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FrediFizzx wrote:Sorry, but I am not going to bother "to do it myself." Too busy with other things. It is up to the writer of a paper to make the paper as understandable as possible for the reader.

gill1109 wrote:

FrediFizzx wrote:

FrediFizzx wrote:Can you put that into a regular equation of the form A(a, lambda) = ??? , etc? I'm not going to try to decipher R code.

IOW, show the measurement functions as regular equations then show the average of the product of the measurement functions. Then do the code. It will be more understandable that way.

Take an even number and angles . Colour the segments "black", "white", ..., "black". If there is just one segment , and it is coloured black. Colour in complementary way: are coloured "white", "black", ..., "white". The colour assigned to end-points does not matter. We have now coloured the entire unit circle with our two colours "white" and "black" except that we didn't determine the colours of the finitely many points on the boundaries between intervals of fixed colour. Each point is opposite a point of the opposite colour, so the total length of white segments and the total length of black segments are equal. Now give the circle a random rotation chosen uniformly between 0 and . Define according to whether the colour of the randomly rotated circle at point is black or white. Define .. A and B aren't defined at finitely many angles, but we don't have to worry about this. The probability is zero that A is undefined at any particular given point.

FrediFizzx wrote:

FrediFizzx wrote:Can you put that into a regular equation of the form A(a, lambda) = ??? , etc? I'm not going to try to decipher R code.

IOW, show the measurement functions as regular equations then show the average of the product of the measurement functions. Then do the code. It will be more understandable that way.

FrediFizzx wrote:Can you put that into a regular equation of the form A(a, lambda) = ??? , etc? I'm not going to try to decipher R code.

FrediFizzx wrote:I took another look at this paper and I am still having trouble figuring out what it is that you are actually presenting. What are the math formulas for all those graphs you present? Can one of them be presented in a complete equation string?

Code: Select all

oneplot <- function() {
    if (nswitch%%2 == 0)  times <- c(times,1)
    timesplus <- c(times,times+1,times+2,times+3)
    count <- function(t,d) {
        sum(timesplus > t & timesplus <= t+d)
    }
    points <- seq(from=0,to=1,by=0.01)
    numbers <- outer(data,points,Vectorize(count))
    corr <- 2*(apply(numbers%%2,2,sum)/1000)-1
    correlation <- c(corr,corr[100:1])
    difference <- pi*(c(points,1+points[2:101]))
    plot(difference,correlation,
        type="l",bty="n",ann=FALSE,xaxt="n",yaxt="n")
    lines(c(0,2*pi,2*pi,0,0),c(+1,+1,-1,-1,+1))
    abline(h=0)
    lines(difference,-cos(difference),col="blue")
    lines(c(0,pi,2*pi),c(-1,+1,-1),col="red")
}

nswitch <- 4
set.seed(11091951)
par(mfrow=c(3,4),oma=c(0,0,0,0),mar=c(0,0,0,0))
for( i in (1:12) ) {
    times <- sort(runif(nswitch))
    data <- 2*runif(1000)
    oneplot()
}

Joy Christian wrote:Steve Gull wrote

Many years ago (about 1984), I used to give a Mathematical Physics course to the Part II students. I illustrated the quantum paradox covered by Bell’s theorem by showing that you can’t program two independently running computers to mimic the results of spin measurements on two spin-1/2 particles in a singlet state. I believe this demonstration is actually better than Bell’s original argument.

Gull's is not a "proof" of anything, let alone of a misnomer called "Bell's theorem." It is more like what John Weeler would call "an idea of an idea"; and what I would call "wishful thinking."

Joy Christian wrote:What is more, it has nothing to do with how the Bell-test experiments are done. To understand how silly "Bell's theorem" is, please read my short paper: https://arxiv.org/abs/1704.02876.

Joy Christian wrote:And whatever Gull's argument is, it is necessarily wrong, because a local-realist model of the singlet correlations based on quaternions already exists: https://arxiv.org/pdf/1103.1879.pdf.

Steve Gull wrote:Many years ago (about 1984), I used to give a Mathematical Physics course to the Part II students. I illustrated the quantum paradox covered by Bell’s theorem by showing that you can’t program two independently running computers to mimic the results of spin measurements on two spin-1/2 particles in a singlet state. I believe this demonstration is actually better than Bell’s original argument.

Richard wrote:An intriguing possible direction involving indeed the Fourier transform is suggested by some lecture slides by Steve Gull, going back 35 years now. On his “MaxEnt 2009” web-page http://www.mrao.cam.ac.uk/~steve/maxent2009/, under the heading "Quantum Acausality and Bell’s Theorem", Steve writes

Steve Gull wrote:Many years ago (about 1984), I used to give a Mathematical Physics course to the Part II students. I illustrated the quantum paradox covered by Bell’s theorem by showing that you can’t program two independently running computers to mimic the results of spin measurements on two spin-1/2 particles in a singlet state. I believe this demonstration is actually better than Bell’s original argument.

This is a lovely proof of Bell’s theorem using the fact that the Fourier transform of the correlation function ρ has to equal the expected squared absolute value of the Fourier transform of the random function A. The actual correlation function only has three non-zero Fourier coefficients. However the Fourier transform of any realisation of A must have infinitely many non-zero coefficients, since otherwise it could not have any jumps. Since their absolute values get squared before averaging, there is no way that all but three can vanish.

Richard wrote:Jaynes (1989) does not make any attempt to specify what he understands by a local model, and expresses great surprise at very new results of Steve Gull, presented at the same conference as Jaynes’ own paper, in which a computer network metaphor is introduced and where it is shown that the singlet correlations cannot be simulated on such a network. Reference: Jaynes, E. T. (1989). Clearing up mysteries—the original goal. In J. Skilling (Ed.), Maximum Entropy and Bayesian Methods, Dordrecht, pp. 1–27. Kluwer.

gill1109 wrote:I put a paper on arXiv in which I show what correlation functions can be produced by simple “local hidden variables”. https://arxiv.org/abs/1312.6403. The triangle wave versus the cosine (how to optimally approximate EPR-B Correlations by classical systems)

Richard D. Gill
(Submitted on 22 Dec 2013 (v1), last revised 27 Dec 2013 (this version, v2))
The famous singlet correlations of a composite quantum system consisting of two spatially separated components exhibit notable features of two kinds. The first kind are striking certainty relations: perfect correlation and perfect anti-correlation in certain settings. The second kind are a number of symmetries, in particular, invariance under rotation, as well as invariance under exchange of components, parity, or chirality. In this note I investigate the class of correlation functions that can be generated by classical composite physical systems when we restrict attention to systems which reproduce the certainty relations exactly, and for which the rotational invariance of the correlation function is the manifestation of rotational invariance of the underlying classical physics. I call such correlation functions classical EPR-B correlations. It turns out that the other three (binary) symmetries can then be obtained for free: they are exhibited by the correlation function, and can be imposed on the underlying physics by adding an underlying randomisation level. We end up with a simple probabilistic description of all possible classical EPR-B correlations in terms of a ``spinning coloured disk'' model, and a research programme: describe these functions in a concise analytic way.

I’m a bit fed up that no one seems to bother to read it.