Energy as a measure for the elapse of time

TL;DR

This paper proposes that energy can serve as a universal measure of elapsed time, explaining how relativistic effects are incorporated into classical and quantum mechanics through the conjugate relationship between energy and time.

Contribution

It introduces the idea that energy, as a conjugate variable to time, inherently accounts for relativistic time dilation effects in classical and quantum frameworks.

Findings

Energy accounts for relativistic time dilation effects.

Classical and quantum mechanics use a universal time scale.

Experimental results support energy as a measure of elapsed time.

Abstract

Clocks in different heights or with different velocities run with different speeds. For global positioning systems these effects are much too large to be ignored. Nevertheless, in classical and quantum mechanics we get high accuracy using a "universal" time scale, not depending on altitudes and velocities. One may ask how this is possible. The answer to this question we may get from the observation that in classical and quantum mechanics time and energy are canonically conjugate variables. We argue that the mentioned modifications of the time scale by relativistic effects are taken into account in the notion of energy. On the basis of the experimental results and the laws of special relativity we argue that we should consider energy as measure for the elapse of time.