Universality of geometry

TL;DR

This paper demonstrates that in emergent gravity models, the physical metric is universal at large scales, resolving the ambiguity of metric candidates and showing that geometry's universality breaks down at Planck-scale distances.

Contribution

It provides a detailed analysis of the quantum effective action for multiple metrics, establishing the universality of the physical metric at long distances in emergent gravity models.

Findings

The physical metric is universal at long distances, representing a massless graviton.

Other metric candidates correspond to massive fields active only at microscopic scales.

Geometry's universality is lost at Planck-scale distances, where time and space lose their classical meaning.

Abstract

In models of emergent gravity the metric arises as the expectation value of some collective field. Usually, many different collective fields with appropriate tensor properties are candidates for a metric. Which collective field describes the "physical geometry"? We resolve this "metric ambiguity" by an investigation of the most general form of the quantum effective action for several metrics. In the long-distance limit the physical metric is universal and accounts for a massless graviton. Other degrees of freedom contained in the various metric candidates describe very massive scalars and symmetric second rank tensors. They only play a role at microscopic distances, typically around the Planck length. The universality of geometry at long distances extends to the vierbein and the connection. On the other hand, for distances and time intervals of Planck size geometry looses its universal meaning. Time is born with the big bang.