Joy Christian wrote:Now consider a large ensemble of such balls, identical in every respect except for the relative locations of the two lumps (affixed randomly on the inner surface of each shell). The balls are then placed over a heater—one at a time—at the center of an EPR-Bohm type setup [6], with the common plane of their shells held perpendicular to the horizontal direction of the setup. Although initially at rest, a slight increase in temperature of each ball will eventually eject its two shells towards the observation stations, situated at a chosen distance in the mutually opposite directions. Instead of selecting the directions a and b for observing spin components, however, one or more contact-less rotational motion sensors—capable of determining the precise direction of rotation—are placed near each of the two stations, interfaced with a computer. These sensors will determine the exact direction of the angular momentum lambda_j (or −lambda_j) for each shell, without disturbing them otherwise, at a designated distance from the center. The interfaced computers can then record this data, in the form of a 3D map of all such directions. Once the actual directions of the angular momenta for a large ensemble of shells on both sides are fully recorded, the two computers are instructed to randomly choose the reference directions, a for one station and b for the other station—from within their already existing 3D maps of data—and then calculate the corresponding dynamical variables sign (lambda_j · a) and sign (−lambda_j · b). This “delayed choice” of a and b will guarantee that the conditions of parameter independence and outcome independence are strictly respected within the experiment [2]. It will ensure, for example, that the local outcome sign (lambda_j · a) remains independent not only of the remote parameter b, but also of the remote outcome sign (−lambda_j · b). If in any doubt, the two computers can be located at a sufficiently large distance from each other to ensure local causality while selecting a and b. The correlation function for the bomb fragments can then be calculated using the formula
E(a, b) = 1/N sum_{j =1}^N {sign (lambda_j · a)} {sign(−lambda_j · b)}, (16)
where N is the number of trials.
Apparently written by Joy Christian (Department of Physics, University of Oxford),
http://arxiv.org/pdf/0806.3078v2.pdf, page 4. Am I missing a later version?
The only change I asked from Joy, and he accepted, was that the bet which we made is determined by just four of these correlations, denoted E(0, 45), E(0, 135), E(90, 45), E(90, 135). The correspondence between the angles 0, 45, 90, 135 degrees and directions a, b is that the four directions a, b are in the same equatorial plane. The angles alpha and beta are the longitude of four points on the equator. Latitude = 0 degrees.
Joy's theory predicts three correlations equal to - 0.7 and one equal to + 0.7. Bell's theory predicts three correlations equal to - 0.5 and one correlation equal to + 0.5. Supposing that the sign pattern comes out as both expect, I have proposed that the bet is settled on whether the average value of the four absolute correlations is larger or smaller than 0.6. The exact value 0.6 would mean that the adjudicators have to toss a coin to choose a winner.
In my new R code
http://rpubs.com/gill1109/Bet_v2 I randomly assign each of the N runs to just one of the four pairs of settings (0, 45), (0, 135), (90, 45), (90, 135). In my opinion we would get identical results if this allocation was done in distributed fashion: one script chooses between alpha = 0 and 90 for each of the N runs, another script chooses between 45 and 135 for each of the N runs. One could then also calculate sign( a. lambda_k) and sign( b . -lambda_k ) by two separate computer programs, generating traditional CHSH style data sets: N runs, giving for Alice N pairs of a setting (0 or 90) and an outcome (+/- 1) , and for Bob N pairs of a setting (45 or 135) and an outcome (+/- 1). Then finally one further computer script computes the four correlations E(alpha, beta) for each of the four disjoint subsets of the runs, defined by the possible pairs of setting values.
Joy's own computer experts are welcome to write the Mathematia or Python versions of the scripts which do this job. I will test that they do the same as my script. Once we are all agreed, we can offer them to the adjudicationg committee. The Vaxjo conference is coming soon.
Conference site:
http://lnu.se/subjects/mathematics/conferences/quantum-theory-from-problems-to-advances---qtpa/qtpa?l=enConference poster:
http://lnu.se/polopoly_fs/1.97904!QTPA%20affisch%20140609.pdfThe adjudicators will all be there. I plan to announce our bet. If it has been called off, I will announce that it is called off. If we are still haggling about whether all N runs are used for all four correlations, or whether four disjoint random samples will be used, I will announce that fact.
Maybe Joy should come too.
Posted: Sat Apr 19, 2014 6:32 am