I was reading the Feynman lectures in physics and after thinking about it for a while it seems particularly unreasonable to talk about hidden variables. Let us say that the electron has some internal variables as yet unknown which determine its trajectory given a set of initial conditions just like in classical mechanics. But since these hidden variables are unobserved, coupling it with a classical system should make their effect unchanged. This is what Feynman says, I think, in the last paragraph of Ch1 Vol 3, that if in the double slit experiment, if these inner variables dictate that the electron goes through the upper slit and land at a particular place on the opposite screen, and some other place for the lower screen, then the probability must neccesarily be the sum of two Gaussian like peaks, which does not agree with experiment.
So if I concluded that inner workings of an electron had some additional hidden variables, then it should yield, as they should be independent of the classical apparatus, mutually exclusive probabilities that do not quiet add up the way as observed. But then I do a hidden variables search on the archive and a lot of smart guys still write about it, as late as Feb 2011.
So the argument I have used might be somehow incomplete, can anyone explain how?
EDIT: Sorry for editing this question almost three years later. I tried to locate the exact reference from the Feynman lectures I was referring to and this is the updated source, Sec 7 Ch 1 Vol 3
We make now a few remarks on a suggestion that has sometimes been made to try to avoid the description we have given: “Perhaps the electron has some kind of internal works—some inner variables—that we do not yet know about. Perhaps that is why we cannot predict what will happen. If we could look more closely at the electron, we could be able to tell where it would end up.” So far as we know, that is impossible. We would still be in difficulty. Suppose we were to assume that inside the electron there is some kind of machinery that determines where it is going to end up. That machine must also determine which hole it is going to go through on its way. But we must not forget that what is inside the electron should not be dependent on what we do, and in particular upon whether we open or close one of the holes. So if an electron, before it starts, has already made up its mind (a) which hole it is going to use, and (b) where it is going to land, we should find P1 for those electrons that have chosen hole 1, P2 for those that have chosen hole 2, and necessarily the sum P1+P2 for those that arrive through the two holes. There seems to be no way around this. But we have verified experimentally that that is not the case. And no one has figured a way out of this puzzle. So at the present time we must limit ourselves to computing probabilities. We say “at the present time,” but we suspect very strongly that it is something that will be with us forever—that it is impossible to beat that puzzle—that this is the way nature really is.
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