Joy Christian wrote:I have produced yet another simulation for the EPR-Bohm correlations which is more satisfactory and faithful to my 3-sphere model than previous attempts by myself and others.
http://rpubs.com/jjc/84238.
Joy Christian wrote:The simulation also contains nothing that would question the Pope's belief in the immaculate conception and the Ayatollah's belief in the prophesy of Mohammad.
Joy Christian wrote:The simulation also contains nothing that would question the Pope's belief in the immaculate conception and the Ayatollah's belief in the prophesy of Mohammad.
Joy Christian wrote:One only needs to test the mathematical properties of the metric {g, t} defined in the simulation to recognize that the true believer is talking nonsense. It is abundantly clear that the metric mathematically excludes the results (+,0), (-,0), (0,+), (0,-) and (0,0), and as a result reproduces the strong correlations entirely as a consequences of the geometrical and topological structures of the 3-sphere as advertised.
Schmelzer wrote:The part of the u which has not been "mathematically excluded" by "the metric" can be seen in Gill's variant http://rpubs.com/gill1109/ChristianSampleSizes .
Joy Christian wrote:... it only exhibits once again that neither of the two true believers in Bell have actually understood the details of the simulation, let alone the details of the analytical 3-sphere model. Over the years both of the true believers have persistently exhibited a mental block which prevents them from switching off their flatland --- R^3 --- prejudices and appreciate the geometry and topology of the 3-sphere. They are still arguing that if Earth is a sphere as I claim, then why aren't we all sliding off its curves. The u in question are in fact mathematically excluded by the metric, but the flatlanders are unlikely to understand that.
Schmelzer wrote:The problem is that I do not even see a necessity to "understand" something about S^3, and in considering Bell's theorem even R^3 does not play any role.
http://libertesphilosophica.info/blog/disproof-of-bells-theorem-book/ wrote:... this mistake lies in the formulation of the very first equation of his famous paper. The correct form of his proposed functions to reproduce the quantum correlations local-realistically must be
instead of
for them to provide a complete local description of the physical reality demanded by Einstein.
Schmelzer wrote:S^3 contains, of course, also a subgroup S^0 = {-1,1}, and if the values would be in this subgroup, nothing would change at all. You could as well use some embedding of S^0 into whatever group one likes. So, behind this replacement is, in fact, the trick that the values are not in the subgroup Z_2 of SU(2) created by {E,-E}, but in some direction depending on a resp. b. And, then, the multiplication gives something different from +-1, thus, we have something completely different from the experiment.
Schmelzer wrote:Because Bell's theorem is about are the results of the measurements, which are simply numbers, and, when the correlations are computed, multiplied like numbers. To compare with these experiments, and the way the experimenters handle the results A, B of the experiments, one has to do what the experimenters do with the measurement results - write down numbers +1 or -1 and then multiply them following the rules of Z_2 = S^0.
Joy Christian wrote:Please do not make bogus claims like these (they remind me of Gill) without actually reading what I have written and explained on my blog page I have linked above.
http://libertesphilosophica.info/blog/disproof-of-bells-theorem-book/ wrote:That is to say, his argument simply does not go through without the assumption of totally disconnected set \cup\,S^0 as the set of all possible measurement results (actual as well as counterfactual).
http://libertesphilosophica.info/blog/disproof-of-bells-theorem-book/ wrote:Because then the measurement results \pm\,1 occur as points of an absolutely parallelized 3-sphere, which is the set S^3 of unit quaternions. As a result, we must specify the joint probability distribution for the occurrence of the four pairs of measurement results on such a 3-sphere,
Joy Christian wrote:In response to the bogus criticism of my simulation by Gill linked above, I have revised the simulation. I have added a new figure which correctly displays the ratio of the total number N of the simultaneous events observed by Alice and Bob and the corresponding initial states (u, s) of the spin system: http://rpubs.com/jjc/84238.
As one can see, the correct figure is somewhat different from what Gill claims it should be! It exposes the fact that Gill has no understanding of my local model.
http://rpubs.com/jjc/84238 wrote:Ls[i, j] = length(s[t(a, u, b, u)]) # The number of initial states (u, s) in S^3.
Schmelzer wrote:It only exposes the fact that you don't get the elementary point that the initial states should not depend on a and b, because a and b are unknown.
Joy Christian wrote:By the way, as a quick check one can add the following few lines in the simulation (at appropriate places) to see that the claims made by Gill and his proxy are false:
M = 1000
(N = length(A[t(a, u, b, u)]))
## [1] 673
(L = length(s[t(a, u, b, u)]))
## [1] 673
(J = length(t(a, u, b, u)))
## [1] 1000
The lengths of N and s in S^3 are the same, as they must, but the length of t(a, u, b, u) is equal to the length of the pre-ensemble M in R^3, independent of a and b.
p. 7 wrote:the value of the expression is a vector with the same length as the longest vector which occurs in the expression
p.10 wrote:A logical vector. In this case the index vector is recycled to the same length as the vector from which elements are to be selected. Values corresponding to TRUE in the index vector are selected and those corresponding to FALSE are omitted. For example
> y <- x[!is.na(x)]
creates (or re-creates) an object y which will contain the non-missing values of x, in the same order. Note that if x has missing values, y will be shorter than x.
s = runif(M, 0, pi) # Initial states of the spins are the pairs (u, s) in S^3
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