# Relative Quantum Time

## TL;DR

This paper develops a framework for quantum theory that maintains global time-shift invariance while allowing for local perception of change, using relative time observables and the Page-Wootters formalism.

## Contribution

It introduces a rigorous formulation of relative time observables that reconcile global invariance with local Heisenberg evolution in quantum mechanics.

## Key findings

- Established a formalism for relative time in quantum theory.
- Demonstrated compatibility of local evolution with global invariance.
- Extended the Page-Wootters approach to a more rigorous setting.

## Abstract

The need for a time-shift invariant formulation of quantum theory arises from fundamental symmetry principles as well as heuristic cosmological considerations. Such a description then leaves open the question of how to reconcile global invariance with the perception of change, locally. By introducing relative time observables, we are able to make rigorous the Page-Wootters conditional probability formalism to show how local Heisenberg evolution is compatible with global invariance.