Rigidity and the Ruler Hypothesis

Abstract

In special relativity, one often speaks of rigid rods, looking at them in one inertial frame or another and observing that they do not always have the same length, despite their rigidity. This paper is about what happens to the rod as it gets from one inertial frame to another, i.e., as it accelerates. The problem is not entirely academic. For those who would like to model extended charge distributions and their fields, and in particular the forces they exert upon themselves via these electromagnetic effects, when they are accelerating, some hypothesis must be made about the way the charge distribution shifts around in the relevant spatial hypersurfaces of Minkowski’s spacetime. A notion of rigidity is indeed usually applied and that is discussed here (Sect. 1), in connection with frames of reference adapted to accelerating observers in the spacetime of special relativity. The physical legitimacy of adapted frames of reference is discussed in some detail throughout the paper, but particularly in the context of the Pound–Rebka experiment in Sect. 1.10. The aim is to elucidate the roles of what are usually referred to as the clock and ruler hypotheses. One would also like to consider rigid motions of any material medium in a more general framework, even in the context of general relativity. The notion of rigidity can be extended (Sect. 2) in a simple but perhaps questionable way. The aim here will indeed be to cast a critical glance.