Pablo Ruiz de Olano (Max Planck Institute for the History of Science)
In this paper, I study the manner in which symmetries and conservation laws relate to each other in quantum and in classical mechanics. The paper contains two main claims. First, I argue that the nature of the connection between symmetries and conservation laws is different in the Hilbert space formulation of quantum mechanics and in the Hamiltonian formulation of classical mechanics. This is because in the latter case, unlike in the former one, there are symmetries of the equations of motion that do not give rise to a conservation law. Secondly, I claim that future research ought to focus on comparing the manner in which symmetries and conservation laws relate to each other in different formulations of the same physical theories.
