Time-System Entanglement and Special Relativity

• URL: http://arxiv.org/abs/2212.13348v3
• Date: Sun, 18 Feb 2024 03:52:42 GMT
• Title: Time-System Entanglement and Special Relativity
• Authors: Ngo Phuc Duc Loc
• Abstract summary: Page-Wootters mechanism of quantum time is a promising starting point. We study how this time-system entanglement depends on the rapidity of the Lorentz boost.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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