Localization POVMs and intrinsic temporal uncertainty

TL;DR

This paper develops a covariant formalism for relativistic quantum localization using proper-time POVMs, resolving causality issues and emphasizing the role of intrinsic temporal uncertainty in single-particle systems.

Contribution

It introduces a proper-time based POVM framework for localization, addressing causality paradoxes in relativistic quantum mechanics.

Findings

Localization described by covariant four-vector POVMs

Physically acceptable states exhibit intrinsic temporal uncertainty

Proper-time evolution avoids causality violations

Abstract

The causality issues concerning the localization of relativistic quantum systems, as evidenced by Hegerfeld's paradox, are addressed through a proper-time formalism of single-particle operators. Starting from the premise that physical variables associated to the proper-time gauge have a prominent role in the specification of position, since they do not depend on classical parameters connected to an external observer, we obtain a single-particle formalism in which localization is described by explicitly covariant four-vector operators associated with POVM measurements parametrized by the system's proper-time. Among the consequences of this result, we emphasize that physically acceptable states are necessarily associated with the existence of a temporal uncertainty and their proper-time evolution is not subject to the causality violation predicted by Hegerfeldt.