Temporal interference of relativistic bosons

TL;DR

This paper proposes a new framework for quantum time evolution based on the projection postulate, enabling a consistent description of time as an observable and explaining temporal interference phenomena observed in experiments.

Contribution

It introduces a novel model for quantum evolution that incorporates time as an observable, addressing longstanding conceptual issues in quantum mechanics.

Findings

Describes a temporal double-slit experiment with single-particle interference.

Provides a theoretical explanation for experimentally observed temporal interference.

Aligns the new model with established quantum mechanics principles.

Abstract

In quantum mechanics, time is introduced as a non-measurable quantity, as there is no possibility to build a hermitian operator canonically conjugated to the Hamiltonian. We cannot have, therefore, the time operator, which means that the temporal structure of the evolution of quantum systems is ill-defined. We present an extension to the model, in which the time evolution is based on the projection postulate rather than the unitary operator. This approach is in agreement with all other aspects of quantum mechanics and allows to discuss time as an observable. Using this framework we present a description of the temporal double-slit experiment in which a~single particle interferes with itself from a different instant of time. Such behaviour has already been observed experimentally but lacked a consistent theoretical explanation.