Teh, Nicholas and Tsementzis, Dimitris (2015) Theoretical Equivalence in Classical Mechanics and its relationship to Duality. [Preprint]

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Abstract

As a prolegomenon to understanding the sense in which dualities are theoretical equivalences, we investigate the intuitive `equivalence' of hyper-regular Lagrangian and Hamiltonian classical mechanics. We show that the symplectification of these theories (via Tulczyjew's Triple) provides a sense in which they are (1) isomorphic, and (2) mutually and canonically definable through an analog of `common definitional extension'.

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Item Type:	Preprint
Creators:	Creators Email ORCID Teh, Nicholas nteh@nd.edu Tsementzis, Dimitris dtsement@princeton.edu
Additional Information:	Forthcoming in Studies in the History and Philosophy of Modern Physics.
Keywords:	Classical Mechanics, Duality, Theoretical Equivalence, Category Theory, Logic, Syntactic, Semantic, Symplectic Geometry, Symplectification
Subjects:	Specific Sciences > Physics > Classical Physics General Issues > Structure of Theories Specific Sciences > Physics > Symmetries/Invariances
Depositing User:	Dr Nicholas Teh
Date Deposited:	29 Sep 2015 14:47
Last Modified:	29 Sep 2015 14:47
Item ID:	11695
Subjects:	Specific Sciences > Physics > Classical Physics General Issues > Structure of Theories Specific Sciences > Physics > Symmetries/Invariances
Date:	28 September 2015
URI:	https://philsci-archive.pitt.edu/id/eprint/11695

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