Dimensionless physics: continuation

TL;DR

This paper explores the concept of dimensionless physics in gravity, proposing that the metric tensor should have a fixed dimension of inverse length squared, which has implications for various quantum gravity models.

Contribution

It extends the idea of dimensionless physics by analyzing the implications of a metric with fixed dimension across different quantum gravity approaches.

Findings

The metric tensor should have dimension 1/[L]^2 in general relativity.

Implications for superplastic vacuum and tetrad models are discussed.

The approach unifies various quantum gravity theories under a dimensionless framework.

Abstract

Several approaches to quantum gravity (including the model of superplastic vacuum; Diakonov tetrads emerging as the bilinear combinations of the fermionis fields; $BF$-theories of gravity; and effective acoustic metric) suggest that in general relativity the metric must have dimension 2, i.e. $[g_{\mu\nu}]=1/[L]^2$, irrespective of the dimension of spacetime. This leads to the "dimensionless physics" discussed in the review paper G.E. Volovik, Dimensionless physics, JETP 132, 727 (2021). Here we continue to exploit this unusual dimension of the metric.