A plea for help. I'm trying to write something about this paper, by John Conway and Simon Kochen of Princeton. Any guidance from physics experts would be greatly appreciated. I'm afraid that when it comes to these sorts of papers I'm like the simple son at the Seder: I don't even know what questions to ask.
On the basis of three physical axioms, we prove that if the choice of a particular type of spin 1 experiment is not a function of the information accessible to the experimenters, then its outcome is equally not a function of the information accessible to the particles. We show that this result is robust, and deduce that neither hidden variable theories nor mechanisms of the GRW type for wave function collapse can be made relativistic. We also establish the consistency of our axioms and discuss the philosophical implications.
UPDATE: Let's try this Wiki style. After struggling with the original paper, here's a writerly summary of it. Please let me know what pertinent facts/presumptions/theorems I got wrong. (Please keep in mind that I've got to summarize 31 pages of dense math in 300 words):
Free will has traditionally been reserved for big things, like brains and people. But what if free will was embedded in the very essence of everything? What if elementary particles - matter in its most minute form - were also endowed with some existential elbow room?
John Conway and Simon Kochen, two Princeton mathematicians, have given this strange idea an elegant mathematical proof. On the basis of three rhyming physical axioms - spin, fin and twin - they have constructed a theory of sub-atomic freedom. After acknowledging their debt to various quantum paradoxes, they argue "that the response of particles to a certain type of experiment is not determined by the entire previous history of that part of the universe accessible to them." The results are also not a function of information accessible to the experimenter. According to Conway and Kochen, even an omniscient mind, capable of knowing everything about everything, would still be unable to predict the position of the particles.What, then, is determining the outcome of the experiment? The obvious yet absurd answer is that the particles themselves are determining the outcome. As Conway and Kochen write, "No theory can predict exactly what these particles will do in the future for the very good reason that they may not yet have decided what this will be!" Of course, most of these sub-atomic choices - the mathematicians call them "ineffectual flutterings" - won't affect very much beyond their own trajectory. Nevertheless, their indeterminacy appears genuine. If we are free, then so are they.
Comments (10)
I haven't read much of it yet, and Chad is way more qualified to think about sort of quantum thing than me...
My first response, despite the condescending warning that physicists shouldn't think that there's nothing new here because the authors are doing things too deep for standard quantum mechanical notation, is that there's absolutely nothing new and mysterious here.
No hidden variables in quantum mechanics? Old news. The result of a quantum state experiment not being determined by information available to the particle? That's another way of saying no hidden variables. Now, I must be missing something, because the authors do refer to EPR and say that lack of hidden variables has been long known... but damn if I can figure out what's really new and deep about this.
It may just be that they're interpreting quantum indeterminacy as "free will" for the particles, but I would say that that interpretation is semantically suspect. I would go farther and say that they're only one step away from What the bleep do we know? level nosense, entangling terms like "free will" with not-intuitive-to-humans aspects of quantum mechanics.
To have a more informed opinion, I'd have to spend a lot more time reading this... but I'm inclined to be lazy and see what somebody like Chad has to say about it first. :)
-Rob
Posted by: Rob Knop | October 12, 2006 4:31 PM