Nick,
I have already suggested the experiment - measure the correlations of entangled pairs of coins.
However, the real issue is not whether Bell's theorem is valid or violated etc. The real issue is, does it have any significance. My claim is that it does not. It is based on a subtle premise that is self-contradictory; it does not apply to the one and only QM case to which it is being applied.
It has been known for decades that Bell's Theorem is based on a subtle premise (Bernard d'Espagnat, "The Quantum Theory and Reality", Scientific American, Nov. 1979, page 166):
"These conclusions require a subtle but important extension of the meaning assigned to a notation such as A. Whereas previously A was merely one possible outcome of a measurement made on a particle, it is converted by this argument into an attribute of the particle itself."
I have pointed-out this statement several times before, but no one seems to understand its significance, so let me spell it out.
The statement is about intrinsic versus extrinsic attributes of a particle. The statement says that the theorem only applies to those cases in which the measurements correspond to intrinsic particle attributes. Any measurement that is performed relative to an external reference (like spin up/down) is an extrinsic parameter. The theorem DOES NOT APPLY to extrinsic parameters!
Here is the problem, Consider three geometric shapes, a cube, a tetrahedron and a coin.
Objects like the cube and the tetrahedron have intrinsic attributes, such as the angles at which the sides meet. So, presumably, one ought to be able to make measurements that reveal correlations that would enable one to deduce those angles. Bell's theorem would apply to such intrinsic attributes.
But what such intrinsic attributes does an idealized coin (a plane) have? None. That's the problem. The coin and the QM particle is, in effect, an encoded, single bit - it has no intrinsic attributes - it has only one attribute at all, an extrinsic one, namely, its extrinsic-state can be measured relative to an external reference.
So, Bell proved a theorem, that only applies to classical objects, and quantum objects with intrinsic, characterizable attributes (like internal structure), but does not apply to the characterization of the extrinsic attributes of any objects (like spin), and then he proceeded to apply it to the very case in which it does not apply!
I have not studied Joy's arguments, but I have noted that he points out extrinsic attributes, like Dirac's Belt, as being connected to his idea of why Bell's Theorem is not valid. Perhaps he has unwittingly found another way of noting the problem between extrinsic attributes, tied to the world outside the particle, and intrinsic attributes, which are not. But Joy did not see the significance in d'Espagnat's statement, when I pointed it out to him previously.
Because of the "no intrinsic attribute" characteristic of entangled coins, entangled coins will violate Bell's theorem, and behave similar to "no intrinsic attribute" entangled spin measurements.
Rob McEachern
