Remarks About the Relationship Between Relational Physics and a Large Kantian Component of the Laws of Nature

TL;DR

This paper explores how relational mechanics, which eliminates absolute space and time, introduces a Kantian perspective by showing that traditional notions of fundamental physics depend on gauge choices.

Contribution

It demonstrates that relational mechanics naturally leads to a Kantian view of physics, where absolute concepts are gauge-dependent and not fundamentally necessary.

Findings

Relational mechanics describes systems via shape space, removing absolute references.

Time in relational mechanics is a gauge-dependent, emergent concept.

Traditional absolute space and time are gauge choices, not fundamental entities.

Abstract

Relational mechanics is a reformulation of mechanics (classical or quantum) for which space is relational. This means that the configuration of an $N$-particle system is a shape, which is what remains when the effects of rotations, translations, and dilations are quotiented out. This reformulation of mechanics naturally leads to a relational notion of time as well, in which a history of the universe is just a curve in shape space without any reference to a special parametrization of the curve given by an absolute Newtonian time. When relational mechanics (classical or quantum) is regarded as fundamental, the usual descriptions in terms of absolute space and absolute time emerge merely as corresponding to the choice of a gauge. This gauge freedom forces us to recognize that what we have traditionally regarded as fundamental in physics might in fact be imposed by us through our choice of gauge. It thus imparts a somewhat Kantian aspect to physical theory.