Time in classical and in quantum mechanics

Abstract

This paper presents an analysis of the time concept in classical mechanics from the perspective of the invariants of a motion. The analysis shows that there is a conceptual gap concerning time in the Dirac–Heisenberg–von Neumann formalism and that Bohr's complementarity principle does not fill the gap. In the Dirac–Heisenberg–von Neumann formalism, a particle's properties are represented by Heisenberg matrices. This axiom is the source of the time problem in quantum mechanics.