- #1

pellman

- 684

- 5

By quantum theory I should perhaps say "relativistic quantum mechanics" since I don't know enought QFT to ask a proper question.

If there were a proper time [tex]\tau[/tex] parameter or dynamical variable, then a rest-mass operator [tex]i\hbar\frac{\partial}{\partial \tau}[/tex] would be its conjugate in the same way that energy is "conjugate" to time in non-relativistic QM. A specific rest mass then, such as we see assumed in the Klein-Gordon equation, would represent a eigentstate of this rest-mass operator.

But there is no degree of freedom associated with rest mass, right? We never see superpositions of states of different rest mass, right?

Of course, proper time is not completely analogous to time-as-parameter in non-relativistic QM. In non-relativistic QM, time is a global parametrization of the whole system, whereas proper time ,as usually understood, is specific to each particle.

So what is the consequence of this to our understanding of proper time within quantum theory?