Christian's thought experiment
http://arxiv.org/abs/0806.3078 (N exploding balls, and analysis of a a lot of video footage of those explosions) would generate two computer files each containing N directions of angular momentum. The files could actually be plain text files with the directions encoded using spherical coordinates theta (azimuth), phi (zenith).
Let's call the directions of angular momentum in Alice's file u_k, k=1,...,N, and in Bob's file v_k, k = 1, ..., N
If I pick measurement directions a and b,thinking now of directions as unit vectors in R^3, then according to the same paper the outcomes left and right are
A_k = sign(a . u_k) and B_k = sign(b . v_k),
and the estimated (observed, sample, experimental ...) correlation is
E(a, b) = 1/N sum_k A_k B_k
= ( N(++) + N(--) - N(+-) - N(-+) ) / ( N(++) + N(--) + N(+-) + N(-+) )
in the obvious notation.
Christian predicts the theoretical (population, large N limit, ensemble) correlation rho(a, b) = - a . b = - cos(angle between a and b)
I will now focus on just two possible directions for Alice and two for Bob. They are all in the equatorial plane so they can be described just by azimuthal angles alpha = 0 and 90 degrees for Alice and beta = 45 and 135 for Bob.
Christian's theory has
rho(0, 45) = - 0.7071...,
rho(0, 135) = + 0.7071...,
rho(90, 45) = - 0.7071...,
rho(90, 135) = - 0.7071....
and he predicts therefore
E(0, 45) = - 0.7071...,
E(0, 135) = + 0.7071...,
E(90, 45) = - 0.7071...,
E(90, 135) = - 0.7071....
up to experimental and statistical error, of course.
I claim that at least one of these four predictions is certain to be off target, by an amount 0.2 or more (ie the absolute value of the difference between observed and predicted is 1/5 or more).
The challenge is to create two computer files named, for instance, "AliceDirections.txt" and "BobDirections.txt". They should be posted on internet. It is a matter of complete indifference to me how they are created.
I will then show that one of the four predictions has failed by a large amount: E(alpha, beta) is off target by 0.2 or more.
If I cannot do this, I will pay the challenger 5 000 Euro (and if it is done before June 11, 2014, I will pay 10 000 Euro). First come, first serve. I will pay the first succesful challenger. In case of dispute we will ask independent and competent adjudicators to decide for us. They are bound by the rules set out here. Any challenger can only call on the adjudicators once.
To summarize: each challenger may make as many attempts as they like. If I believe the challenge has succeeded, I will pay up. If not, and if the challenger insists, we will go to adjudication. After an unsuccesful adjudication (from the point of view of the challenger) the challenger is disqualified from further attempts.
There will be at most one prize - it goes to the first succesful challenger.