Rob, Jonathan, all,
I believe part of the problem is 'whose?' uncertainty principle we're discussing. The above arguments seem to assume there is AN uncertainty principle. I suspect (without going to the trouble to prove it) that both Rob and Jonathan can find a reputable text or paper that supports very closely their own interpretation. So, without arguing about what THE uncertainty principle says, I believe the issue is 1) the informational approach, largely based on Fourier analysis, that Rob describes and 2) the fact that the order of measurement *does* determine the outcomes in the cases of interest, when the measurements interact with the system under consideration to a degree that changes the system. This is the significance of "weak measurement". (Jonathan, thanks for the link to Physics World. It shows the same 'wave function measurement' diagram that is on the first page of my FQXI essay, "The Nature of the Wave Function", and I provide 3 references to such articles.)
Rob, I had the same problem with Kauffmann's 'mandatory' phraseology, and yet I believe that this is the perspective of most quantum field theorists, "the most successful theory ever". My own goal is not to dismiss it as a stupid misinterpretation but to try to understand the physical essence of what's going on. I was in a discussion night before last with a very bright physicist who was singing the theme song, "but our intuitions did not evolve to understand quantum reality, yada-yada-yada. That's what Bohr, claimed, and is the basis of the Copenhagen interpretation, yet the weak measurements clearly show, as stated in Jonathan's Physics World link: "But it is striking that the average result of such a measurement will yield exactly what common sense would have suggested."
I began my above comment by stating my belief that 'quantum action' is the fundamental reality of our universe, more fundamental than momentum, energy, what have you, as there is no universal measure of momentum, or of energy, but Planck's constant IS the universal measure of action. Action has units of mass*length-squared*inverse-time (MLL/T), but it is the product of these terms that is constant, not the terms themselves, the mass, the length, or the time. Thus when one analyzes energy over very short durations, the constant is divided by time, and if there are no limits on the time interval, the energy heads toward infinity. I don't believe this happens, but neither do I believe that there is a "shortest time" in the universe, so the question is what to believe about physical reality. I think most quantum field theorists agree with Kauffmann's wording. For this reason I was happy to see his 'self-gravitating' approach as a possible self-limiting solution to the 'problem'. I do not believe in the physical reality of infinity, so when the math seems to imply infinity, I look for the point or mechanism at and by which it breaks down. Kauffmann may have found one.
Rob, while I agree with your information-based analysis, and with your FM examples, there is still a physical aspect that is interaction-based in the sense that measurement of quantum 'objects' interacts with, interferes with, and changes what is being observed. That's why weak measurement theory and approach is so significant.
Constantinos, I am speaking of action as the fundamental unit of the universe. We speak of momentum and energy because our minds find it easier to grasp these, since everyday experience does not illuminate units of action. Yet quantum theory began with Planck's discovery that action allowed him to match the data when all else failed, and quantum theory is intertwined with action every step of the way, from variational principles, to uncertainty principles, to spin, Bohr orbits, you name it. There appears to be no meaningful physics between zero action and a Planck unit of action, hence nothing to 'accumulate'. When you refer to h/kT you are working with the thermodynamic relation based on statistical ensembles (indicated by your use of the Boltzmann constant, k) and temperature T, which is a measure of average energy. Averages, of course, are NOT limited to integral multiples of h, as they are mathematical, not physical. The statistics show that the averaging scale factor, 1/kT, is useful in probability in terms of units of h, which is multiplied by a frequency to get the energy that is then compared to the average energy. The T in h/T is not temperature but time, and refers to what one gets when one tries to separate time from energy in a world built around quantum action. I hope this clarifies it somewhat.
Best,
Edwin Eugene Klingman