Dynamical Phase as Physical

However, before validating this claim, it is worthwhile to remind oneself that the phase function $S'$ is not a floating abstraction, i.e. disconnected from reality. It is a sum of five parts,

$$S'=W_0(u)+W_1(v)+W_2(x)+W_3(y)+(\tau-\tau_0)P_\tau~.$$

The first four are the contributions to the phase which depend on $(u,v,x,y)$ and thus express the dependence on the arrangement of laboratory meter sticks and clocks used to establish spacetime events.

The last part, which depends on the proper time $\tau$ (the particle's ``wrist watch'' time), is the contribution which depends on the intrinsic properties of the particle. Its rest mass, or more precisely its quantum mechanical Compton frequency ( $mc^2/\hbar$), determines the rate at which it contributes to the dynamical phase. This phase, in turn, gives rise to interference effects measurable in the laboratory. It is, as it were, that the particle carries its own intrinsic clock.