An effective approach to the problem of time

TL;DR

This work presents an effective-constraint framework to address the problem of time in quantum gravity by employing local internal times (Zeitgeister) and semiclassical states. Time becomes complex in non-global clock settings, with gauge transformations enabling clock switches to traverse turning points and maintain coherent relational evolution. The concept of fashionables captures local relational observables tied to a chosen Zeitgeist, while the imaginary part of time is shown to be universal to leading order and physically meaningful within the effective description. The approach provides a practical route to analyze quantum cosmology and gravity in semiclassical regimes and outlines how time might behave in highly quantum states, where relational evolution becomes inherently local and patch-dependent.

Abstract

A practical way to deal with the problem of time in quantum cosmology and quantum gravity is proposed. The main tool is effective equations, which mainly restrict explicit considerations to semiclassical regimes but have the crucial advantage of allowing the consistent use of local internal times in non-deparameterizable systems. Different local internal times are related merely by gauge transformations, thereby enabling relational evolution through turning points of non-global internal times. The main consequence of the local nature of internal time is the necessity of its complex-valuedness, reminiscent of but more general than non-unitarity of evolution defined for finite ranges of time. By several general arguments, the consistency of this setting is demonstrated. Finally, we attempt an outlook on the nature of time in highly quantum regimes. The focus of this note is on conceptual issues.