2021/11/18 by Sheldon Goldstein, Nino Zanghı̀, Goldstein, Sheldon +2
Arts and Humanities · Mathematics · Physics and Astronomy · #Absolute time and space #Analytical mechanics #Classical mechanics #Classical physics #Component (thermodynamics) #FOS: Physical sciences #Gauge (firearms) #Mathematics #Philosophy #Philosophy and History of Science #Physical law #Physics #Quantum #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Quantum mechanics #Quantum statistical mechanics #Relativity and Gravitational Theory #Space (punctuation) #Theoretical physics #Theory of relativity #quant-ph
paper · pdf · doi:10.48550/arxiv.2111.09609
37 pages, 1 figure
arxiv created 2021/11/18 · openalex publication_date 2021/11/18 · arxiv updated 2021/11/19 · openalex created_date 2022/05/05 · openalex updated_date 2026/08/05
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.