Symplectic Reduction and the Problem of Time in Nonrelativistic Mechanics

Thébault, Karim P. Y. (2012): Symplectic Reduction and the Problem of Time in Nonrelativistic Mechanics. In: British Journal for the Philosophy of Science, Vol. 63, No. 4: pp. 789-824

Abstract

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 reparameterisation 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 precisely 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.

• Item Type: Journal article
• Form of publication: Publisher's Version
• Keywords: Problem of Time, Constraints, Symplectic Reduction, Gauge, Quantum Gravity, Reparameterization Invariance
• Faculties: Philosophy, Philosophy of Science and Religious Science > Munich Center for Mathematical Philosophy (MCMP); Philosophy, Philosophy of Science and Religious Science > Munich Center for Mathematical Philosophy (MCMP) > Philosophy of Physics
• Subjects: 100 Philosophy and Psychology > 100 Philosophy
• Language: English