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Theoretical Equivalence in Classical Mechanics and its relationship to Duality

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:
CreatorsEmailORCID
Teh, Nicholasnteh@nd.edu
Tsementzis, Dimitrisdtsement@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: http://philsci-archive.pitt.edu/id/eprint/11695

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