Ideal quantum clocks and operator time

TL;DR

This paper introduces a general operator-based concept of time in quantum theory, focusing on ideal quantum clocks that define a symmetric time operator satisfying the time-energy uncertainty relation, challenging Pauli's argument.

Contribution

It proposes a new framework for defining a symmetric time operator using ideal quantum clocks within quantum theory, bypassing Pauli's no-go theorem.

Findings

Defined a symmetric time operator T for ideal quantum clocks

Showed T and H satisfy the time-energy uncertainty relation

Challenged Pauli's argument against the existence of a time operator

Abstract

In the framework of any quantum theory in the Schroedinger picture a general operator time concept is given. For this purpose certain systems are emphasized as ideal quantum clocks. Their definition follows heuristically from a common property of ideal clocks and from general postulates of traditional quantum theory. Any such ideal quantum clock allows the definition of a symmetric time operator T. T and the Hamiltonian H necessarily satisfy the time-energy uncertainty relation. The argument of Pauli against the existence of any time operator does not strike, because T is symmetric but not selfadjoint.