  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.

Quantum Physics;General Relativity and Quantum Cosmology;High Energy Physics - Theory