On the Structure of Classical Mechanics
Bibliographic Data
| ID | 8397493 |
|---|---|
| Authors | Thomas William Barrett (Princeton University, corresponding author) |
| Year | 2015 |
| Volume | 66 |
| Issue | 4 |
| Pages | 801-828 |
| Publication date | 2015-12-01 |
| Open Access | No |
| Type | ARTICLE |
| Venue | The British Journal for the Philosophy of Science (JOURNAL) |
| Journal identifiers | ISSN: 0007-0882 • E-ISSN: 1464-3537 |
| Publisher | Oxford University Press (PUBLISHER • GB) |
| DOI | 10.1093/bjps/axu005 |
| OpenAlex | W2111611584 |
| Language | EN |
| Citations received | 27 |
| References cited | 5 |
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 Introduction2 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 > symplectic3 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 incomparable4 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 equivalence6 Conclusion
Classical mechanics · Covariant Hamiltonian field theory · Hamiltonian (control theory) · Hamiltonian mechanics · Hamiltonian system · Phase space · Physics · Pure mathematics · Quantum mechanics · Superintegrable Hamiltonian system · Symplectic geometry · Symplectic manifold · Mathematical Physics · Mathematics · Origins and Evolution of Life · Philosophy and History of Science · Quantum Mechanics and Applications
Structuralism with and without causation
What Do Privileged Coordinates Tell Us about Structure
The Logic in Philosophy of Science
Physical Theories are Prescriptions, not Descriptions
On Putnam’s Proof of the Impossibility of a Nominalistic Physics
What theoretical equivalence could not be
How to count structure
The Conventionality of Geometry Is Merely Incomplete
An Epistemic Account Of Metaphysical Equivalence1
On Einstein algebras and relativistic spacetimes
Spacetime structure
Quine’s conjecture on many-sorted logic
Deduction and definability in infinite statistical systems
On automorphism criteria for comparing amounts of mathematical structure
Fiber bundles, Yang–Mills theory, and general relativity
What are empirical consequences? On dispensability and composite objects
Deformation quantization as an appropriate guide to ontic structure
Comparing the structures of mathematical objects
Mutual translatability, equivalence, and the structure of theories
Is the classical limit “singular”
The curvature argument
No-go theorems
What Do Symmetries Tell Us about Structure
Structure and Equivalence
Equivalent and Inequivalent Formulations of Classical Mechanics
Sophistication about Symmetries
Part 2
| Citations per year | 2.45 |
|---|---|
| Citation span | 2015 - 2025 (11) |
| Highly cited | No |