Minkowski’s Proper Time and the Status of the Clock Hypothesis

Abstract

In this chapter I argue that the concept of proper time must be regarded as one of Minkowski’s enduring contributions to physics. I examine some confusions that still interfere with an appreciation of this, including a conflation of proper time with the co-ordinate time of the inertial frame of a system at rest, and the related mistaken notion that Special Relativity cannot be applied to accelerating systems. This sets the stage for a treatment of the so-called clock hypothesis, according to which the instantaneous rate of a clock depends only on its instantaneous speed. I argue that this does not have the status of an independent hypothesis, but is simply a description of the behaviour of an ideal clock as predicted by (classical, special and general) relativity theory. The question whether this hypothesis holds, moreover, must be distinguished from the question of whether the restorative acceleration of the mechanism within any real system acting as a clock is sufficiently great (relative to the acceleration undergone by the system) that the system will be able to approximate such an ideal clock. The failure of the clock hypothesis would entail the falsity of relativity theory in the form proposed by Einstein, as Weyl had sought to demonstrate with his unified theory of gravity and electromagnetism in 1918. I argue that it is the Strong Equivalence Principle in General Relativity that preserves the chronometric significance that the metric had in Special Relativity, and thereby preserves the relation of inertia to time assumed classically.