gill1109 wrote:Michel, I think I have a way to explain something to you. I need to run your epr-simple Python program with some slight modifications and I need to save the experimental results in a way so that I can do some simple data-processing with R of the results.
Here are my requests:
Alice's settings are *only* the famous 0 and 90 degrees
Bob's settings are *only* the famous 45 and 135 degrees
It will be fine just to have
NUM_ITERATIONS = 100000
so that there will be approximately 25 000 pairs of particles measured according to each of the pairs of settings. Even one tenth of these numbers would be fine: the statistical error in the correlations will only be of size approximately +/- 0.01
The outcome of measuring each particle is either +1 or -1 or "nothing" (no particle detected). For convenience, code this with a 0 (zero).
I would like to have the following data output: for each of the four pairs of settings, a 3 x 3 table of the numbers of each kind of outcome.
Alternatively, generate a 100 000 by four data matrix containing in each row:
Alice's setting (0 or 90), Bob's setting (45 or 135), Alice's outcome (-1, 0, or 1), Bob's outcome (-1, 0, or 1).
Your simulation is what I would call a simulation of a pulsed or clocked experiment: there will be exactly 100 000 pairs of particles generated and emitted from the source, we know how they are matched with one another; we also know when either or both particle is not detected. This is what is called a 2x2x3 experiment (two parties, two settings per party, three outcomes per setting per party).
The experiment generates, as I have explained, four 3x3 tables of counts (absolute frequencies). Convert to relative frequencies, per table, and we have four 3x3 tables of empirical probabilities. If we would let the sample size go to infinity these would stabilize at certain true probabilities. Four sets of nine probabilities adding up to +1, per set.
I would like to see the empirical probabilities (relative frequencies) for a reasonably large N, say 10 000 or 100 000. And I would like to compare them with the predictions of local realism for a 2x2x3 experiment, which are namely a whole bunch of CHSH inequalities got by grouping three outcomes to two in all possible different ways, together with a bunch of CGLMP inequalities.
My prediction is that all of these inequalities will be satisfied, up to statistical error of size roughly 1 divided by square root of N.
But my prediction might be wrong, and then I might have to withdraw some papers I have written ...
gill1109 wrote:I tried very hard to make a careful and true factual statement. Notice the qualification "in the opinion of many readers".
gill1109 wrote:Here are some names of such readers: Scott Aaronson, Lucien Hardy, Florin Moldoveanu, Bryan Sanctuary, Han Geurdes, Adrian Kent, Abner Shimony, David Hestenes, Manfried Faber, Azhar Iqbal, Chantal Roth, Samson Abramsky, Reinhard Werner, James Weatherall, ...
Ben6993 wrote:
It is impossible to make a 4XN table of observables to beat the CHSH limit. So it is impossible for nature to beat the CHSH limit in laboratory space, else the outcomes of the experiment could be put into such a table.
Joy Christian wrote:Apart from Scott Moronson and a couple of other unqualified and uninformed individuals like Moldoveanu, Weatherall, and Gill, no knowledgeable individual has ever objected to my work in any way, let alone claimed that there is an error in it of any kind.
minkwe wrote:Richard. You have the code. The way this works is that if you have new insight, modify the code, run it yourself and present any results you get explaining what the results mean. In an appropriate thread. Then we can discuss what you want to explain.
epr-simple is not a pulsed clocked simulation, despite what you call it.
gill1109 wrote:Michel:
When deriving the CHSH inequality we are not talking about measurements at all, and certainly not about multiple measurements on the same particles.
We are talking about mathematical relations between functions A(a, lambda), B(b, lambda) and a probability distribution rho(lambda). The functions A and B only take the values -1 and +1.
We determine that the functions E(a, b) = int A(a, lambda) B(b, lambda) rho(lambda) d lambda are not completely arbitrary but have to satisfy certain relations, in particular we find
E(a, b) + E(a, b') + E(a', b) - E(a', b') <= 2
Tsirelson inequality
E(a, b) + E(a, b') + E(a', b) - E(a', b') <= 2 sqrt 2.
If we only assume no action at a distance (at the surface level), one can only prove the PR inequality (Popescu-Rohrlich)
E(a, b) + E(a, b') + E(a', b) - E(a', b') <= 4
Hidden variables = {e, p, s}, e ∈ [0..2π), s = {1/2, 1}
p = ½ sin²t, t ∈ [0..π/2)
e' = e + 2πs
A(a,λ) = sign(-1ⁿ cos n(a − e)) if |cos n(a − e)| > p, 0 otherwise
B(b,λ) = sign(-1ⁿ cos n(b − e')) if |cos n(b − e')| > p, 0 otherwise
where n = 2s
set.seed(1234)
N <- 10000
s <- 1/2
n <- 2*s
e <- runif(N, 0, 2*pi)
ep <- e + 2 * pi * s
alpha <- c(0, 90) * pi / 180 # Alice's possible two settings
beta <- c(45, 135) * pi / 180 # Bob's possible two settings
t <- runif(N, 0, pi/2)
p <- (sin(t)^2)/2
a <- sample(c(1, 2), N, replace = TRUE) # Alice setting names (1, 2)
b <- sample(c(1, 2), N, replace = TRUE) # Bob setting names (1, 2)
ca <- cos(n * (alpha[a] - e))
cb <- cos(n * (beta[b] - ep))
A <- ifelse(abs(ca) > p, sign(((-1)^n) * ca), 0)
B <- ifelse(abs(cb) > p, sign(((-1)^n) * cb), 0)
mean((A*B)[a == 1 & b ==1 & A*B != 0])
mean((A*B)[a == 1 & b ==2 & A*B != 0])
mean((A*B)[a == 2 & b ==1 & A*B != 0])
mean((A*B)[a == 2 & b ==2 & A*B != 0])
> mean((A*B)[a == 1 & b ==1 & A*B != 0])
[1] -0.6933718
> mean((A*B)[a == 1 & b ==2 & A*B != 0])
[1] 0.6740563
> mean((A*B)[a == 2 & b ==1 & A*B != 0])
[1] -0.7009967
> mean((A*B)[a == 2 & b ==2 & A*B != 0])
[1] -0.7050147
> data.out <- data.frame(a, b, A, B)
> head(data.out)
a b A B
1 1 2 -1 -1
2 2 2 1 0
3 2 1 1 -1
4 2 1 1 -1
5 2 2 1 -1
6 2 2 1 -1
> nrow(data.out)
[1] 10000
> tail(data.out)
a b A B
9995 2 2 -1 1
9996 1 1 1 1
9997 2 1 0 -1
9998 1 1 1 -1
9999 2 2 -1 1
10000 2 1 0 1
minkwe wrote:gill1109 wrote:Michel:
When deriving the CHSH inequality we are not talking about measurements at all, and certainly not about multiple measurements on the same particles.
