Relative Quantum Time

Abstract

The need for a time-shift invariant formulation of quantum theory arises from fundamental symmetry principles as well as heuristic cosmological considerations. Such a description then leaves open the question of how to reconcile global invariance with the perception of change, locally. By introducing relative time observables, we are able to make rigorous the Page-Wootters conditional probability formalism to show how local Heisenberg evolution is compatible with global invariance.

References in corpus (7)

• Quantum Time
• Conditional probabilities with Dirac observables and the problem of time in quantum gravity
• Evolution without evolution, and without ambiguities
• Symmetry, Reference Frames, and Relational Quantities in Quantum Mechanics
• Relativity of Quantum States and Observables
• Approximating relational observables by absolute quantities: A quantum accuracy-size trade-off
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Cited by in corpus (15)

• The Trinity of Relational Quantum Dynamics
• Equivalence of approaches to relational quantum dynamics in relativistic settings
• There is only one time
• Non-inertial quantum clock frames lead to non-Hermitian dynamics
• Operational Quantum Reference Frame Transformations
• Flow of time during energy measurements and the resulting time-energy uncertainty relations
• A relational perspective on the Wigner-Araki-Yanase theorem
• Gravitational entropy is observer-dependent
• Robustness of the Page-Wootters construction across different pictures, states of the universe and system-clock interactions
• Measurement events relative to temporal quantum reference frames
• Crossed products and quantum reference frames: on the observer-dependence of gravitational entropy
• Generalised second law beyond the semiclassical regime
• Perspective-neutral approach to quantum frame covariance for general symmetry groups
• Infinitesimal reference frames suffice to determine the asymmetry properties of a quantum system
• Gravitational null rays: Covariant Quantization and the Dressing Time