On the Structure of Classical Mechanics


Authors
Thomas William Barrett
University of California at Santa Barbara
Abstract
The standard view is that the Lagrangian and Hamiltonian formulations of classical mechanics are theoretically equivalent. Jill North, however, argues that they are not. In particular, she argues that the state-space of Hamiltonian mechanics has less structure than the state-space of Lagrangian mechanics. I will isolate two arguments that North puts forward for this conclusion and argue that neither yet succeeds. 1 Introduction2 Hamiltonian State-space Has less Structure than Lagrangian State-space2.1 Lagrangian state-space is metrical2.2 Hamiltonian state-space is symplectic2.3 Metric > symplectic3 Hamiltonian State-space Does Not Have Less Structure than Lagrangian State-space3.1 Lagrangian state-space has less than metric structure3.1.1 A potential worry3.1.2 General Lagrangians3.2 Hamiltonian state-space has more than symplectic structure3.2.1 A dual structure on the Hamiltonian state-space3.2.2 Simple Hamiltonians3.3 Comparing Lagrangian and Hamiltonian structures3.3.1 Counting mathematical structure3.3.2 Symplectic and metric structure are incomparable4 An Alternative Argument for LS4.1 The argument for P3*4.2 Symplectic manifold vs. tangent bundle structure4.3 Trying to patch up the argument for P3*5 Interpreting Mathematical Structure5.1 State-space realism5.2 Model isomorphism and theoretical equivalence6 Conclusion
Keywords classical mechanics  theoretical equivalence  structure
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Reprint years 2015
DOI 10.1093/bjps/axu005
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References found in this work BETA

What Scientific Theories Could Not Be.Hans Halvorson - 2012 - Philosophy of Science 79 (2):183-206.
Classical Mechanics Is Lagrangian; It Is Not Hamiltonian.Erik Curiel - 2014 - British Journal for the Philosophy of Science 65 (2):269-321.
World Enough and Space-Time: Absolute Versus Relational Theories of Space and Time.John S. Earman - 1992 - British Journal for the Philosophy of Science 43 (4):573-580.

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Citations of this work BETA

Glymour and Quine on Theoretical Equivalence.Thomas William Barrett & Hans Halvorson - 2016 - Journal of Philosophical Logic 45 (5):467-483.
Morita Equivalence.Thomas William Barrett & Hans Halvorson - 2016 - Review of Symbolic Logic 9 (3):556-582.
On Einstein Algebras and Relativistic Spacetimes.Sarita Rosenstock, Thomas William Barrett & James Owen Weatherall - 2015 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 52 (Part B):309-316.
What Do Symmetries Tell Us About Structure?Thomas William Barrett - 2017 - Philosophy of Science (4):617-639.
Categories and the Foundations of Classical Field Theories.James Owen Weatherall - forthcoming - In Elaine Landry (ed.), Categories for the Working Philosopher. Oxford, UK: Oxford University Press.

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