Dynamical nonlocality in quantum time via modular operators

TL;DR

This paper introduces a formalization of the modular energy operator in quantum mechanics, revealing nonlocality in time analogous to spatial nonlocality, with applications demonstrated through examples.

Contribution

It elevates the modular energy operator to a central role in the Page-Wootters framework, establishing temporal nonlocality similar to spatial cases.

Findings

Modular energy operator formalized within the Page-Wootters framework

Temporal nonlocality analogous to spatial modular momentum

Illustrative examples demonstrate applications of the formalization

Abstract

We formalize the concept of the modular energy operator within the Page and Wootters timeless framework. As a result, this operator is elevated to the same status as the more studied modular operators of position and momentum. In analogy with dynamical nonlocality in space associated with the modular momentum, we introduce and analyze the nonlocality in time associated with the modular energy operator. Some applications of our formalization are provided through illustrative examples.