On Relativistic Entanglement and Localization of Particles and on their Comparison with the Non-Relativistic Theory

TL;DR

This paper critically compares relativistic and non-relativistic quantum mechanics, focusing on particle localization, entanglement, and the implications of relativistic non-separability for measurements and experiments.

Contribution

It clarifies the differences in particle localization and entanglement between relativistic and non-relativistic theories, highlighting the non-measurable nature of relativistic center of mass and the role of relative variables.

Findings

Relativistic center of mass is non-local and decoupled from particles.

Relativistic entanglement involves spatial non-separability not present non-relativistically.

Experiments measure relative variables, aligning with classical trajectories.

Abstract

We make a critical comparison of relativistic and non-relativistic classical and quantum mechanics of particles in inertial frames and of the open problems in particle localization at the two levels. The solution of the problems of the relativistic center of mass, of the clock synchronization convention needed to define relativistic 3-spaces and of the elimination of the relative times in the relativistic bound states leads to a description with a decoupled non-local (non-measurable) relativistic center of mass and with only relative variables for the particles (single particle subsystems do not exist). We analyze the implications for entanglement of this relativistic spatial non-separability not existing in non-relativistic entanglement. Then we try to reconcile the two visions showing that also at the non-relativistic level in real experiments only relative variables are measured with their directions determined by the effective mean classical trajectories of particle beams present in the experiment. We discuss some of the existing problems with the observers and their reference frames, leaving to the future the discussion in non-inertial frames.