Response to the Gill Challenge

[Joy Christian]

Hi Everyone,

I have written another version of the second of the above two simulations: http://rpubs.com/jjc/18915.

Both versions of the simulation can be understood as respecting the parity change intrinsic to my 3-sphere model for the EPR-Bohm correlation.

The vectors for Alice and for Bob are now defined by the ordered sets



and

.

Note the differences in the definitions. The last two of the four correlations in the simulation are now calculated using left-handed basis for the spins instead of right-handed basis . Not surprisingly, all four correlations once again match exactly with the corresponding quantum mechanical predictions.

[gill1109]

Please will *anyone* who wants to help Joy and Fred

write a piece of computer code which

(a) reads two files each containing N directions u_k and v_k,

(b) accepts as inputs from the user two directions a and b, and

(c) calculates E(a, b) = 1/N sum_k {sign(a . u_k)} {sign(b . v_k)}

treating of course, the product A_k B_k here as a geometric product, whatever that means. Isn't the product of two numbers +/-1 the same whether or not we think of the product as geometric? Possibly Fred is thinking of the dot product between real three-dimensional vectors a and u (and similarly b and v) as being some other new product? If that is the case, please define the mappings ".", "sign", and the product between A_k and B_k.

All directions to be specified by vectors in R^3, represented by Cartesian coordinates (x, y, z).

Earlier, I wrote an R program which did this task. Other people supplied Perl, Python, Excel, Mathematica. No one complained about those programs. They have all been tested and give the same output on the same inputs. However they were not written by experts on Joy's model and apparently there is something badly wrong with all of them.

PS: in case that the N u_k's are a large random sample from the uniform distribution on S^2, and a and b are vectors of unit length, and for each k, v_k = - u_k, we want E(a, b) to approximately equal - a . b (ordinary dot product).

PPS: since the u_k, v_k, a and b all specify directions of classical angular momentum of classical massive spinning rigid bodies in classical three dimensional space (zero gravity, vacuum), they all should be non-zero when represented as vectors in R^3. The lengths of the vectors (provided they are positive) should be irrelevant. For simplicity all vector-directions could be taken to have unit length.

[FrediFizzx]

If you can do this before June 11, and if Christian will resubmit two files of directions u_k and v_k before that date, then he can still win his 10 000 Euro. Proof of principle will have been supplied that his experiment can be successful. I will announce my capitulation at the Vaxjo conference. My talk is at 9:00 a.am. on Wednesday morning June 11.

Oh, so now you are NOT withdrawing the challenge? Pehaps you should put that 10K Euros into an escrow account where the adjudicators have control of it. That will let us all know that you are really serious about it. Otherwise, I am not wasting my time with it. Joy has already won anyways.

[gill1109]

If you can do this before June 11, and if Christian will resubmit two files of directions u_k and v_k before that date, then he can still win his 10 000 Euro. Proof of principle will have been supplied that his experiment can be successful. I will announce my capitulation at the Vaxjo conference. My talk is at 9:00 a.am. on Wednesday morning June 11.

Oh, so now you are NOT withdrawing the challenge? Pehaps you should put that 10K Euros into an escrow account where the adjudicators have control of it. That will let us all know that you are really serious about it. Otherwise, I am not wasting my time with it. Joy has already won anyways.

I never withdrew the challenge.

Joy is welcome to make a valid submission, so are you, so is Hugh.

If I say that a submission is invalid and the submitter disagrees, then we can try to recruit adjudicators.

Joy made a submission with two sets of directions for Alice and two sets for Bob. He has to tell me which one he wants me to use. I am not going to let him give Bob a different data-set deoending on Alice's setting. That is called action-at-a-distance, or perhaps "conspiracy".

Please help Joy create a legal submission on time.

While you are at it, write a Mathematica program for doing the calculation 1/N sum sign a.u sign b.v according to the principles of geometric algebra. So far Joy always used the ordinary dot product and sign function in his R scripts ... which originally were written by me. No wonder they don't work.

[FrediFizzx]

My challenge is withdrawn till such time as a revision of the experimental paper is posted on arXiv.

No one is going to take the challenge serious unless you put the 10K Euros in an escrow account.

[gill1109]

My challenge is withdrawn till such time as a revision of the experimental paper is posted on arXiv.

No one is going to take the challenge serious unless you put the 10K Euros in an escrow account.

Sorry Fred, you are right, I did say the challenge was withdrawn!

I hereby withdraw that withdrawal.

