Quantum proper time: A Finsler space from entropy and purity
arXiv:2503.06667 · doi:10.1103/2pn6-h5j4
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.
40 pages, v2: extended discussion of quantum information properties
References in corpus (20)
- Reference frames, superselection rules, and quantum information
- Planck-scale modified dispersion relations and Finsler geometry
- Effective Equations of Motion for Quantum Systems
- Finsler geometric extension of Einstein gravity
- Quantum Gravity and Higher Curvature Actions
- Quantizing time: Interacting clocks and systems
- Quantum clocks observe classical and quantum time dilation
- Finsler gravity action from variational completion
- Constraining the energy-momentum dispersion relation with Planck-scale sensitivity using cold atoms
- Effective Constraints for Relativistic Quantum Systems
- Effective Constraints for Quantum Systems
- Geometry of physical dispersion relations
- Effective potentials from semiclassical truncations
- Finsler-Randers-Sasaki gravity and cosmology
- Faithful realizations of semiclassical truncations
- Entanglement Dynamics in Dispersive Optomechanics: Non-Classicality and Revival
- Ultra-high energy cosmic rays threshold in Randers-Finsler space
- Multimetric Finsler Geometry
- Geometry and proper time of a relativistic quantum clock
- Sum-Over-Histories Quantization of Relativistic Particle