), it being understood that that y = y ′ = z = z ′ = 0. The two postulates are that, the LT must be a single-valued function of its arguments, and a restricted form of the special relativity principle that may be called the 'Measurement Reciprocity Postulate' (MRP): Reciprocal space-time measurements of similar measuring rods and clocks in two different inertial frames by observers at rest in these frames give identical results