Sorry. I did not mean to provoke a skirmish with my post.

Hi Richard, I see nothing wrong with Joy's derivation of the cosine correlation and do not wish at this point to review the criticisms. I read many of them a year or two ago and the only point I was unsure about was the use of dual handedness which was said by some to be inappropriate, yet seemed fine and necessary to me, though it puts (maybe in my interpretation only) the correlation in CA space (a double cover of laboratory space) and not in (the single cover) of laboratory space.

You say that QM correlations have been found in the laboratory. Well those correlations apply to Joy's model, too, as he gets the same cosine relationship. Just because his cosine correlation was derived (if that is correct) for CA space does not rule out finding such a correlation in some experiments in the laboratory.

The CHSH is, however, the stringent experimental test in the laboratory and so far has not been exceeded validly, i.e. without loopholes.

As time goes by I am moving closer to Michel's view that CHSH is irrelevant. 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.

To allow QM and Joy's model and nature to use a cosine correlation, it follows that the correlation is not in the laboratory space, but in the higher dimensions where the particle resides.

There is no way of predicting individual observables using QM because of randomness applied at the last instant, rather than being a result of a calculation. That is a good reason to excuse QM from being used constructing a 4xN table of observables. But a set of QM outcomes, exceeding the 0.5 limit of correlation, should be imaginable. Say we imagine generating every possible outcome of CHSH experiments in a very large set of 4xN tables. We cannot use QM to predict individual outcomes, but one of these tables in the very large set of tables should correspond by chance to the outcomes matching a CHSH experiment. Assuming QM matches the experimental outcomes, then the QM observables must be one of the tables in the set. But we know that no such table in the very large set will exceed a correlation of 0.5.

And as we know that such a table of observables cannot be simulated, it follows that neither nature not QM can beat the limit in the stringent CHSH experiment simulation. So the CHSH test cannot be relevant to nature.

Hi Richard, I see nothing wrong with Joy's derivation of the cosine correlation and do not wish at this point to review the criticisms. I read many of them a year or two ago and the only point I was unsure about was the use of dual handedness which was said by some to be inappropriate, yet seemed fine and necessary to me, though it puts (maybe in my interpretation only) the correlation in CA space (a double cover of laboratory space) and not in (the single cover) of laboratory space.

You say that QM correlations have been found in the laboratory. Well those correlations apply to Joy's model, too, as he gets the same cosine relationship. Just because his cosine correlation was derived (if that is correct) for CA space does not rule out finding such a correlation in some experiments in the laboratory.

The CHSH is, however, the stringent experimental test in the laboratory and so far has not been exceeded validly, i.e. without loopholes.

As time goes by I am moving closer to Michel's view that CHSH is irrelevant. 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.

To allow QM and Joy's model and nature to use a cosine correlation, it follows that the correlation is not in the laboratory space, but in the higher dimensions where the particle resides.

There is no way of predicting individual observables using QM because of randomness applied at the last instant, rather than being a result of a calculation. That is a good reason to excuse QM from being used constructing a 4xN table of observables. But a set of QM outcomes, exceeding the 0.5 limit of correlation, should be imaginable. Say we imagine generating every possible outcome of CHSH experiments in a very large set of 4xN tables. We cannot use QM to predict individual outcomes, but one of these tables in the very large set of tables should correspond by chance to the outcomes matching a CHSH experiment. Assuming QM matches the experimental outcomes, then the QM observables must be one of the tables in the set. But we know that no such table in the very large set will exceed a correlation of 0.5.

And as we know that such a table of observables cannot be simulated, it follows that neither nature not QM can beat the limit in the stringent CHSH experiment simulation. So the CHSH test cannot be relevant to nature.

- Ben6993
**Posts:**287**Joined:**Sun Feb 09, 2014 12:53 pm

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 ...

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.

- minkwe
**Posts:**1441**Joined:**Sat Feb 08, 2014 10:22 am

gill1109 wrote:I tried very hard to make a careful and true factual statement. Notice the qualification "in the opinion of many readers".

As I have pointed out many times before, this is a slanderous lie---a calculated attempt by Gill to mislead the physics community for political and selfish reasons.

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, ...

This is another mixture of lies and calculated misrepresentation. 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.

