Quantum mechanics doesn’t work if you use hidden variables. For instance, if you have two polarizers that are at 90 degrees to each other, no light can pass through them both, but if you insert a 45 degree polarizer between them, some light can pass through all three. This can only be explained if the polarization of each photon depends on random probability and isn’t predetermined by a hidden variable.
Except that this only applies to local hidden variables. A non-local hidden variable theory can still work. The thing is, I can’t figure out how this result would be interpreted in a non-local hidden variable theory.
You can deal with the situation you describe just fine using even a local hidden variable model. Difficulties only come in when you have multiple particles entangled in some way.
I don’t think your scenario captures the key elements of the Bell test experiments. The key feature is that observations of distant entangled particles are statistically correlated in a manner that implies that each particle instantaneously “knows” what is observed about its partner - yet it a manner that can not be explained by hidden information propagating along with the entangled particles since they separated.
I think the technical loopholes have now been closed pretty much conclusively, so the Bell test experiments allow the following possibilities to explain reality:
(1) Quantum nonlocality, “spooky action at a distance”. But note that it’s the nonlocality that’s remarkable, I think it’s now philosophically relatively unimportant whether hidden variables are still involved. You must still accept nonlocality in some formulation, i.e. if there are hidden variables they can no longer “rescue” reality to make it operate in a manner that comports with our macroscopic common sense intuition. In any event, DeBroglie-Bohm pilot wave theory, which is certainly nonlocal, is usually considered a hidden variable theory.
(2) Many Worlds may be considered local, although that’s open to debate, a debate that I think is both technical and philosophical.
(3) Superdeterminism - a universal conspiracy theory, the rather bizarre loophole that we can’t assume the sampling is random, implying that we can’t rely upon statistical inference at all. But some people have considered this possibility quite seriously, including Bell himself.
I personally came to this conclusion after reading all available literature aimed at bright laypeople. It’s the only conclusion that makes sense with everything else we know about the universe in my opinion. There’s no reason why it can’t be true; it just makes us feel really icky.
One problem with superdeterminism is that it lacks explanatory force: the Bell expressions in quantum mechanics are violated up to a certain degree, and that degree agrees with predictions of quantum mechanics; but, with superdeterminism, any degree of violation would be possible. So why is it that exactly the quantum value pops out?
It’s also difficult to see how superdeterminism even fits with a general scientific outlook. Whatever data you have to accept a hypothesis—including that of superdeterminism—in a superdeterministic world, will be jury-rigged, and hence, not accurately reflect the way things actually are. So the assumption of superdeterminism means that strictly speaking, non of your empirical claims about the world are justified—the thing kicks the legs out from under itself.
Fundamentally, is there any difference between superdeterminism and god? Believers in either acknowledge, implicitly, that any explanatory system must be incomplete.
And it’s worth reiterating here that the interpretation favored by most physicists is the non-interpretation (also known as “shut up and calculate”). We know how to do the calculations, and how to predict the results of the experiments. What does it matter, to ask “what’s really happening?”, if all of the answers yield the same ultimate results? An interpretation of quantum mechanics might be a useful way of organizing one’s thoughts, to guide one as to how to set up the equations most easily, but even so, a physicist might flit from one interpretation to another, to make different sorts of calculations easier to set up, secure in the knowledge that they’re all equivalent.
That used to be the case, but I don’t think it is that way any longer, largely due to the rise of quantum information theory—I’m in fact attending a mini-workshop today about quantum foundations/interpretational issues which will feature participants from quantum gravity, particle physics, philosophy and quantum information theory. One reason to care about interpretational issues is that they might guide the way towards novel theory-building—there’s different ways to generalize from, say, Bohmian mechanics than from many-worlds theory. In a sense, that’s what happened with special relativity: Minkowsky spacetime is really an interpretation of the theory; Bell showed how to interpret it in terms of a Lorentz ether, but that interpretation doesn’t lend itself to generalizing to GR nearly as well.
Sure, physicists will use some particular interpretation when it’s convenient, but if some other interpretation is more convenient for some other problem, they’ll switch to that one.
The point of hidden variables is that things that appear to be random in quantum mechanics are actually deterministic; we only see them as random because they are governed by hidden variables we can’t directly measure. How would that apply to entangled particles? Local hidden variables won’t work because there’s no way for them to match the measured results. If the variables were non-local, what would actually be different?
Different models of QT are almost wildly different. Yes, they seem to give the same result for simple questions, but what if you want to stretch your model? Use it to predict the first femtosecond of the Big Bang for example, understand dark matter, or produce a ToE?
Isn’t it at least plausible that there is some “God’s view” of QT, a best explanation which yields the best insights? (I’m certainly not suggesting I have a clue to what the “best” interpretation might be, just that it seems plausible there might be one.)
But now we see the image of the apocryphal gallant who picks a beautiful flower in the morning, but tosses it the next day.
Nobody takes any interpretation of quantum mechanics seriously until/unless it’s been mathematically proven to be exactly equivalent to all of the others. So even in extreme circumstances like quantum gravity, one is still just as correct as another (which might or might not be completely correct, but that’s another matter).
And why would God’s view of quantum mechanics be the simplest one? I would tend to assume that God’s understanding of it (or of any other subject) is so complicated as to be beyond any possibility of human comprehension.
