Time-System Entanglement and Special Relativity
arXiv:2212.13348 · doi:10.1142/S0217732323501833
Abstract
We know that space and time are treated almost equally in classical physics, but we also know that this is not the case for quantum mechanics. A quantum description of both space and time is important to really understand the quantum nature of reality. The Page-Wootters mechanism of quantum time is a promising starting point, according to which the evolution of the quantum system is described by the entanglement between it and quantum temporal degrees of freedom. In this paper, we consider a qubit clock that is entangled with a quantum system due to the Wigner rotation induced by Lorentz transformation. We study how this time-system entanglement depends on the rapidity of the Lorentz boost. We consider the case of a spin-1/2 particle with Gaussian momentum distribution as a concrete example. We also compare the time-system entanglement entropy with the spin-momentum entanglement entropy and find that the former is smaller than the latter.
arXiv comment7 pages + 7 figures; published version
References in corpus (26)
- A computable measure of entanglement
- The entropy of Hawking radiation
- Quantum Entanglement of Moving Bodies
- Quantum entropy and special relativity
- Space from Hilbert Space: Recovering Geometry from Bulk Entanglement
- Quantum Time
- Time from quantum entanglement: an experimental illustration
- Entanglement and the Thermodynamic Arrow of Time
- Multiple-time states and multiple-time measurements in quantum mechanics
- A quantum solution to the arrow-of-time dilemma
- The arrow of causality and quantum gravity
- Evolution without evolution, and without ambiguities
- Bulk Entanglement Gravity without a Boundary: Towards Finding Einstein's Equation in Hilbert Space
- Experimental entanglement of temporal order
- Arrow of Time for Continuous Quantum Measurement
- History state formalism for scalar particles
- Quantum-first gravity
- Time and Quantum Clocks: a review of recent developments
- History state formalism for Dirac's theory
- Entangled Histories
- System-time entanglement in a discrete time model
- Quantum Time: experimental multi-time correlations
- Entangled Histories vs. the Two-State-Vector Formalism - Towards a Better Understanding of Quantum Temporal Correlations
- Spacetime Quantum Actions
- Possibility of a minimal purity-measurement scheme critically depends on the parity of dimension of the quantum system
- Unitary paradox of cosmological perturbations