Emergent diffeomorphism invariance in toy models

TL;DR

This paper explores toy models with emergent time-reparametrization invariance to shed light on conceptual issues in quantum gravity, showing that these problems are resolved when invariance is understood as emergent rather than fundamental.

Contribution

It demonstrates how classical diffeomorphism invariance can emerge from energy conservation in toy models, clarifying conceptual issues in quantum gravity.

Findings

Emergent time-reparametrization invariance from energy conservation.

Resolution of quantum gravity problems by recognizing invariance as emergent.

Toy models illustrate that fundamental theories need not be diffeomorphism invariant.

Abstract

Conceptual difficulties in semiclassical and quantum gravity arise from diffeomorphism invariance of classical general relativity. With a motivation to shed some light on these difficulties, we study a class of toy models for which one-dimensional diffeomorphism invariance, namely time-reparametrization invariance, emerges at the classical level from energy conservation. An attempt to quantize the models while taking the invariance seriously leads to toy versions of the problem of time in quantum gravity, of the cosmological constant problem, and of the black hole firewall problem. Nevertheless, all these problems are easily resolved by taking into account that the invariance emerges only at the classical level, while the fundamental theory that needs to be quantized is not diffeomorphism invariant.