Hi Joy,
Just to clarify that we are on the same page:
1) Individual objects are rotationally invariant under SO(3) - generator J angular momentum - whereas the relative rotations of two or more objects are rotationally invariant under SU(2) - generator S spin.
2) It is easy to see in classical physics that the true relative rotation group is SU(2) spin and not SO(3) angular momentum e.g. plate trick and tangloids
3) For the EPR scenario of a spin singlet eigenstate S=0 of two spin ½ eigenstates, the collected papers in your book prove that the spin correlations found by two observers (Alice and Bob) can be due to this SU(2) orientation entanglement.
4) There are two critical physical conditions for this:
a) the tip of each spin vector of the pair lies on S2
b) the spins of the pair are correlated to be equal and opposite by being part of an initial singlet state of spin group SU(2).
5) Because the two spheres S2 of the spins of the singlet state are subspaces of S3, the S3 orientation of the initial correlated spin state can given by variable L=±1.
6) As we discussed earlier, the variable L can either be hidden by not being measurable by any means, or just by not being measurable in a correlation experiment - it makes no difference to your analysis.
7) This means that there could also be a third option of knowing what the value of L was, but then forgetting it - still will make no difference. In thought experiment terms, the initial state with known value of L can be prepared by a third person (say Simon) who then just doesn't tell Alice or Bob what the value of L is.
These points intuitively convince me that the underlying proposition of your paper is true:
There-exists a purely classical physics scenario of orientation entanglement where rotation/spin correlation measurements by two independent observers display the same correlation results as the spin measurements of the EPR scenario.
The only question is what exactly is this classical physics scenario. Are we agreed so far?
We have been blowing things up for a few hundred years without noticing this effect, from which I conclude that the sought-for scenario must require a non-trivial twist of some kind. Are we agreed that the rotation given to the weighted halves of an exploded sphere only lie on a plane and not the required S2?
The next point is that an explosive force on asymmetrically weighted shell halves means that angular momentum is *not* conserved. Even for the symmetric weight positioning of my Figure 1 angular momentum is *not* conserved: J=0 before the explosion, but net angular momentum afterwards. It is only in the scenario of Figure 2 that the angular momentum of the shell halves is equal and opposite after the explosion. Angular momentum conservation is a constraint that has to be added by hand through the weight placement because of the explosive force. Agreed?
To have a S=0 singlet state before and after the explosive separation, where the rotation vectors of each half lie on a sphere S2, requires the two halves to be set spinning on their axis in *opposite* directions by the explosion somehow. At the though experiment level this could be by a spring mechanism that spins the two halves about their axis in opposite directions as it exploded the shell halves apart. This gives a thought experiment scenario of a correlated S=0 singlet state before and after the explosive separation - this singlet condition seems to me to be required for your correlation analysis (point 4b above). Are we agreed on this?
Turning such a thought experiment into a practical experiment is a different matter. As is whether it does actually physically meet all the required conditions or not.
Best,
Michael
