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arXiv · 2203.12393

Proper time operator and its uncertainty relation

Hou Y. Yau
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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.

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Hou Y. Yau. 2022-02-27. Proper time operator and its uncertainty relation. https://doi.org/10.1088/2399-6528%2Fac2941

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