some_dude wrote:I've had two QM courses but they've been pretty much exclusively about the mathematics of QM (which is okay since that is the most important in practice) so I'm still unsure about some really basic interpretative issues that I'd like to know even though they seem embarrassing to ask.
When some quantity of a system hasn't been measured in a while it seems as if half the time someone says it's in a superposition so that it really has multiple values at the same time and the other half of the time I hear that its value is undefined. The first view seems to suggest that, say, some particle is in multiple places at the same time while the latter view suggests that it in fact is nowhere until measured. They seem mutually exclusive to me, so which explanation is right?
It's in a superposition, where it exists in multiple states at once.
What's undefined is which of those states you'll measure it to be in once you interact with it. That is really, truly random.
At time t=t0 Alice measures some quantity q of system A. At a later time t=t1 Bob measures q in system A. If you ask Alice to give the value of q at time t=t1 she will say it's either in a superposition or undefined (depending on the answer to the first question) while Bob will say that he has just caused wavefunction collapse and q has the value just measured. I remember reading somewhere that they're both correct, but it seems to me that Alice would be wrong because the conditions have changed since her measurement because of Bob's measurement. I think this question have different answers depending on the interpretation used, this might be a non-issue in MWI, but it would be interesting nonetheless to know how collapse interpretations deal with it. This is obviously all assuming a non-relativistic situation, if it was the situation would be entirely different because they wouldn't agree on when t=t0 and t=t1 and they might both be right. You can argue that they can never be certain whether they both really measured the same system (at least they couldn't be measuring exactly the same system because Alice's measurement would have changed it) but I'm not sure whether "they're not really talking about the same system so they can both be right" is the answer to the question.
If Alice measured q, then it has a particular value. As long as Bob measures it in a compatible way, they'll get the same answers.
I measure, say, the momentum in the x-direction of some particle causing its momentum wavefunction to collapse. Then the momentum wavefuntion px is given by a dirac delta function and the Heisenberg uncertainty principle seems to suggest that the uncertainty in the particle's x-position tends to infinity so that its position wavefunction is a constant and if you then measure its position it might as well be somewhere in the Andromeda Galaxy. Obviously this doesn't happen but I can't see why not? (Again this is only an issue in collapse interpretations but I want to know how they deal with it)
You can't measure the momentum with infinite certainty, so this is luckily a non-issue. The momentum is never described by a dirac delta; it's always a more "standard" curve with amplitude spread over a possibly-small region.