At 12:04 PM 10/14/4, Grimer wrote: On Mon, 11 Oct 2004 11:36:20 Keith Nagel wrote
>> * because I know from my meagerstudy of statistics * >> * that the first thing that gets thrown away in a * >> * statistical analysis is causality, a requirement * >> * for any communication scheme. * > > >Interesting, that last comment. > >Many years ago I realised that research engineers had a tendency to >hide their sloppy experimental techniques and designs behind a >statistical smoke screen - so I wrote a Note [as one does :-) ] Even more true I think in some other fields. I majored in phsychology briefly in the early 1960's, too briefly in fact to really call it a major, though I had an interesting student job training rats and doing decortications, etc. I was quickly discouraged when I saw published experiments considered important yet having a correlation coefficient of only 0.7. It was just too fuzzy an art for me. Psychiatric principles seemed to me to be even more fuzzily justified. Anyone who studies communication theory, however, knows that statistics play an important role in communication systems design. Randomness is an inherent part of the process of communication. Information can not be transmitted with complete certainty. There is always some finite chance of error in the transmission of any bit. I managed analog communication networks some decades ago, and know first hand that the probability of a bit error can be very high in practice. This is why the design of error correction schemes is so important. The design and testing of error correction schemes requires the use of probability and statisitics. As with communication theory, probability and statistics are an inherent and even definitve part of the theory of quantum mechanics. As for the role of probability in Bell's theorem, as applied to the subject experiments, I think (hope) that might be summarized fairly easily. I'll take a shot at that now. 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, 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