Most of the names Gill has conjured up above to support his lies have actually verified my work and recognized the silly blunders Gill has made. He has no evidence whatsoever to support his fallacious claims. It is scandalous to list names of individuals from thin air without any evidence to back up his story. He might as well claim that he had dinner last night with Barack Obama. It is evidently a political ploy by him to hide his own incompetence in mathematics. I consider such a calculated negative propaganda against my work to be a criminal act---a crime not only against me, but also against physics, against physics community, and above all against Nature. Making a false and unjustified claim against someone's perfectly sound work is to mislead the physics community for political and selfish reasons, and Gill should be held accountable for such acts. His is a cheap trick and we all know that negative propaganda work extremely well, whether in science or in politics.

As for the few criticisms of my work that do exist, it is important to recall that I have systematically debunked them all, for example here, here, and here.

In fact, any competent reader with only basic skills in mathematics should be able to reproduce all of the equations of my work rather effortlessly.

Moreover, all of the so-called arguments against my disproof to date are based on an elementary logical fallacy---the Straw-man Fallacy. What the critics do is replace my model X with its grossly distorted misrepresentation Y, and then pretend---by refuting their own distortion Y (by resorting to deliberate dishonesty or out of sheer incompetence)---that they have undermined my actual model X. Such a dishonest strategy is an insult to scientific process (for details, see, for example, this paper).

Unlike Bell himself, some of the followers of Bell are naïve, uninformed, and dishonest.

Last edited by Joy Christian on Mon Jun 02, 2014 4:58 am, edited 1 time in total.

- Joy Christian
- Research Physicist
**Posts:**2793**Joined:**Wed Feb 05, 2014 4:49 am**Location:**Oxford, United Kingdom

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.

This is totally irrelevant.

In the laboratory we generate not a Nx4 table of 4 observables but an Nx4 table containing pairs of settings of Alice and Bob (Alice: 0 or 90; Bob: 45 or 135), and pairs of outcomes of measurements of Alice and Bob's observables (+/-1). We then calculate four correlations based on the four different subsets of the pairs of particles formed by the four pairs of settings.

According to quantum mechanics, and if N is large, it is very unlikely to observe

E(a, b) - E(a, b') + E(a', b) + E(a' b') larger than 2 sqrt 2 by more than a few multiples of 1 / sqrt N (Tsirelson inequality)

However if a local hidden variables model would "explain" these correlations, then if N is large it would be very unlikely to observe.

E(a, b) - E(a, b') + E(a', b) + E(a' b') larger than 2 by more than a few multiples of 1 / sqrt N (CHSH inequality)

If we allow more general theories than QM, then as long as there is no violation of locality (no way Alice to see from her outcome what setting Bob is using), then even in the limit of large N

E(a, b) - E(a, b') + E(a', b) + E(a' b') could equal 4. (Popescu Rohrlich limit)

- gill1109
- Mathematical Statistician
**Posts:**2812**Joined:**Tue Feb 04, 2014 10:39 pm**Location:**Leiden

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.

What a wonderfully clever and amusing remark.

- gill1109
- Mathematical Statistician
**Posts:**2812**Joined:**Tue Feb 04, 2014 10:39 pm**Location:**Leiden

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. Moreover I am not good with Python and you are. These modifications would take you five minutes, they would take me a day.

Whatever you like to call epr-simple, it generates two files of length N which go to Alice and Bob's measurement stations, where each line, together with a randomly chosen setting, is converted into an outcome -1, +1, or a "no detection".

That's what I call a pulsed experiment, and so do other people too. I also call it clocked because the emissions and detections occur at discrete time steps, fixed in advance. Other people call this an experiment with "event-ready detectors".

What I can do is try to rewrite your simulation in R. But I'll need you to agree with my implementation before I show you what I am going to get out of it.

- gill1109
- Mathematical Statistician
**Posts:**2812**Joined:**Tue Feb 04, 2014 10:39 pm**Location:**Leiden

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.

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

The derivation of the above inequality assumes the strongly objective interpretation. It can't be derived under the weakly objective view.

Tsirelson inequality

E(a, b) + E(a, b') + E(a', b) - E(a', b') <= 2 sqrt 2.

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.

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

The above inequality assumes 4 independent terms which is the weakly objective view. There is nothing whatsoever about action at a distance involved in deriving any of the above inequalities. They are simply mathematical tautologies relating numbers which happen to represent expectation values of measurement outcomes. The fact that it is all theoretical does not change the fact that in the context of the EPRB discussion, we are talking of measurement outcomes.