Not true as anyone can verify by asking what E(a,b) means. It is an expectation value of the paired product of measurement outcomes at angles a and b.We are talking about mathematical relations between functions A(a, lambda), B(b, lambda) and a probability distribution rho(lambda). The functions A and B only take the values -1 and +1.
And what do those functions mean? A(a, lambda) is the measurement outcome at Alice's station when her setting isthe angle a and the hidden variables are lambda.
You can't escape from by claiming measurement is not involved.
minkwe wrote:Tsirelson inequality is just the mathematical tautology
cos(a, b) + cos(a, b') + cos(a', b) - cos(a', b') <= 2 sqrt 2
There is nothing quantum about it. It is all geometry.
As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.
gill1109 wrote:minkwe wrote:Richard. You have the code. The way this works is that if you have new insight, modify the code, run it yourself and present any results you get explaining what the results mean. In an appropriate thread. Then we can discuss what you want to explain.
epr-simple is not a pulsed clocked simulation, despite what you call it.
I'm afraid it doesn't work like that. I can't mess with your program and then expect you to believe what comes out of it.
But I'll need you to agree with my implementation before I show you what I am going to get out of it.
minkwe wrote:I don't have time to babysit while you are playing with your toys.
gill1109 wrote:minkwe wrote:Tsirelson inequality is just the mathematical tautology
cos(a, b) + cos(a, b') + cos(a', b) - cos(a', b') <= 2 sqrt 2
There is nothing quantum about it. It is all geometry.
Tsirelson's beautiful inequality is indeed in a sense "just geometry" but I think that if you look at the proof you will see it is a little harder than you think. After all, the Hilbert spaces can have arbitrary dimension. It is not a theorem about spin half particles.
The bridge between mathematics and reality is causing us all the trouble here.
Especially when randomness is involved, the bridge between the two worlds becomes quite delicate. Part of it is built on statistics, and statistics is built on probability theory. Unfortunately these topics are not taught very well to physicists.
gill1109 wrote:minkwe wrote: I'm not your lab technician who sits by idly and executes your commands.
Things for Michel to do: ....
minkwe wrote:gill1109 wrote:minkwe wrote: I'm not your lab technician who sits by idly and executes your commands.
Things for Michel to do: ....
Priceless
minkwe wrote:gill1109 wrote:minkwe wrote:Tsirelson inequality is just the mathematical tautology
cos(a, b) + cos(a, b') + cos(a', b) - cos(a', b') <= 2 sqrt 2
There is nothing quantum about it. It is all geometry.
Tsirelson's beautiful inequality is indeed in a sense "just geometry" but I think that if you look at the proof you will see it is a little harder than you think. After all, the Hilbert spaces can have arbitrary dimension. It is not a theorem about spin half particles.
There is no Hilbert space necessary to derive 2 sqrt 2. The proof is a lot easier than you think. If you want I can show you how it is done (in a different thread), much simpler without any Hilbert space confusion, maybe you will have another eureka moment from it.
minkwe wrote:http://bayes.wustl.edu/etj/prob/book.pdf
http://www.amazon.com/Probability-Theor ... 0521592712
Chapters 9 "Repetitive experiments: probability and frequency" and 10 "Physics of random experiments" are particularly relevent here.
minkwe wrote:I claim that whatever the experimental correlations are, they will agree with the QM prediction for the experiment, whatever the experiment is.Heinera wrote:Well, QM disagrees. According to QM, this particular macroscopic experiment reduces to classical mechanics, for which the correlations are easily derived. And they are not the cosine correlations.
You claim that the QM prediction for the experiment is not the cosine correlation, Joy claims that it is the cosine correlation, you can attempt to prove him wrong by producing the QM calculation showing that it is not the cosine correlation.
Heinera wrote:My advice would be that you should really get another QM teacher than Joy Christian. Already in the first lecture of QM 101 it is demonstrated that QM reduces to classical mechanics for macroscopic bodies. The easiest proof is to use the QM action integral and see that the action trivially reduces to the classical action when due to a macroscopic mass term. It means that the correlations in the exploding balls experiment will be the good old classical correlations, even according to QM.
So if Joy was successful in his experiment, it means his theory would contradict QM as well as classical mechanics. And not to mention the contradiction with mathematics itself. Go figure.
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