What is General Relativity?

TL;DR

This paper explores fundamental questions about the scale and validity of Einstein's field equations in general relativity, especially in cosmological and quantum contexts, proposing that foundational principles may need reformulation.

Contribution

It addresses open questions about the scale of matter-geometry coupling, the validity of field equations across scales, and the role of foundational principles in cosmology and quantum gravity.

Findings

Questions about the scale of matter-geometry coupling.

Implications of quantum gravity approaches on spacetime structure.

The need for reformulating general relativity principles in cosmology.

Abstract

General relativity is a set of physical and geometric principles, which lead to a set of (Einstein) field equations that determine the gravitational field, and to the geodesic equations that describe light propagation and the motion of particles on the background. But open questions remain, including: What is the scale on which matter and geometry are dynamically coupled in the Einstein equations? Are the field equations valid on small and large scales? What is the largest scale on which matter can be coarse grained while following a geodesic of a solution to Einstein's equations? We address these questions. If the field equations are causal evolution equations, whose average on cosmological scales is not an exact solution of the Einstein equations, then some simplifying physical principle is required to explain the statistical homogeneity of the late epoch Universe. Such a principle may have its origin in the dynamical coupling between matter and geometry at the quantum level in the early Universe. This possibility is hinted at by diverse approaches to quantum gravity which find a dynamical reduction to two effective dimensions at high energies on one hand, and by cosmological observations which are beginning to strongly restrict the class of viable inflationary phenomenologies on the other. We suggest that the foundational principles of general relativity will play a central role in reformulating the theory of spacetime structure to meet the challenges of cosmology in the 21st century.