We prove a classical analogue of Pauli’s theorem, showing that there is no time observable in classical mechanics in the very same sense that there is no time observable in quantum mechanics. We then examine how this result can be circumvented, and argue the result suggests a certain Aristotelian interpretation of time in classical mechanics.

In this letter we analyze two local extensions of a model introduced some time ago to obtain a path integral formalism for Classical Mechanics. In particular, we show that these extensions exhibit a nonrelativistic local symmetry which is very similar to the well known κ-symmetry introduced in the literature almost 20 years ago. Differently from the latter, this nonrelativistic local symmetry g...

(1) irii'ii = -gradiU(ql9 ..., qn), i = 1, ..., n, where gradf denotes the gradient with respect to q(. Thoughout this paper we use a single dot over a variable to represent its derivative with respect to time t and a double dot to represent its second derivative with respect to t. The potential energy U has a singularity whenever q(=q^ We write this singular set ^v = {€€(«?: *, = *,}, A = U Au...