Time-System Entanglement and Special Relativity

TL;DR

This paper explores how Lorentz boosts affect the entanglement between a quantum system and a quantum clock, revealing insights into the relativistic quantum nature of time.

Contribution

It introduces a model of time-system entanglement influenced by Lorentz transformations, connecting quantum information with relativistic effects.

Findings

Time-system entanglement varies with Lorentz boost rapidity.

Time-system entanglement entropy is smaller than spin-momentum entanglement.

The model uses a spin-1/2 particle with Gaussian momentum distribution.

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.