The challenge
http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=52#p1898
remains standing exactly as formulated, but with the following clarifications:

The formulas

A_k = sign(a . u_k) and B_k = sign(b . v_k)

E(a, b) = 1/N sum_k A_k B_k

should be interpreted as follows:

a, b, u_k, and v_k are non-zero vectors in R^3, represented with Cartesian coordinates (x, y, z);

"." is the ordinary scalar or dot product

"sign" is the ordinary sign function

multiplication, additions, and division are all done by ordinary arithmetic of real numbers

N is a non-negative integer, not larger than 100 000; but N = 10 000 should be perfectly adequate for purpose.

Data files may also be submitted by submission of a short computer script using a pseudo-random number generator with a pre-set seed, and containing two "write" statements which create the files.

Fred: you are still welcome to write a Mathematica script with an alternative interpretation of page 4 of Christian's experimental paper, if you think that a different interpretation is needed than the one which Christian and I earlier agreed to.

[gill1109]

PS no escrow account is needed with 10 000 already placed in it, since it is certain that no one will win the challenge. This follows from the famous Nx4 spreadsheet theorem which we discussed here many times. However, I am a man of my word, so, in a counterfactual universe where the elementary rules of logic are different from ours and some-one did come up with a successful challenge, I would pay up (though it is doubtful I would ever have set the challenge in that alternative, impossible, universe ... so this is doubly counterfactual. Probably an example where a double negative is a positive).

[Joy Christian]

PS no escrow account is needed with 10 000 already placed in it, since it is certain that no one will win the challenge. This follows from the famous Nx4 spreadsheet theorem which we discussed here many times. However, I am a man of my word, so, in a counterfactual universe where the elementary rules of logic are different from ours and some-one did come up with a successful challenge, I would pay up (though it is doubtful I would ever have set the challenge in that alternative, impossible, universe ... so this is doubly counterfactual. Probably an example where a double negative is a positive).

No challenge can be defeated if one of the rules of the challenge says that the rules of the challenge will be altered, modified, abandoned, or changed beyond recognition every time someone defeats the so-called challenge. Your money is safe. But, please, stop calling yourself a gentleman: viewtopic.php?f=6&t=57.

And please stop insulting me by endlessly repeating the lie that we drew up the rules of the challenge together. We didn't. You only imagined that we did.

[gill1109]

PS no escrow account is needed with 10 000 already placed in it, since it is certain that no one will win the challenge. This follows from the famous Nx4 spreadsheet theorem which we discussed here many times. However, I am a man of my word, so, in a counterfactual universe where the elementary rules of logic are different from ours and some-one did come up with a successful challenge, I would pay up (though it is doubtful I would ever have set the challenge in that alternative, impossible, universe ... so this is doubly counterfactual. Probably an example where a double negative is a positive).

No challenge can be defeated if one of the rules of the challenge says that the rules of the challenge will be altered, modified, abandoned, or changed beyond recognition every time someone defeats the so-called challenge. Your money is safe. But, please, stop calling yourself a gentleman: viewtopic.php?f=6&t=57.

And please stop insulting me by endlessly repeating the lie that we drew up the rules of the challenge together. We didn't. You only imagined that we did.

The rules have never been altered, modified, abandoned, or changed beyond recognition; they have only been refined, i.e., from time to time we became aware of ambiguities and each time we clarified the ambiguities. It's always been a matter of open negotation. If at any stage we can't agree, then the bet c.q. challenge obviously has to be cancelled.

One cannot make a bet under terms which keep changing ... but one also cannot make a bet under terms which are ambiguous. If ambiguity arises it needs to be resolved. If it can be resolved, we go ahead, if not, we abort. No harm done. After all, we are both gentlemen, right?

For instance, recently it turned out that you have a rather different idea about what is meant by a "set of directions", and about the representation of a set of directions in computer files, than I did. As far as I can see your ideas were rather novel, they did not already exist written down in your papers, so I think I may be excused from objecting. Tell me if I'm wrong.

So, do I understand that you do not accept my most recent proposed dis-ambiguation (concerning the interpretation of a, b, u_k, v_k, dot product, sign, and multiplication?) We are talking about how to interpret page 4 of your "experimental paper". If you think that it should be interpreted in a different way from how I interpreted it so far, then please go ahead and clarify.

A. Do you have an alternative proposal?

B. Or do you wish to let the adjudicators decide on your latest submission, to be evaluated under the rules then in force?

C. Or do you want to forget the whole thing?

I am happy, either way.

As far as new submissions are concerned, the old challenge with the newest disambiguation remains open.

All this also applies to Hugh's submission.