Relativistic Quantum Mechanics and Relativistic Entanglement in the Rest-Frame Instant Form of Dynamics

TL;DR

This paper introduces a novel relativistic quantum mechanics framework using the rest-frame instant form, addressing localization, bound states, and entanglement with non-local properties distinct from non-relativistic quantum theory.

Contribution

It develops a frame-independent formalism with Wigner-covariant variables, providing new insights into relativistic localization, bound states, and the nature of entanglement.

Findings

Relativistic entanglement is kinematically non-local and non-separable.

The formalism naturally solves the relativistic localization problem.

In the non-relativistic limit, it reduces to standard quantum mechanics.

Abstract

A new formulation of relativistic quantum mechanics is proposed in the framework of the rest-frame instant form of dynamics with its instantaneous Wigner 3-spaces and with its description of the particle world-lines by means of derived non-canonical predictive coordinates. In it we quantize the frozen Jacobi data of the non-local 4-center of mass and the Wigner-covariant relative variables in an abstract (frame-independent) internal space whose existence is implied by Wigner-covariance. The formalism takes care of the properties of both relativistic bound states and scattering ones. There is a natural solution to the \textit{relativistic localization problem}. The non-relativistic limit leads to standard quantum mechanics but with a frozen Hamilton-Jacobi description of the center of mass. Due to the \textit{non-locality} of the Poincar\'e generators the resulting theory of relativistic entanglement is both \textit{kinematically non-local and spatially non-separable}: these properties, absent in the non-relativistic limit, throw a different light on the interpretation of the non-relativistic quantum non-locality and of its impact on foundational problems.