Joy Christian's colourful exploding balls experiment

[Joy Christian]

Can we add a little more precision to the numbers? Recall that cos(45 degrees) = sqrt(2) / 2 = 0.7071...

So to be more precise, your four targets are

E(0, 45) = - 0.7071..., E(0, 135) = + 0.7071..., E(90, 45) = - 0.7071..., E(90, 135) = - 0.7071....

I bet that at least one will be missed by an amount 0.2 (= 1/5) or more.

I don't mind how large N will be.

As a matter of interest, will the two files contain exactly equal and opposite directions u_k and - u_k or only approximately equal and opposite directions? In the former case, just one file of N directions is enough. The second file contains the set of exactly opposite directions. Add 180 degrees to the longitude (azimuthal angle) theta, change the sign of the co-latitude (zenith angle, polar angle) phi.

I use mathematician's notation. I read on wikipedia that physicists tend to use theta for the zenith angle, phi for the azimuthal angle. We have to be agreed on what is in the files (azimuth and zenith, or zenith and azimuth).

It's important that everything is completely clear and agreed by the two bettors and the three adjudicators.

I am happy with the predictions

E(0, 45) = - 0.7071...,

E(0, 135) = + 0.7071...,

E(90, 45) = - 0.7071...,

E(90, 135) = - 0.7071....

Nothing is known about the relationship between Alice's N u_k's and Bob's N u_k's until the experiment is done---apart from the fact that the index k in the kth run would be the same for both Alice and Bob (well, I do know a lot about the u_k's, but we are not talking about my theoretical model). In the experiment we will produce two independent files of N u_k's, one for Alice and one for Bob. We will then match the k's and compute the correlation in the usual manner [as described in eq.(16) of my experimental paper].

It is irrelevant to me which convention or coordinate system is used to record the two sets of u_k's on the two sides as long as just one, consistent coordinate system is used.

[gill1109]

Excellent

In the meantime, here is a movie of the picture I showed you earlier

http://www.math.leidenuniv.nl/~gill/Images/movie.gif

[Joy Christian]

Excellent

In the meantime, here is a movie of the picture I showed you earlier.

Very nice.

Two questions: (1) Can you slow down the rotation speed of the plot? And (2), can you add red dots showing all eight points?

[gill1109]

Excellent

In the meantime, here is a movie of the picture I showed you earlier.

Very nice.

Two questions: (1) Can you slow down the rotation speed of the plot? And (2), can you add red dots showing all eight points?

I think I can do all these things but it will take me some time ...

Regarding the issue of the two files of directions:

Let's call the directions of angular momentum in Bob's file v_k, k = 1, ..., N and the directions in Alice's file u_k, k=1, ..., N.

In theory one would have v_k = - u_k, but in practice that might not be exactly the case. It shouldn't matter, right?

If I pick measurement directions a and b, then we agree that the outcomes left and right should be

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

and the estimated (observed, sample, experimental ...) correlation is

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

[Joy Christian]

Regarding the issue of the two files of directions:

Let's call the directions of angular momentum in Bob's file v_k, k = 1, ..., N and the directions in Alice's file u_k, k=1, ..., N.

In theory one would have v_k = - u_k, but in practice that might not be exactly the case. It shouldn't matter, right?

If I pick measurement directions a and b, then we agree that the outcomes left and right should be

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

and the estimated (observed, sample, experimental ...) correlation is

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

This is fine.

[gill1109]

Here's a new version of the movie. Now it's nearly 10 MB

http://www.math.leidenuniv.nl/~gill/Images/movie2.gif

I suggest you download it to your computer and then play it locally in a browser. It's a gif file, and browsers know how to display them

alpha and beta run from 0 to 180 degrees, corr from -1 to +1

One should imagine lots of copies of this cube, half of them upside down, tiling the whole alpha-beta plane, chess-board fashion.

For instance, restricting alpha and beta both to between 0 and 360 degrees, we have a 2x2 chessboard, with this cube twice, on the two diagonal squares, and this cube twice but upside down, on the two off diagonal squares.

Hard to picture!

[Joy Christian]

Here's a new version of the movie. Now it's nearly 10 MB

http://www.math.leidenuniv.nl/~gill/Images/movie2.gif

I suggest you download it to your computer and then play it locally in a browser. It's a gif file, and browsers know how to display them

alpha and beta run from 0 to 180 degrees, corr from -1 to +1

One should imagine lots of copies of this cube, half of them upside down, tiling the whole alpha-beta plane, chess-board fashion.

For instance, restricting alpha and beta both to between 0 and 360 degrees, we have a 2x2 chessboard, with this cube twice, on the two diagonal squares, and this cube twice but upside down, on the two off diagonal squares.

Hard to picture!

Cool gif. I wish I can control its turning.

[gill1109]

Cool gif. I wish I can control its turning.

I hope to make an interactive web-page version of this, where the user can do what they like. In the meantime, you can just run the R code which draws the picture on your own computer, and rotate it yourself by hand.

