Peter thank you for replying. I'm going to complain though. The experiment you are talking about uses the polarization of the light and so is using a photon as the entangled quantum particle. The macroscopic version of that is to be using many, many photons. The two lions are merely the means to set up the entanglement of the two "independent' photon streams.
The two observers can be very far apart where they view the photon data. If they are opposite each other with the lions in the middle it would take twice as long for them to signal each other than for them to receive data that is leaving the surface of the lions. Bear in mind it is the photons that are the entangled particles under consideration not the lions. Once the sensory data s.d.-lion has left the surface of the lion it is independent of the a-lion. Any communication between a-lions is not going to alter the sensory data already spreading through the environment.Thinking about lion communication is the equivalent of a problem with the production of entangled quantum particles, not communication between particles already entangled.
In a macroscopic example where there are many photons rather than just one it will be hard to get the two streams identical but the lions could be equally illuminated with the same intensity and wavelengths of photons. Each encoding one of a pair of non mirror symmetric lions.
I like your explanation of the poles. Also I understand, Quote "So two spheres head off on the SAME SPIN AXIS [2 identical lions, front half pale rear dark go in opposite direction but with one walking backwards!]" Thanks for that explanation.It makes it very easy to visualize.
Peter said,Quote "Now the shutter settings on the camera 'click', making the lions turn round by some angle subject to setting, up to 360^o. (the spin 'axis' itself rotates, but this may be in BOTH the y and z planes. i.e. the lions may also roll over but we need curves for the 'intermediate cosine^2 distribution'.) The 'flip' from pale to dark (N to S) IS important as it defrocks 'non-locality."
I've got two streams of photons. Changing how they are looked at will change what is seen. The stances of the lions mean that knowledge is incomplete if its body colour is known its belly colour is uncertain and vice versa. To overcome that I suppose the lions must be on a glass platform. So there will be some sensory data from the underside of the glass in each stream. Now instead of using sunglasses (which haven't done the trick) The observer Alice will have to
change her body position so that her head is held low to the ground and looking slightly up (would that work?) if she is able to intercept the light rays that have come from the underside of the glass the colour of her lion manifestation changes colour as she is seeing the part that was obscured. There has to be the assumption by the investigator that the lions are just of one colour. Correlation is transformed by doing that change of position because she is now seeing the underside of her lion, its belly if its standing and its back if its resting and Bob is looking at the top side. If Alice's lion manifestation is standing Alice is looking at its belly. Bob is also looking at his lions belly manifestation. If Alice's lion is resting she is looking at its back manifestation and Bobs lion also appears standing and he is looking at its back manifestation. Alices' lion manifestation colour has changed and Bob's lion manifestation colour is now complementary rather than matching.
Let me try this, modifying your paragraph--> Now the statistician analyzing the 1,000's of A and B's photo's sorts them into piles. But he does NOT KNOW that both A and B can find matching back-back and belly-belly from the same pair of lions! He assumes from the initial runs that there's one set of pale lion sensory data one set of dark lion sensory data as Alice and Bob always get opposite colours. So when he's told that Alice can 'flip'her colour (by changing her veiwing position), he assumes that means she must change Bob's lion manifestation as well!
But couldn't individual runs be conducted and each analysed in turn for the different angles??? Then it would be clear that the correlation has gone from matching colours to different colours. And we know that's because it has gone from back-belly and belly-back pairs to back-back to belly-belly pairs.Or vice versa if the two lions start with the same stance.
Peter I often find your explanations confusing. Your explaining your version of the analogy to me has helped me understand what you are describing. I can easily visualize a piebald lion walking backwards,a photon is not so easy. The type of explanations that I need. knowing very little about quantum physics, would probably be considered patronizingly simple/ naive by those who already have a good grasp of whats going on.