Does relationalism alone control geometrodynamics with sources?

TL;DR

This paper examines whether relational first principles alone can determine geometrodynamics with sources, revealing limitations and complexities in deriving general relativity and related principles from these foundational ideas.

Contribution

It clarifies the slow convergence of the Dirac procedure with matter fields and introduces a less pathological Einstein--aether theory violating the equivalence principle within relational frameworks.

Findings

The exhaustive Dirac procedure with matter is slower than previously thought.

A less pathological equivalence principle violating theory exists within relational premises.

Limitations are identified in deriving the universal light cone principle from relational first principles.

Abstract

This paper concerns relational first principles from which the Dirac procedure exhaustively picks out the geometrodynamics corresponding to general relativity as one of a handful of consistent theories. This was accompanied by a number of results and conjectures about matter theories and general features of physics -- such as gauge theory, the universal light cone principle of special relativity and the equivalence principle -- being likewise picked out. I have previously shown that many of these matter results and conjectures are contingent on further unrelational simplicity assumptions. In this paper, I point out 1) that the exhaustive procedure in these cases with matter fields is slower than it was previously held to be. 2) While the example of equivalence principle violating matter theory that I previously showed how to accommodate on relational premises has a number of pathological features, in this paper I point out that there is another closely related equivalence principle violating theory that also follows from those premises and is less pathological. This example being known as an `Einstein--aether theory', it also serves for 3) illustrating limitations on the conjectured emergence of the universal light cone special relativity principle.