Some unexpected aspects of mass and proper time in quantum mechanics, and why they should be considered as dynamical objects, represented by Hermitian operators
In classical physics, and non-relativistic quantum mechanics, mass enters the theory as a simple parameter. This leads to paradoxical behavior, which can only be cured by considering it as an operator. Proper time is determined by geometry, but it also has no dynamical role to play, which also leads to paradoxes. Again the cure is to consider it as an operator. The standard formalism is perfectly attuned to extend to accomodate them as such, where they will be conjugate variables, which leads to new phenomena.