2020/11/03 by Henrique Gomes, Sean Gryb
Mathematics · Physics and Astronomy · #Angular momentum #Classical mechanics #History and Theory of Mathematics #Orthodoxy #Philosophy #Physics #Quantum Mechanics and Applications #Relativity and Gravitational Theory #Theoretical physics #physics.hist-ph
paper · pdf · doi:10.1016/j.shpsa.2021.05.006
published as Studies in History and Philosophy of Science, Vol 88 (2021): pp 138-155 · 41 pages, 1 figure
arxiv created 2020/11/03 · openalex publication_date 2021/06/23 · arxiv updated 2021/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Rotation is a challenging riddle for the relationalist. In early versions of the absolute-relational debate for example, Newton's rotating bucket poured cold water on the relationalist position. While the parameters of the debate have changed, a more recent analysis in 1999 by Belot proclaimed rotation to be "the downfall of relationalism." In this paper, we provide a relational response to the riddle of rotation. 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 global 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 all 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.