Thomas William Barrett (Author)
British Journal for the Philosophy of Science
Volume: 66
Issue: 4
Pages: 801-828
The standard view is that the Lagrangian and Hamiltonian formulations of classical mechanics are theoretically equivalent. Jill North ([2009]), 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 Introduction 2 Hamiltonian State-space Has less Structure than Lagrangian State-space 2.1 Lagrangian state-space is metrical 2.2 Hamiltonian state-space is symplectic 2.3 Metric > symplectic 3 Hamiltonian State-space Does Not Have Less Structure than Lagrangian State-space 3.1 Lagrangian state-space has less than metric structure 3.1.1 A potential worry 3.1.2 General Lagrangians 3.2 Hamiltonian state-space (often) has more than symplectic structure 3.2.1 A dual structure on the Hamiltonian state-space 3.2.2 Simple Hamiltonians 3.3 Comparing Lagrangian and Hamiltonian structures 3.3.1 Counting mathematical structure 3.3.2 Symplectic and metric structure are incomparable 4 An Alternative Argument for LS 4.1 The argument for P3* 4.2 Symplectic manifold vs. tangent bundle structure 4.3 Trying to patch up the argument for P3* 5 Interpreting Mathematical Structure 5.1 State-space realism 5.2 Model isomorphism and theoretical equivalence 6 Conclusion
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