gill1109 wrote:Joy Christian wrote:The evidence presented in the above simulation is completely consistent with the terms of the Gill challenge. To reiterate: (1) a single set of spin directions u for Alice are used to calculate all four correlations, the negative of which, -u, being the spin directions used for Bob; (2) the same number of trials, N, are used in the calculations of all four correlations; and (3) the standard dot product, in the standard formula for the mean value, is used to calculate all four correlations. That is what Gill has been demanding. Moreover, these calculations are not only fully consistent with the terms of the Gill challenge, but also with the eq. (16) of my paper.
I'm afraid this is not quite correct.
I am afraid Gill's arguments above are incorrect. It is surprising that after all these months of my repeatedly pointing out what my model is all about, he still makes ridiculous statements that have nothing to do with my model. Let us recall that
(1) his challenge is about my proposed experiment,
(2) my proposed experiment is about testing my local model for the EPRB correlation, and
(3) my local model for the EPRB correlation is based on my hypothesis that we live in a parallelized 3-sphere, S^3, and our usual perceptions that we live in R^3 is just an illusion (a bit like looking around and thinking that the planet we live on is flat).
With this in mind, we can see where Gill has gone wrong. He writes: "In Christian's script, first of all a total of N = 10 000 pairs of particles are generated."
Wrong!!!
This is his biggest mistake. The number of particles generated in my script is approximately 7,070, not 10,000. Remember that the state of the system in my model is given by a pair (u, s), where s is the parameter that appears in p (for details, see
the simulation itself, or this paper:
http://arxiv.org/abs/1405.2355). Consequently there are only about 7,070 pairs of particles (or states) generated in my script, not 10,000. The "other" particles simply do not exist in S^3. This is the point Gill has failed to understand. This is surprising, because it is not difficult to understand: The state of the system in my model is given by the pair (u, s), not just by u itself.
Next he writes: "For each correlation (each pair of directions a, b) a different subset of a different size is used, as is easily observed by adding a line in the code printing "N" each time one of the correlations is calculated."
This too is not correct. The same number of trials for all four correlations is used in my script. Contrary to Gill's claim, N = 7070. Check this out for yourself:
alpha <- 0 * pi/180
beta <- 45 * pi/180
a <- c(cos(alpha), sin(alpha))
b <- c(cos(beta), sin(beta))
ca <- colSums(u * a) ## Inner products of cols of 'u' with 'a'
cb <- colSums(u * b) ## Inner products of cols of 'u' with 'b'
(E_0_45 <- sum(sign(ca) * sign(-cb))/N)
## [1] -0.6993
(N)
## [1] 7070
alpha <- 0 * pi/180
beta <- 135 * pi/180
a <- c(cos(alpha), sin(alpha))
b <- c(cos(beta), sin(beta))
ca <- colSums(u * a) ## Inner products of cols of 'u' with 'a'
cb <- colSums(u * b) ## Inner products of cols of 'u' with 'b'
(E_0_135 <- sum(sign(ca) * sign(-cb))/N)
## [1] 0.703
(N)
## [1] 7070
alpha <- 90 * pi/180
beta <- 45 * pi/180
a <- c(cos(alpha), sin(alpha))
b <- c(cos(beta), sin(beta))
ca <- colSums(u * a) ## Inner products of cols of 'u' with 'a'
cb <- colSums(u * b) ## Inner products of cols of 'u' with 'b'
(E_90_45 <- sum(sign(ca) * sign(-cb))/N)
## [1] -0.699
(N)
## [1] 7070
alpha <- 90 * pi/180
beta <- 135 * pi/180
a <- c(cos(alpha), sin(alpha))
b <- c(cos(beta), sin(beta))
ca <- colSums(u * a) ## Inner products of cols of 'u' with 'a'
cb <- colSums(u * b) ## Inner products of cols of 'u' with 'b'
(E_90_135 <- sum(sign(ca) * sign(-cb))/N)
## [1] -0.7276
(N)
## [1] 7070
## The Bell-CHSH inequality is violated:
abs(E_0_45 - E_0_135 + E_90_45 + E_90_135)
## [1] 2.829
Please do note that N is the same for all four correlations: N = 7,070.
Next he writes: "The two files of directions saved in AliceDirections.txt and BobDirections.txt are the subset of directions which are used for just one of the correlations."
This too is incorrect. As I explained above, the state of the system in my model is given by the pair (u, s), not just by u itself. Gill continues to think in terms of u alone, and interprets my results accordingly, despite the fact that I have repeatedly pointed out to him that the state of the system in my model is the pair (u, s).
The rest of his comments are misguided. They show that he is not talking about my model, or my proposed experiment, or the above simulation, but something else.
