Dynamical nonlocality in quantum time via modular operators

Understand

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.