Thus the wave is not moving relative to the inertial reference frame of the cavity. Thus it now has no kinetic energy within this reference frame at all.
No, you're wrong.
In quantum mechanics, kinetic energy is not "rate of change of time of the position of the center of mass". Kinetic energy is proportional to the 2nd derivative of the wavefunction, and the 2nd derivative of the wavefunction is not zero.
Let me give you an example where the physics is as obvious as possible. Take one laser beam and shoot a pulse to the left. Take another laser and shoot a pulse to the right. Let the pulses fly through space, at some point, cross and overlap. The region of space where
both, counterpropagating pulses are present has---uh-oh---a photon wavefunction with
exactly the same properties as an ensemble of photons in a cavity. In other words, it looks in every detail like a standing wave; it has zero NET momentum; the center-of-momentum isn't moving anywhere; etc. (In fact, if you were standing in this region you would be
unable to tell whether the light you're seeing is passing-in-the-night or trapped-in-a-cavity. Go ahead, do the math.) But you must agree that this region of space contains photons with ordinary kinetic energy---50% of it, on average, heading left and 50% heading right.
The laws of quantum mechanics---i.e., KE = (p-hat)^2/2m---will look at this wavefunction and get that fact right. (It'll say p = {left or right}, <p> = 0, <p^2> != 0, KE != 0, etc.) Your heuristic----"this is the wavefunction of a standing wave, so let's ignore Schrodinger and think about relativity"---will not.
Johan was talking about a light wave, not a massive particle. I'm afraid you're all getting this wrong, making a meal of it, and digging a hole for yourselves.
Johan has been denying that massive particles, in bound states, have kinetic energy. I diverted him onto photons only briefly.
I beg to differ. I'm seeing sentences like this whole argument contradicts standard quantum mechanics in response to simple statements associated with relativity. A radiating body loses mass.
No, Farsight, I think you've got hold of the wrong end of the stick. The gist of the conversation was "what are the properties of an particle in a box"---properties like whether <p^2/2m> was or was not zero, whether <p^2/2m> reflects something about energy, whether that energy can be called kinetic, and (most importantly) whether or not could escape from the box without an acceleration.
Johan's discussion of all of
this contradicts standard quantum mechanics, in very simple ways that contradict Niels-Bohr-era
experimental facts, like "which measurements give predictable answers and which have random scatter?" and "does small delta-x mean large delta-p?" This has nothing to do with
interpretation, which asks detailed questions about whether the wavefunctions-that-give-the-right-answers are hiding some underlying physics. Johan is disagreeing with the fact that the wavefunctions give the right answers at all.
(Then:
you, and you alone, are volunteering to turn this into a relativity problem where the disagreement is about how mass/energy are labeled in different frames. Nothing to do with Copenhagen, and nothing to do with
my statements that Johan makes quantum mistakes.)
From a senior condensed matter physicist who told me that he and his colleagues took a "realist" view that was in total conflict with the Copenhagen Interpretation of quantum mechanics. And from other people in the related spheres of optics and electronics.
Likewise, I have plenty of colleagues who
use Newton's Laws on a daily basis, and who don't have to think about relativity at all. This fact has
nothing to say about whether Special Relativity is or is not correct; to see that, you have to specifically look for experiments that distinguish between the cases. Yes, there are plenty of experiments where "the full apparatus of modern quantum mechanics" and "the student version of quantum mechanics where you pretend photons are classical waves" will give the same answer, just like Newton and Einstein will give the same answers in many experiments.
If your acquaintances have done an experiment that
disagrees with Schrodinger's equation, they're welcome to publish it. They have not done so, unless you're referring to Johan. I repeat: there is
no experimental evidence of any violation of standard quantum mechanics. That's how it got to be standard quantum mechanics.
Oh come on ben. Theorists and experimentalist have a long history of Who ordered that? rivalry.
Well, I'm sitting here as an experimentalist in a department chock-full of theorists, and I will say bluntly that you have no idea what you're talking about. Other than generic-griping-about-string-theory (which is unidirectional), I have a hard time coming up with an
anecdote, much less a pattern, of a recent "who ordered that" rivalry or an "erudite vs. greaseheads" dichotomy.
Especially not in solid-state and atomic physics, for crying out loud, where you have experimentalists who get excited about critical exponents, and theorists who get excited about graphene CVD.