A forum for student comments on, and discussion of, readings for PH430 and PH431: Introduction to the Philosophy of Physics, taught by Matthew Parker at the London School of Economics and Other Stuff, in the 2014-15 academic year.
I'm not entirely sure about your argument that rejecting hidden variables leads one to also reject locality. Bell's theorem is meant to show that hidden variables, locality, and the statistical predictions of quantum mechanics are inconsistent. Having rejected hidden variables then Bell's theorem won't necessitate rejecting locality. That being said I think I can see what you mean when you say that without hidden variables there's no way to make the events A and B independent. However I think there is a problem in that the definition of independence in terms of factorisability of the probability function somehow presupposes a hidden variable interpretation; having rejected hidden variables we might have to think more carefully about what independence of the events and hence locality means.
I don't have too much to say, I think you are both right and the argument looks like a powerful challenge of EPR. It seems that not only are the successful predictions of QM, locality and a hidden variable interpretation inconsistent, it even seems difficult to see how one could reject a hidden variable view and at the same time defend locality and vice versa. And then it seems implausible to think of QM as incomplete, because it does just not allow for any extension of the kind EPR had in mind.
Perhaps it is not even a problem that, in case we reject hidden variables, this by definition rules out independence and locality. Because this means that it is the formalism of QM that is inherently incompatible with the two states being independently real before a measurement. But if QM is true (and its success is taken as evidence that it is) and it cannot be completed, then locality and a hidden variable view must be wrong.
So I'm wondering whether locality and the hidden variable view must be given up together or what solutions of rejecting just one would look like.
I'm not really sure how to contribute to your discussion as to be honest I don't really understand your formalizations. However I think Jon has raised an important issue - I also fail to see why locality has to be rejected in virtue of a rejection of hidden variables. I also wonder if these difficulties can be made more clear by establishing an adequate definition of independence that doesn't presuppose the notion of hidden variables from the outset. In any case, as Michel has said, neither locality nor hidden variables look like very promising options if QM is true and cannot be completed. I'm still trying to understand this topic further as I think I was a bit confused as to the difference between a quantity corresponding to a reality and a quantity corresponding to some fixed reality - I conflated the two when doing the readings and made things difficult for myself. Sorry my comments aren't more helpful!
I'm not entirely sure about your argument that rejecting hidden variables leads one to also reject locality. Bell's theorem is meant to show that hidden variables, locality, and the statistical predictions of quantum mechanics are inconsistent. Having rejected hidden variables then Bell's theorem won't necessitate rejecting locality. That being said I think I can see what you mean when you say that without hidden variables there's no way to make the events A and B independent. However I think there is a problem in that the definition of independence in terms of factorisability of the probability function somehow presupposes a hidden variable interpretation; having rejected hidden variables we might have to think more carefully about what independence of the events and hence locality means.
ReplyDeleteI don't have too much to say, I think you are both right and the argument looks like a powerful challenge of EPR. It seems that not only are the successful predictions of QM, locality and a hidden variable interpretation inconsistent, it even seems difficult to see how one could reject a hidden variable view and at the same time defend locality and vice versa. And then it seems implausible to think of QM as incomplete, because it does just not allow for any extension of the kind EPR had in mind.
ReplyDeletePerhaps it is not even a problem that, in case we reject hidden variables, this by definition rules out independence and locality. Because this means that it is the formalism of QM that is inherently incompatible with the two states being independently real before a measurement. But if QM is true (and its success is taken as evidence that it is) and it cannot be completed, then locality and a hidden variable view must be wrong.
So I'm wondering whether locality and the hidden variable view must be given up together or what solutions of rejecting just one would look like.
Hi Somayeh,
ReplyDeletethanks for the helpful video!
I'm not really sure how to contribute to your discussion as to be honest I don't really understand your formalizations. However I think Jon has raised an important issue - I also fail to see why locality has to be rejected in virtue of a rejection of hidden variables. I also wonder if these difficulties can be made more clear by establishing an adequate definition of independence that doesn't presuppose the notion of hidden variables from the outset. In any case, as Michel has said, neither locality nor hidden variables look like very promising options if QM is true and cannot be completed. I'm still trying to understand this topic further as I think I was a bit confused as to the difference between a quantity corresponding to a reality and a quantity corresponding to some fixed reality - I conflated the two when doing the readings and made things difficult for myself. Sorry my comments aren't more helpful!