I came across this very intriguing statement in another thread:

I vaguely recall seeing this elsewhere, and there is something extremely seductive about it -- if nothing else, its ratio of simplicity to explanatory / predictive power is pretty massive.

However, I'm having trouble with the interpretation / ramifications, and I think it comes back to uncertainty relations / Fourier duality -- and maybe also wave/particle duality.

For instance, even the statement that there is a "rate of change of phase" poses some difficulty -- because what is it that "has" this phase? I suppose if you took the integral of a wavefunction's energy over any region at time t=a, you could say that this is the instantaneous rate of change of that wavefunction's "phase in that region", but can you even define "phase" in a region -- or for that matter, at an instant? I suppose you can take it a step further and integrate over a 4-volume, and then somehow have an "average" phase / energy over that 4-volume, but being an average, the value it would necessarily be less precise the larger the volume (and therefore, the more 'confident' you can be of the value)?

This is basically one aspect of de Broglie. He postulated (extending from photons) that E is proportional to an intrinsic frequency. As mass increases relativistically with velocity, frequency increases. That rule is quite simple.

The trick is to get this all to work with SR, since a moving clock runs slower -- phase velocity has to increase, beyond c, to compensate. (Read his thesis for a better explanation.)

You may be overcomplicating. I believe the intended meaning is that "rate of change of phase" is frequency, which has to be measured over an extended waveform, with operators, etc.