On the Problem of Time(s) in Quantum Mechanics and Quantum Gravity: recent integrating developments and outlook

TL;DR

This paper reviews recent developments addressing the Problem of Time(s) in quantum mechanics and quantum gravity, highlighting how entanglement and relativistic quantization introduce new perspectives on time's role and its operator status.

Contribution

It presents novel insights into how entanglement and relativistic quantization can restore a meaningful notion of time in quantum theories, challenging Pauli's objection to a time operator.

Findings

Entanglement with classical environment yields a time-dependent Schrödinger equation.

Relativistic quantization introduces a self-adjoint time operator linked to system mass.

Invalidates Pauli's objection, enabling a new two-times perspective in quantum theories.

Abstract

Canonical quantization applied to closed systems leads to static equations, the Wheeler-deWitt equation in Quantum Gravity and the time independent Schr\"odinger equation in Quantum Mechanics. How to restore time is the Problem of Time(s). Integrating developments are: a) entanglement of a microscopic system with its classical environment accords it a time evolution description, the time dependent Schr\"odinger equation, where t is the laboratory time measured by clocks; b) canonical quantization of Special Relativity yields both the Dirac Hamiltonian and a self adjoint "time" operator, restoring to position and time the equivalent footing accorded to energy and momentum in Relativistic Quantum Mechanics. It introduces an intrinsic time property {\tau} associated with the mass of the system, and a basis additional to the usual configuration, momentum and energy basis. As a generator of momentum displacements and consequently of energy, it invalidates Pauli's objection to the existence of a time operator. It furthermore complies with the requirements to condition the other observables in the conditional interpretation of QG. As Pauli's objection figures explicit or implicitly in most current developments of QM and QG, its invalidation opens to research the effect of this new two times perspective on such developments.