kith said:
That depends on the interpretation. You have to repeat your measurement to confirm that Bob always gets the predicted value. So you always have to do experiments with (sometimes abstract) ensembles of systems. Now if all experiments are done with ensembles, why should the physical theories we deduce from them be about single systems and not only about the ensembles? Personally, I don't stick to this interpretation, but it certainly is a valid one.
Well, I don't agree that all experiments are done with ensembles. I only have one car, one cell phone, one home computer (okay, actually I have two or three, but that's not really enough to count as an ensemble). I notice certain regularities in their behavior: if you do such and such, then such and such will happen. The point of science (it seems to me) is to understand those regularities. The "ensemble interpretation" seems to miss the point: The reason that my computer behaves such and such a way when I do such and such is because there is an imaginary ensemble of a huge number of identical computers, and the vast majority of them behave in that way?
But there is another question about the ensemble view, which is: what varies from one member of the ensemble to another?
Notice that there is a definite answer to this question in classical statistical mechanics (modulo coarse-graining, which brings up conceptual problems in classical probability theory, as well, which I don't want to get into right now). You imagine an ensemble of systems, all of which have the same values for
macroscopic quantities (such as total energy, total number of particles, total momentum, total charge, etc.) but differ in their
microscopic descriptions. So the ensemble interpretation there is a way of dealing with lack of knowledge: We know certain facts about the actual system under consideration. This knowledge gives rise to an imaginary ensemble of systems, all of whom agree with our actual system in the details that we've measured. So our actual system is assumed to be one of the systems in that ensemble, we just don't know which.
Using ensembles for quantum systems is a little stranger, it seems to me, because of the questions of what is the same for all systems in the ensemble, and what varies. If we assume a hidden variables interpretation, then we can assume that the systems in the ensemble differ in the values for those variables. Alternatively, we could just say that different systems in the ensemble differ in the results of measurements. In that case, the ensembles are more like "alternate histories", kind of like in the "many worlds interpretation".
So I don't see that ensembles do anything for us, in terms of
interpretations of quantum mechanics. We need an interpretation even to make sense of the ensembles.
[edit]:
Why need they be understandable?
I think that the impetus for doing any science is understanding the world. We certainly can't demand that the world be understandable, but the assumption that it is understandable has great power in developing science. It's possible to develop science as just mysterious rules for manipulating data to get predictions, but I think that the real advances in science come from those who attempt to actually understand what's going on.
Locality is an assumption. Bell's theorem tells us that we can't have locality, realism and independent choices of measurement simultaneously. So if locality is important for you, you can pick a local interpretation. Of course, you probably get a different drawback by violating one of the other assumptions. ;-)
Personally, I don't care about locality, except for the fact that it makes physics simpler. One could imagine an interpretation in which a measurement instantaneously collapses the wavefunction everywhere in the universe. But that interpretation opens up a huge can of worms: In which rest frame is the collapse instantaneous? What makes an interaction a "measurement"? Giving up locality is not an answer, it's just choosing a different set of questions.