{"id":11056,"date":"2019-06-11T22:26:38","date_gmt":"2019-06-12T02:26:38","guid":{"rendered":"http:\/\/www.math.columbia.edu\/~woit\/wordpress\/?p=11056"},"modified":"2019-06-16T09:43:38","modified_gmt":"2019-06-16T13:43:38","slug":"not-so-spooky-action-at-a-distance","status":"publish","type":"post","link":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/?p=11056","title":{"rendered":"Not So Spooky Action at a Distance"},"content":{"rendered":"

I’ve recently read another new popular book about quantum mechanics, Quantum Strangeness<\/a> by George Greenstein. Before getting to saying something about the book, I need to get something off my chest: what’s all this nonsense about Bell’s theorem and supposed non-locality?<\/p>\n

If I go to the Scholarpedia entry for Bell’s theorem<\/a>, I’m told that:<\/p>\n

Bell’s theorem asserts that if certain predictions of quantum theory are correct then our world is non-local.<\/p><\/blockquote>\n

but I don’t see this at all. As far as I can tell, for all the experiments that come up in discussions of Bell’s theorem, if you do a local measurement you get a local result, and only if you do a non-local measurement can you get a non-local result. Yes, Bell’s theorem tells you that if you try and replace the extremely simple quantum mechanical description of a spin 1\/2 degree of freedom by a vastly more complicated and ugly description, it’s going to have to be non-local. But why would you want to do that anyway?<\/p>\n

The Greenstein book is short, the author’s very personal take on the usual Bell’s inequality story, which you can read about many other places in great detail. What I like about the book though is the last part, in which the author has, at 11 am on Friday, July 10, 2015, an “Epiphany”. He realizes that his problem is that he had not been keeping separate two distinct things: the quantum mechanical description of a system, and the every-day description of physical objects in terms of approximate classical notions.<\/p>\n

“How can a thing be in two places at once?” I had asked – but buried within that question is an assumption, the assumption that a thing can be in one<\/em> place at once. That is an example of doublethink, of importing into the world of quantum mechanics our normal conception of reality – for the location of an object is a hidden variable, a property of the object … and the new science of experimental metaphysics has taught us that hidden variables do not exist.<\/p><\/blockquote>\n

I think here Greenstein does an excellent job of pointing to the main source of confusion in “interpretations” of quantum mechanics. Given a simple QM system (say a fixed spin 1\/2 degree of freedom, a vector in C<\/strong>2<\/sup>), people want to argue about the relation of the QM state of the system to measurement results which can be expressed in classical terms (does the system move one way or the other in a classical magnetic field?) . But there is no relation at all between the two things until you couple your simple QM system to another (hugely complicated) system (the measurement device + environment). You will only get non-locality if you couple to a non-local such system. The interesting discussion generated by an earlier posting<\/a> left me increasingly suspicious that the mystery of how probability comes into things is much like the “mystery” of non-locality in the Bell’s inequality experiment. Probability comes in because you only have a probabilistic (density matrix) description of the measurement device + environment.<\/p>\n

For some other QM related links:<\/p>\n