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arXiv · 2111.09609

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

Sheldon Goldstein·Nino Zanghi
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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.

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Sheldon Goldstein, Nino Zanghi. 2021-11-18. Remarks About the Relationship Between Relational Physics and a Large Kantian Component of the Laws of Nature. https://arxiv.org/abs/2111.09609

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