Maximum acceleration and quantum clock: on the existence of a new universal constant

Abstract

In the pseudo-Euclidean Minkowski space, the four-dimensional volume element is invariant under Lorentz transformations. By hypothesising that in this space there is a minimum volume, it is possible to demonstrate the existence of a maximum acceleration. The volume element cannot be derived from the theory and must be obtained through direct measurement, thus it assumes the role of a bona fide universal constant. Two different estimates of the elementary volume are given, which differ by several orders of magnitude: the first is obtained in a pseudo-Euclidean space for particles with mass, and the second represents an absolute minimum volume, independent of the mass.