At 1:39 PM 10/18/4, Keith Nagel wrote: [snip bunch of good stuff] >... I >also seem to remember that what initially puzzled researchers >is that the particles all deflected an equal distance, rather >than distribute based on their (random) orientation as they >entered the magnet. Right there the 3D spin model as assumed >in our discussion fails. >
I can't seem to get anything right the first time lately! There are 8 poossibilites, not 16. Corrected version of last post follows below. I feel the spinning ball model results in a 2/3 probability of a match. However, the model wherein each possible combination has an arbitrary weight, as I presented in DRAFT #6, accounts for much more than the spinning ball model. In fact, I think all possible stochastic process results, without instantaneous knowlege of Both Alice and Bob's choices, are accomodated. There are only 8 possible combinations of final results. There has to result from any such process columns A, B and C, no matter what process is used. Those are the only possibilities. Given that, corresponding columns D, E and F also are necessary. The only way the final outcome of any such process can affect the 8 possible outcomes is to change their frequency. This is true no matter how many dimesions from which those final outcomes are chosen. This is true even if an infinite number of angels ride with each particle and can all interact to make the final choices. There are three and only three sensors available to Alice and Bob each, and final results for each must be produced because none of the three can be left out a priori as a possibility. None can be left out without knowing at least slightly in advance, or instantaneously, what choices Alice and Bob both made. A choice must be provided for each of the 3 axes. There are exactly 8 ways this is possible. The lower bound of 5/9 probability of a match, when axes are chosen at random, and only hidden variables are involved, is thus an absolute lower boundary, and is not dependent at all on a ball-like model of spin. It is a boundary that is inherent to the experiment design. Regards, Horace Heffner
