Proper time operator and its uncertainty relation
General Physics
2022-03-24 v1
Abstract
We study the quantum properties of an oscillator in proper time. This proper time oscillator is a particle model with mass that is on shell. Its internal time can be treated as a self-adjoint operator. The displaced time and displaced time rate of the oscillator obey an uncertainty relation resembling the one between position and momentum, which is different from the usual energy-time uncertainty relation. In addition, we demonstrate that a matter field with proper time oscillators satisfies the Klein-Gordon equation. It has properties of a zero-spin quantum field. The formulations adopted permits a more symmetrical treatment between time and space in a matter field.
Cite
@article{arxiv.2203.12393,
title = {Proper time operator and its uncertainty relation},
author = {Hou Y. Yau},
journal= {arXiv preprint arXiv:2203.12393},
year = {2022}
}
Comments
11 pages. Published version