Physical Sciences: Reversibility of the Equations of Classical Dynamics

Abstract

IN a recent series of papers, one of us has derived the equation of motion¹ of a free particle in the presence of the expanding universe by a priori methods, and constructed an associated dynamics. The observers' clocks were supposed so graduated² that the expansion appeared uniform, and the resulting scale of time was called the t-scale. But the equations of motion reduced to their classical form³ only if observers' clocks were regraduated from t to τ where and all derived measures correspondingly changed. Accordingly, the 'uniform time' of mechanics was identified as τ-time. In this measure of time, the universe appears as a stationary, non-expanding system, and the red-shift is shown⁴ to be attributable to an acceleration of atomic absorption- or emissionfrequency with time in τ-measure, so that the light, emitted long ago by a distant nebula, appears relatively displaced to the red. In a joint paper about to appear in Zeitschrift für Astrophysik, we have analysed generally all monotonic graduations of our temporal experience, that is, all possible modes of clock-graduation, and shown that of these there is just one, τ-measure, which reduces the members of any 'linear equivalence' to relative rest. This again we have identified as the time of mechanics.