Time evolution in quantum mechanics with a minimal time scale

• URL: http://arxiv.org/abs/2410.18044v1
• Date: Wed, 23 Oct 2024 17:11:50 GMT
• Title: Time evolution in quantum mechanics with a minimal time scale
• Authors: Ziemowit Domański,
• Abstract summary: We show a quantum theory exhibiting a minimum measurable time scale. We use the Page-Wootters formalism to describe time evolution of a quantum system. A minimal time scale allows also to introduce a discrete Schrodinger equation describing time evolution on a lattice.
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• Abstract: The existence of a minimum measurable length scale was suggested by various theories of quantum gravity, string theory and black hole physics. Motivated by this we examine a quantum theory exhibiting a minimum measurable time scale. We use the Page-Wootters formalism to describe time evolution of a quantum system with the modified commutation relations between the time and frequency operator. Such modification leads to a minimal uncertainty in the measurement of time. This causes breaking of the time-translation symmetry and results in a modified version of the Schrodinger equation. A minimal time scale allows also to introduce a discrete Schrodinger equation describing time evolution on a lattice. We show that both descriptions of time evolution are equivalent. We demonstrate the developed theory on couple simple quantum systems.

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