Some unexpected aspects of mass and proper time in quantum mechanics, and why they should be considered as dynamical objects, represented by Hermitian operators
Abstract:
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.