Time as a quantum observable: Revisiting the tunneling time problem through time-of-arrival operators

Abstract

The incorporation of time as a quantum dynamical observable has long been a subject of intense debate since the inception of quantum theory. Unlike position, momentum, and energy observables, the absence of a well-defined time operator in standard quantum mechanics represents a significant theoretical gap. This highlights a chief weakness of the theory, since experimental measurements of time are routinely conducted in laboratories. In this talk, we will explore the incorporation of time as a quantum observable in the context of the time of arrival (TOA) of an elementary particle. We will present the construction of time-of-arrival (TOA) operators through the quantization and supraquantization of the classical arrival time for arbitrary analytic potentials. We will then discuss how the TOA operator formalism resolves the quantum tunneling time problem, which has divided the scientific community over the question of whether quantum tunneling occurs instantaneously or not.