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Originally Posted by Len Moran
Does the mathematics of the prediction (in terms of the joint wave function) give the information, or do you mean the information stems from the measurement at one detector?
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That's an interesting question. I suppose one must distinguish "independent information" from "information transformed via a calculation". The former is the result of something that couples to reality (i.e., a measurement), and the latter is like a function that always gives the same output from the same input (i.e., the information out is just a reprocessed version of the information in, like a coded message). I see the process as gathering actual information from your experiment, then using a calculation to make a prediction about another measurement. That prediction is a form of information too, but it just converts the information you got from your experiment into a prediction. If it sounds like you are ending up with more information than you started with by doing that calculation, then you have overestimated how much information was "really there" in the first place.
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I can see the joint probabilities for both electrons as being predictive, but when we talk about specific measured states, none of that is predictive is it?
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We don't get information about that except by doing the measurements. The predictions are only about joint results (which is why the experiments always involve coincidence detectors).
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I mean I cannot predict from the joint wave function that an entangled particle at source will evolve to have a specific measured up state at detector A and a specific measured down state at detector B can I?
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You can get three things from the joint wavefunction of two particles. The first two are a statistical prediction of an observation on one particle, or on the other. Nothing at all strange will happen if you do that.
Or, you can get a prediction about joint probabilities for observations on both particles, and then you will get some results that people concern themselves with, but it will always be what the joint wave function predicted. So the "problem" is already there as soon as you accept a joint wavefunction as your representation-- yet we couldn't get very far in quantum mechanics if we didn't do that.
It's as though people were expecting joint wave functions to successfully predict the Pauli Exclusion Principle in white dwarf stars, and the "exchange energy" correction in two-electron atoms and molecules, all bizarre yet perfectly well documented, but expected them to break down somehow whenever they disagree with our classical intuition in EPR-type experiments. Go figure. One could say that the value of Bell's theorem is simply to elucidate the ramifications of quantum mechanics, but why this somehow is interpreted as throwing quantum mechanics into a tizzy is beyond me because I never attributed that theory with a particular set of philosophical principles based on classical expectations.
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Are you saying that the book keeping is just recording the nature of the predictive outcome, it is just the final part of the quantum prediction that gives a chance to tabulate the probability outcomes - the measurement should not be thought of as some kind of deterministic event that kicks in to ensure the other particle follows the rules, but rather the rules are inherent in the wave function which is a product of our experimental set up.
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Yes, that sounds like what I'm saying indeed.
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I don't wish go back over ground that was amply covered in the thread ("Spooky Matter at a Distance" - in General Science I think) but it seems like an opportunity to clarify a few points.
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I don't mind at all, this point comes up a lot and it stands to get it out there. If I'm right, the more places it appears the better, and if someone can refute me, then I want to give them the best possible opportunity (because I'd like to know).