Code: Select all

library(rgl)
alpha <- seq(from = 0, to = 180, length = 20)
beta <- alpha
surfQ <- expand.grid(x = alpha, y = beta)
surfQ$z <- with(surfQ, {-cos((x-y)*pi/180)})

corQ <- matrix(surfQ$z, 20 ,20)

surfC <- surfQ
surfC$z <- with(surfC, {- 1 + 2 * abs((x-y)/180)})

corC <- matrix(surfC$z, 20 , 20)

alphaE <- c(0, 90)
betaE <- c(45, 135)
ptsQ <- expand.grid(x = alphaE, y = betaE)
ptsQ$z <- with(ptsQ, {-cos((x-y)*pi/180)})

ptsC <- ptsQ
ptsC$z <- with(ptsC, {- 1 + 2 * abs((x-y)/180)})


persp3d(alpha, beta, corQ, front = "line", back = "line", col = "red", axes = FALSE, xlab="alpha", ylab="beta", zlab="corr")
surface3d(alpha, beta, corC, front = "line", back = "line", col = "blue")

lines3d(c(0, 180), c(0, 0), c(-1, -1))
lines3d(c(0, 0), c(0, 180), c(-1, -1))
lines3d(c(0, 0), c(0, 0), c(-1, 1))

spheres3d(ptsC$x, ptsC$y, ptsQ$z, col = "red", radius = 3)
spheres3d(ptsC$x, ptsC$y, ptsC$z, col = "blue", radius = 3)

lines3d(rep(ptsC$x[1], 2), rep(ptsC$y[1], 2), c(-1, 1), col = "green")
lines3d(rep(ptsC$x[2], 2), rep(ptsC$y[2], 2), c(-1, 1), col = "green")
lines3d(rep(ptsC$x[3], 2), rep(ptsC$y[3], 2), c(-1, 1), col = "green")
lines3d(rep(ptsC$x[4], 2), rep(ptsC$y[4], 2), c(-1, 1), col = "green")
save <- read.table("save.txt")
par3d(userMatrix = as.matrix(save))


The following isn't R code, but the contents of a file you need to create called "save.txt"

Code: Select all

"V1" "V2" "V3" "V4"
"1" 0.89551317691803 -0.445017099380493 -0.00404098257422447 0
"2" 0.00934700295329094 0.00972943194210529 0.999908864498138 0
"3" -0.444936990737915 -0.89546924829483 0.0128725711256266 0
"4" 0 0 0 1


The following line just spins the thing for 60 seconds, 4 revolutions per minute:

Code: Select all

play3d(spin3d(rpm = 4), duration = 60)


These lines reset the viewing point

Code: Select all

save <- read.table("save.txt")
par3d(userMatrix = as.matrix(save))


You need an R package called "rgl" so you might need to do

Code: Select all

install.packages("rgl")


once, to get what you need on your computer.

[Joy Christian]

In the meantime, you can just run the R code which draws the picture on your own computer, and rotate it yourself by hand.

OK, thanks. This will do.

[gill1109]

Now here's a web page with an interactive graphics display:

http://www.math.leidenuniv.nl/~gill/surface/

Not quite what I wanted but OK, this was just the first try!!!

[Joy Christian]

I am reproducing here what Michel Fodje wrote elsewhere, because (1) his observations are relevant for all realizable physical experiments, and (2) they beautifully spell out elementary facts of logic, arithmetic, and physics that the vast majority of the Bell-believers among us seem to be incapable of understanding:

1 - If you measure (A,B), (A',B), (A,B'), (A,B') on a different particle pair, the A in (A,B) can be different from the A in (A,B') without any mistake or cheating.
2 - If you measure the same particle at a (A,B), and exactly the same particle again at (A,B'), then A in (A,B) can be different from the A in (A,B') without any mistake or cheating.
3 - The only way to measure (A,B), (A',B), (A,B'), (A,B') on the same particle, and make sure the A in (A,B) and the A in (A,B') are the same (and each outcome is the same in each pair), is to measure the same particle pair, simultaneously at (A, A', B, B'), an impossibility. Therefore a genuine experiment testing S <= 2 is impossible.
4 - If the probability of obtaining H for a coin is 0.75, the probability of the counter-factual H outcome for the same coin cannot be 0.75 too. It must be 0.25.
5 - No 4xN spreadsheet can violate the S <= 2. It doesn't matter where you get your data to put in the spreadsheet, from LHV/QM/non-local model/non-real model/statistical error etc.
6 - The correct inequality for 4 different 2XN spreadsheets is S<= 4, it doesn't matter where you get your data to put in the spreadsheet, from LHV/QM/non-local model/non-real model/statistical error etc. 4 *different* 2xN spreadsheets can easily violate S <= 2, because that inequality does not apply to such data. It is a mathematical error to even compare them.
7 - It is utter nonsense to compare an inequality derived from a 4xN spreadsheet, with data in the form of 4 different 2xN spreadsheets, even if your 4 *different* 2xN spreadsheets are randomly sampled from a single 4xN spreadsheet. What determines the upper bound is the degrees of freedom in the data, not the degrees of freedom in the original spreadsheet you randomly sampled from.
8 - These inequalities have nothing to do with physics, they are mathematical tautologies about real numbers and degrees of freedom. Please read the Rosinger paper carefully. Their violation points to a mathematical error in their application. Nothing can violate them.
9 - No EPRB experiment will ever be done which produces a 4xN spreadsheet, as it must if it purports to *test* the S <= 2 relationship. As long as they keep producing 4 *different* 2XN spreadsheets, the appropriate inequality is S <= 4, and it will never be violated.

