Symplectic reduction and the problem of time in nonrelativistic mechanics’. The British Journal for the Philosophy of Science 63

The deep connection between the interpretation of theories invariant under local sym-metry transformations (i.e. gauge theories) and the philosophy of space and time can be illustrated nonrelativistically via the investigation of reparameterization-invariant refor-mulations 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 con-straints 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 abso