Evolution without evolution, and without ambiguities

TL;DR

This paper revisits the timeless quantum approach to time, demonstrating that the model can be refined to eliminate ambiguities and be extended for new applications, thus strengthening the foundation of the evolution without evolution concept.

Contribution

The paper clarifies and resolves ambiguities in the timeless quantum model of evolution, updating it for broader applicability.

Findings

No ambiguities in the model's dynamics

Updated model compatible with new applications

Reinforces the timeless approach to quantum evolution

Abstract

In quantum theory it is possible to explain time, and dynamics, in terms of entanglement. This is the timeless approach to time, which assumes that the universe is in a stationary state, where two non-interacting subsystems, the clock and the rest, are entangled. As a consequence, by choosing a suitable observable of the clock, the relative state of the rest of the universe evolves unitarily with respect to the variable labelling the clock observable's eigenstates, which is then interpreted as time. This model for an evolution without evolution (Page and Wootters, 1983), albeit elegant, has never been developed further, because it was criticised for generating severe ambiguities in the dynamics of the rest of the universe. In this paper we show that there are no such ambiguities, we also update the model, making it amenable to possible new applications.