A general perspective on time observables

• A general geometric framework for discussing time observables is proposed.
• In this framework, there is a local sense in which time observables always exist.
• A restricted class of time observables can exist in a global sense.
• Pauli׳s prohibition on quantum time observables is derived as a corollary.
• Time observables are shown to be regained in some extensions of quantum theory.

I propose a general geometric framework in which to discuss the existence of time observables. This framework allows one to describe a local sense in which time observables always exist, and a global sense in which they can sometimes exist subject to a restriction on the vector fields that they generate. Pauli׳s prohibition on quantum time observables is derived as a corollary to this result. I will then discuss how time observables can be regained in modest extensions of quantum theory beyond its standard formulation.