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When scale is surplus

Gryb, Sean and Sloan, David (2021) When scale is surplus. [Preprint]

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Abstract

We study a long-recognised but under-appreciated symmetry called 'dynamical similarity' and illustrate its relevance to many important conceptual problems in fundamental physics. Dynamical similarities are general transformations of a system where the unit of Hamilton's principal function is rescaled, and therefore represent a kind of dynamical scaling symmetry with formal properties that differ from many standard symmetry. To study this symmetry, we introduce a novel set of principles for identifying the surplus structure of a theory designed to accommodate the distinct features of dynamical similarities. We test our framework on a variety of examples and find that it sidesteps tensions between dynamic and epistemic aspects of symmetry while reproducing orthodox intuitions. When applied to cosmology, our framework prescribes that dynamical similarities should be associated with surplus structure. We then review previous technical results showing that an elimination of this surplus structure leads to a resolution of a large class of singularities in general relativity and suggests a novel explanation for the arrow of time. We conclude by highlighting the potential relevance of dynamical similarity to thermodynamic and quantum systems.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Gryb, Seans.gryb@hef.ru.nl0000-0002-0439-3548
Sloan, Daviddavidjasloan@gmail.com
Keywords: symmetry, dynamical similarity, surplus structure, cosmology, singularity resolution, arrow of time, contact geometry
Subjects: Specific Sciences > Physics > Cosmology
Specific Sciences > Physics > Relativity Theory
Specific Sciences > Physics > Symmetries/Invariances
Depositing User: Dr Sean Gryb
Date Deposited: 13 Mar 2021 00:09
Last Modified: 13 Mar 2021 00:09
Item ID: 18811
Subjects: Specific Sciences > Physics > Cosmology
Specific Sciences > Physics > Relativity Theory
Specific Sciences > Physics > Symmetries/Invariances
Date: 12 March 2021
URI: http://philsci-archive.pitt.edu/id/eprint/18811

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