The R script (html notebook) at
http://rpubs.com/gill1109/ChaoticUnsharpBall3
shows simulation results for Caroline Thompson's "chaotic spinning ball" model for various values of R, the radius of the circular caps on the sphere.
http://freespace.virgin.net/ch.thompson1/Papers/The%20Record/TheRecord.htm
It is pretty clear from the pictures that there is a continuous convex combination of these curves which exactly matches the cosine curve (the curve predicted by quantum mechanics, for the so-called singlet state).
Questions:
1. can you give a rigorous mathematical proof of my claim?
2. can you find a convenient analytical formula for the resulting mixing distribution?
3. can you compute it numerically to a high degree of accuracy so that the result can be used for high-precision simulation experiments?
"1. can you give a rigorous mathematical proof of my claim?"
A) what about the "burden of proof": the one who makes the statement shall prove it himself?
B) If you write: "It is pretty clear from the pictures", when you have proved it all already. You want the people to discover the proof? When do not be so convinced in own rightness.
Clarification: "it is pretty clear from the pictures" ... but maybe it is not true! I am not claiming a theorem. I am proposing a research project (stating a conjecture).
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