Angular momentum without rotation: turbocharging relationalism

TL;DR

This paper introduces a gauge-theoretic relational framework that accounts for rotational effects without relying on absolute rotation, challenging traditional absolutist views in physics.

Contribution

It proposes a novel relational theory incorporating an SO(3) charge, explaining rotational phenomena without fixed standards of rotation, using gauge theory tools.

Findings

Accounts for all rotational effects without absolute rotation

Uses SO(3) charge coupled to relations via gauge theory

Weakens the absolutist position on rotation

Abstract

Newton's rotating bucket pours cold water on the naive relationalist by vividly illustrating how certain rotational effects, particularly those due to non-zero angular momentum, can depend on more than just relations between material bodies. Because of such effects, rotation has played a central role in the absolute-relational debate and poses a particularly difficult challenge to the relationalist. In this paper, we provide a qualified response to this challenge that significantly weakens the absolutist position. We present a theory that, contrary to orthodoxy, can account for all rotational effects without introducing, as the absolutist does, a fixed standard of rotation. Instead, our theory posits a universal SO(3) charge that plays the role of angular momentum and couples to inter-particle relations via terms commonly seen in standard gauge theories such as electromagnetism and the Standard Model of particle physics. Our theory makes use of an enriched form of relationalism: it adds an SO(3) structure to the traditional relational description. Our construction is made possible by the modern tools of gauge theory, which reveal a simple relational law describing rotational effects. In this way, we can save the phenomena of Newtonian mechanics using conserved charges and relationalism. In a second paper, we will further explore the ontological and explanatory implications of the theory developed here.