Symplectic Reduction and the Problem of Time in Nonrelativistic Mechanics
Bibliographic Data
| ID | 8398044 |
|---|---|
| Authors | Karim P Y Thébault (0000-0002-3440-3030, The University of Sydney, corresponding author) |
| Year | 2012 |
| Volume | 63 |
| Issue | 4 |
| Pages | 789-824 |
| Publication date | 2012-12-01 |
| Peer Reviewed | Yes |
| 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/axr045 |
| OpenAlex | W2095945737 |
| Language | EN |
| Citations received | 7 |
| References cited | 21 |
The deep connection between the interpretation of theories invariant under local symmetry transformations (i.e. gauge theories) and the philosophy of space and time can be illustrated nonrelativistically via the investigation of reparameterization-invariant reformulations of Newtonian mechanics, such as Jacobi's theory. Like general relativity, the canonical formulation of such theories feature Hamiltonian constraints; and like general relativity, the interpretation of these constraints along conventional Dirac lines is highly problematic in that it leads to a nonrelativistic variant of the infamous problem of time. I argue that, nonrelativistically at least, the source of the problem can be found precsely within the symplectic reduction that goes along with strict adherence to the Dirac view. Avoiding reduction, two viable alternative strategies for dealing with Hamiltonian constraints are available. Each is found to lead us to a novel and interesting re-conception of time and change within nonrelativistic mechanics. Both these strategies and the failure of reduction have important implications for the debate concerning the relational or absolute status of time within physical theory. 1 Introduction 2 Mechanics with a Fixed Parameterization 2.1 Lagrangian mechanics 2.2 Hamiltonian mechanics 2.3 Symplectic mechanics 2.4 Presymplectic geometry and symplectic reduction 3 Reductionism, Haecceitism, and Gauge Symmetry 4 Reparameterization-Invariant Mechanics 4.1 Extended Lagrangian mechanics 4.2 Extended Hamiltonian mechanics 4.3 Jacobi's principle and timeless theory 4.4 Degeneracy, indeterminacy, and triviality 5 Representing Change and Observables in Timeless Mechanics 5.1 The emergent time strategy 5.2 The correlation strategy 6 Interpretational Implications 6.1 The relationalist versus substantivalist dispute with regard to time 6.2 An ontology of timeless change?
Analytical dynamics · Analytical mechanics · Classical mechanics · Hamiltonian (control theory) · Hamiltonian mechanics · Lagrangian mechanics · Mathematical analysis · Physics · Quantum mechanics · Quantum statistical mechanics · Symplectic geometry · Theoretical physics · Mathematical Physics · Mathematics · Noncommutative and Quantum Gravity Theories · Quantum Mechanics and Applications · Relativity and Gravitational Theory
Regarding the ‘Hole Argument’ and the ‘Problem of Time’
Three denials of time in the interpretation of canonical gravity
Change in Hamiltonian general relativity from the lack of a time-like Killing vector field
Deformation quantization as an appropriate guide to ontic structure
Quantization as a Guide to Ontic Structure
Time Remains
Sophistication about Symmetries
| Unique citing works | 7 |
|---|---|
| Citations per year | 0.5 |
| Citation span | 2012 - 2021 (10) |
| Citation velocity | historical |
| Highly cited | No |
| Citation types | Neutral: 6 |