Quantum proper time: A Finsler space from entropy and purity

• URL: http://arxiv.org/abs/2503.06667v1
• Date: Sun, 09 Mar 2025 15:38:59 GMT
• Title: Quantum proper time: A Finsler space from entropy and purity
• Authors: Joseph Balsells, Martin Bojowald,
• Abstract summary: A quantum clock cannot be modeled as a point mass moving along a single geodesic if it is in a state with nonzero position fluctuations.<n>A geometrical formulation of quantum mechanics is used to show that additional quantum properties representing correlations between different directions imply a non-Riemannian geometrical structure.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: A quantum clock cannot be modeled as a point mass moving along a single geodesic if it is in a state with nonzero position fluctuations. Instead, it is an extended object subject to tidal forces and a superposition of time dilations at different altitudes. Here, a geometrical formulation of quantum mechanics is used to show that additional quantum properties representing correlations between different directions imply a non-Riemannian geometrical structure experienced by a quantum clock. A specific version of Finsler geometry parameterized by entropy and purity of the state provides a novel setting for a combination of quantum and gravitational effects. A crucial ingredient is given by a new parameterization of quantum-information properties related to second-order moments of a state and may also be useful in other applications.

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