Eckard,
You stated:
"If I understood you correctly, you argued that redundancy might be to blame for some problems. While this comes close to suspicions I uttered in the last but two (?) essay of mine, I feel too weak as to intensively deal with this matter. Looking for EPR-Bohm, I found an illustration of how to imagine a full rotation over not 2 pi but 4 pi"
Let me address your last point first. This is something I learned while taking a class in Quantum Field Theory, 40 years ago: cut out a piece of cardboard in the shape of a capital letter "L". Tape one end of a piece of string (total of three pieces) to each of the three points at the ends of the two line-segments that form the "L". Then tape the other end of each string to a table top, so that the strings are laid out flat and untangled. Now rotate (flip) the "L" by 2 pi (360 degrees). This will entangle the strings in such a manner that they cannot be untangled without un-taping the stings. However, if you rotate the "L" by an additional 2 pi, it is possible to untangle the strings without removing the tape: so a 4 pi rotation brings the device back to a zero-pi state, but a 2 pi rotation does not.
The first point is not exactly a case of redundancy, rather, it is a case of misinterpretation, as the result of using bad analogies to visualize the problem. For example, in Roger Penrose's book "The Emperor's New Mind", Penrose discusses the EPR paradox, and makes a bad analogy between two entangled spin-one-half particles and a pair of balls, one white and one black. Penrose says that " Suppose that the balls are taken out and removed to two opposite corners of the room, without either being looked at. Then if one ball is examined and found to be white - hey presto - the other turns out to be black..."
Others have used a pair of cloves, as another bad analogy. The reason that these are both bad analogies is the the whiteness or blackness of the ball, like the handedness of the cloves is an actual attribute, or property, of those objects.
The false claim is then made, that there is no other classical analogy for which this would not be the case. But there is such an analogy: two parallel or anti-parralel coins, floating in space. The heads or tails of the coins, like the up or down spin of the particle, is not an attribute of the coins per se. Thus, neither coin is in the state of being either heads or tails, until an observer chooses to treat it as though it is. But as soon as the observer makes such a choice - hey presto - the state of the entangled coin is also known. No "weird non-local" phenomenon is needed to explain such behaviors. A better analogy will suffice.
But how do you describe this correct analogy mathematically. Somehow or other, symbols/variables must appear in the mathematical description, that refer to the observer's yet-to-be-made choice, and not just the properties of the coins; they pertain to the aspect angle which the observer must choses when the coin is finally observed.
If you misinterpret these extra symbols/variables as being attributes of the coins themselves, then you will encounter all the same weirdness found in the EPR paradox.
In his original paper, Bell never even imagined such a possibility, so he failed to consider it. Later, more astute physicists, like Bernard d'Espagnat, in his Nov., 1979 article in Scientific American, took note of this problem. Nevertheless, he dismissed the problem because he was unaware of the coin analogy. Hence, he claimed that "the physicist has been led to the conclusion that both protons in each pair have definite spin components at all times..."
In other words, he believes that, like the balls and gloves analogies, which do indeed have definite states at all times, ALL classical analogies MUST have definite states at all times, even before they are ever observed. But the coins do not.
Joy Cristian claims that Bell made a MATH mistake. I claim Bell made a much more fundamental mistake in the PHYSICS. My claim is that EVEN IF BELL"S THEOREM WERE VALID, it has no relevance to PHYSICS, because the only thing linking the MATH to the PHYSICS is a set of bad analogies and misinterpretations about what the symbols appearing in Bell's equations actually symbolize. They DO NOT symbolize attributes of the particles.
It is also significant that d'Espagnat took note of the fact that Bell had to introduce this unstated, additional assumption (that there is a one-to-one mapping between the variables in the math and the physical attributes of the particles), precisely because this assumption was never made anywhere else within QM, because it is not needed. It is only needed to reach Bell's erroneous conclusion.
Rob McEachern
