Hi Horace. Thanks for the analysis!
What bothers me about this is that the crux of the argument is based on the modelling of spin as being just that, like a ball spinning about an axis in 3 space. Yet QM makes a point of telling us that QM spin is NOT the same as a macroscopic spin. In fact this analysis points that fact out very clearly; for if it was you'd see the results predicted by Bell. We could come up with some arbitrary model for spin that would conform to the experimental results; and it would seem the hidden variable would return. If you're correct in your analysis of Bells argument, it would seem to prove that QM spin is not like a macroscopic spin rather than that all hidden variables are impossible. The logic I do not argue; the assumptions seem questionable to me. Do they seem so to you? We know one thing; that what model we choose does have to conform to the Aspect type experiments and thus spin cannot be as simple as modelling of a particle revolving in 3 space. K. -----Original Message----- From: Horace Heffner [mailto:[EMAIL PROTECTED] Sent: Thursday, October 14, 2004 10:20 PM To: [EMAIL PROTECTED] Subject: RE: FTL Triad Quantum Communication Method A slight typo is corrected at point marked ***. Assume the state of cojugates is set at the time of the creation of the conjugates, at the moment of entanglement. Assume there are, as in the Aspect experiment, three independent quantum values involved. That is to say there are three axes of spin observation, in which a particle is in either a clockwise or counterclockwise spin state upon observation. Unfortunately, spin can only be observed in one axis, not all three at the same time. However, Bell figured out how to see if the quantum variables were set before measurment, i.e. how to see if a hidden variable was involved. The situation is shown in Table 1, below. i A B C D E F 1 0 0 0 1 1 1 Key: 2 0 0 1 1 1 0 3 0 1 0 1 0 1 i - possibile combination 4 0 1 1 1 0 0 A, B, C - Alice's possible observations 5 1 0 0 0 1 1 D, E, F - Bob's corresponding observations 6 1 0 1 0 1 0 7 1 1 0 0 0 1 8 1 1 1 0 0 0 Table 1 - Possible observations by Alice and Bob Table 1 assumes that when an entangled particle pair is created that all three quantum variables, i.e. spins, are set at that time and carried as "hidden variables". Columns A, B and C are possible spins observed by Alice in orthogonal axes A, B and C, and are denoted "o" for clockwise spin and "1" for counterclockwise spin. Columns D, E, and F are the corresponding spins observed by Bob. It is assumed there is no error in the detection of the spins or the transmission of the hidden variables. As the variables are independent, and it is well known from observation of single particles that the spin probability of clockwise spin being observed in any axis is 0.5, we see that there are exactly 8 equally probable combinations, possibilities denoted 1 - 8 in column i. Bell suggested that Alice and Bob, for each particle pair, select a column at random and observe the spin. That's all there is to the experiment. To see the expected results, look at Table 2. a b matches - - ------- A D 8/8 A E 4/8 A F 4/8 B D 8/8 B E 4/8 B F 4/8 C D 8/8 C E 4/8 C F 4/8 Table 2 - Expected results In Table 2 column a indicates the axis Alice choses to observe. Column b indicates the axis Bob choses to observe at the same time. We can determine the probability of a match by comparing the two columns of equally probable outcomes shown in table in Table 1. By "match" here we mean the observation of opposed, i.e. conjugate, spins. For example, the first row of Table 2 has the entries, A, D, and 8/8. This means that when Alice choses axis A, and Bob coincidentally also choses axis A, *** [The above "... Bob coincidentally also choses axis A... " really should say "... Bob coincidentally also choses axis D ...". Axis A is in the same direction as axis D, axis B is in the same direction as axis E, and axis C is in the same direction as axis F.] then both will always observe complimentary spins. We get 8 out of 8 matches. This is the principle of, the definition of in this case, entanglement. When we look at row 2 of Table 2, we have the entries A, E, 4/8. This is beacuse there are only 4 possible ways out of 8 outcomes, each equally probable, that a match occurs. Summing up the entries in Table 2, we see that there are 9*8 = 72 possible outcomes to the observation of a single entangled pair, and there 48 possible matches. There is thus a 2/3 probability of a match for a given particle pair. That is all there is to it! If there are hidden variables, then there will be a 2/3 probability of a match. The Aspect experiment actually yields a 1/2 probability of a match. There is no hidden variable involved. What I have suggested is using the polarity of three separate photons in lieu of using the independent 3 spin axes of a single photon. This meets the implied requirement that the probabilities of spin observed on each of the 3 axes, or the equivalent observations, be independent. Now, if Alice doesn't observe the unchosen columns, and Bob behaves similarly, using photon triads should be identical to the Aspect experiment using spins. At least that is true under some of the possible quantum reality interpretations. Note that the 3 bundles, the 3 photons of a triad, might even be light years apart, with Bob and Alice, or even some third party referee, not knowing the actual results of their experiments for years. What is different about the protocol I suggest is that it is possible to discern and refine what exactly constitutes an observation. Unlike the spins in differing axes for a given photon, it *is* possible to determine all the polarization states for a given triad. Alice can force Bob's photons to carry hidden variables simply by observing all three of the photons in each triad before Bob observes his. Bob can achieve a similar result. There is now defined an experimental means to decide whether an "observation" is occuring or not, via the percentage of matches observed. Regards, Horace Heffner