[gill1109]

Exactly the same message has been posted on three different topics. I have already responded on another. The one about the still open bet. What I said there is extremely relevant to the experiment bet, as well as to the simulation challenge.

Finally JJC realizes that the experiment is flawed, the bet unwinnable, and the challenge unbeatable. Perhaps he will now revise his experimental paper which contains (at least) one howler of a mistake because JJC is apparently not aware of relevant elementary facts of logic and arithmetic.

[Joy Christian]

Finally JJC realizes that the experiment is flawed, the bet unwinnable, and the challenge unbeatable. Perhaps he will now revise his experimental paper which contains (at least) one howler of a mistake because JJC is apparently not aware of relevant elementary facts of logic and arithmetic.

Your statement actually proves what I wrote above: "... Michel Fodje ... beautifully spells out elementary facts of logic, arithmetic, and physics that the vast majority of the Bell-believers among us seem to be incapable of understanding:"

[Ben6993]

Hi

Just a request for more clarity in point 1.

"Minkwe wrote:
1 - If you measure (A,B), (A',B), (A,B'), (A,B') on a different particle pair, the A in (A,B) can be different from the A in (A,B') without any mistake or cheating.

I suggest replacing the wording "on a different particle pair", by "each on a different particle pair, making eight measurements on eight different particles". As it currently stands I think I could read it as eight measurements on two particle pairs.

[gill1109]

Unfortunately Bell-deniers tend to be unaware of elementary facts of probability theory and statistics. As well as being ignorant of the relevant literature (Bell, "Speakable and Unspeakable", chapters 13 and 16).

[Joy Christian]

Unfortunately Bell-deniers tend to be unaware of elementary facts of probability theory and statistics. As well as being ignorant of the relevant literature (Bell, "Speakable and Unspeakable", chapters 13 and 16).

Unfortunately Bell-believers tend to be unaware of elementary facts of geometry, topology, and algebra. As well as being ignorant of the relevant literature (Bell, "Speakable and Unspeakable", Second Edition, chapters 24).

[minkwe]

Hi

Just a request for more clarity in point 1.

"Minkwe wrote:
1 - If you measure (A,B), (A',B), (A,B'), (A,B') on a different particle pair, the A in (A,B) can be different from the A in (A,B') without any mistake or cheating.

I suggest replacing the wording "on a different particle pair", by "each on a different particle pair, making eight measurements on eight different particles". As it currently stands I think I could read it as eight measurements on two particle pairs.

Thanks Ben, though I really intended to write:

1 - If you measure (A,B), (A',B), (A,B'), (A,B') , each on a different particle pair...

So, there are 4 pairs not 8.

[gill1109]

Chapter 24 is one of my favourites. Michel should study it carefully. As well as 13, 14 and 16.

[minkwe]

Chapter 24 is one of my favourites. Michel should study it carefully. As well as 13, 14 and 16.

Yes everybody else should study every chapter of every article, and every book they've already studied, since Richard doesn't understand it enough to clearly enunciate what concept in them is relevant for any discussion.

[Joy Christian]

In the light of some persistent but entirely unjustified scepticism about my proposed experiment, let me make a list of evidence here in support of the experiment:

The readers of this forum have two options: (1) they can either believe the propaganda produced by Richard Gill against the experiment, or (2) they can evaluate the evidence after evidence, and explanation after explanation, I have presented in support of my discovery that EPR-Bohm correlations are correlations among the points of a parallelized 3-sphere (which is one of the solutions of Einstein's field equations, namely the Friedmann-Robertson-Walker solution). The choice is theirs.

Let me present my evidence once again:

(1) A simple explanation of my proposed experiment, with links to relevant papers.

(2) The proof that there indeed exist N vectors, s_k and -s_k, appearing in equation (16) of my first experimental paper: http://rpubs.com/jjc/16531.

(3) Detailed explanation of my local-realistic framework for the quantum correlations, presented in 15 papers and one of my books on the subject.

(4) A spectacular 2D simulation of my 3-sphere model for the EPR-Bohm correlation.

(5) The most accurate simulation of my 3-sphere model for the EPR-Bohm correlation.

And finally, a nice summary by Michel Fodje of how Richard Gill operates---it is quite revealing.

His present tactic is to avoid paying up the 10,000 Euros he owes me for producing the N vectors in the item (2) above.