So you can't escape the fact that you are confused about weakly objective and strongly objective interpretations of the expectation values.

- minkwe
**Posts:**1441**Joined:**Sat Feb 08, 2014 10:22 am

Dear Michel

Do you agree that this is a "true" implementation in R of your epr-simple simulation?

Here is the output on my computer:

Do you get exactly the same?

Here is a glimpse at the data:

Do you agree that this is a "true" implementation in R of your epr-simple simulation?

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

- Code: Select all
`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])

Here is the output on my computer:

- Code: Select all
`> 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

Do you get exactly the same?

Here is a glimpse at the data:

- Code: Select all
`> 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

Last edited by gill1109 on Mon Jun 02, 2014 5:47 am, edited 1 time in total.

- gill1109
- Mathematical Statistician
**Posts:**2812**Joined:**Tue Feb 04, 2014 10:39 pm**Location:**Leiden

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.

E(a, b) stands for the expectation value of the paired product of measurement outcomes at angles a and b.

According to a local hidden variable theory it moreover should be equal to int A(a, lambda) B(b, lambda) rho(lambda) d lambda where A(a, lambda) is the measurement outcome which would, in theory, be generated if Alice chose setting a and the particles carried the hidden variable lambda, while B(b, lambda) measurement outcome which would, in theory, be generated if Bob chose setting b and the particles carried the hidden variable lambda. But these are just mathematical functions of mathematical variables. If I tell you that theta = 60 degrees and cos(theta) = 1/2 we don't have to believe that I actually measured an angle. I can even tell you that if cos(theta) = 1/2 then sin(theta) = +/- sqrt(3)/2. There doesn't have to be a triangle in sight.

Pythagoras' theorem is true whether or not we actually measure three sides a, b, c of a right angled triangle.

Euclid's theorem that sqrt 2 is irrational is true whether or not we have to draw a square with area equal to two square centimeters. The area of a circle of radius 1 is irrational whether or not any real circles go floating by outside the window.

- gill1109
- Mathematical Statistician
**Posts:**2812**Joined:**Tue Feb 04, 2014 10:39 pm**Location:**Leiden

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.

All of mathematics is a tautology. 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.

CHSH is "just arithmetic".

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.

The bridge between mathematics and reality is causing us all the trouble here. One has to distinguish between the two worlds and one has to know how to cross the bridge in either direction. Getting the two worlds confused leads to endless circular arguments.

http://www-groups.dcs.st-and.ac.uk/history/Extras/Einstein_geometry.html

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. This is a big problem in science. I find physicists just about equally ignorant about probability and statistics as lawyers, but they (the physicists) have less excuse to be ignorant; after all, they can at least read mathematical formulas.

- gill1109
- Mathematical Statistician
**Posts:**2812**Joined:**Tue Feb 04, 2014 10:39 pm**Location:**Leiden

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.

Tough luck then. I'm not your lab technician who sits by idly and executes your commands. You'll have to do the ground work and present your results and arguments and convince everyone, not just me, that your arguments are correct. My code is open source, you can mess with it to your hearts content. Your modifications will not be mine, they will be yours. If your argument is true, I will believe it whether it comes out of my code or your code.

But I'll need you to agree with my implementation before I show you what I am going to get out of it.

Sorry, it doesn't work like that. Do your own home work and present your results and argument. I don't have time to babysit while you are playing with your toys.

- minkwe
**Posts:**1441**Joined:**Sat Feb 08, 2014 10:22 am

minkwe wrote:I don't have time to babysit while you are playing with your toys.

What a pleasant person, such fun to collaborate with!

Take a look at http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=59 and http://rpubs.com/gill1109/epr-simple.

Things for Michel to do: confirm or deny that this is indeed his algorithm which I'm using to simulate the hidden variables and measurements.

Things for Michel to notice: three different valid modified Bell inequalities all invented to take account of non-detections give "non-violation" results. Is this just chance, or could it be that some people's mathematical theorems actually make true predictions about the behaviour of his simulation model? (Of course we must allow for statistical error. The theorems I mentioned say something about the large N limit of the estimated correlations).

- gill1109
- Mathematical Statistician
**Posts:**2812**Joined:**Tue Feb 04, 2014 10:39 pm**Location:**Leiden

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.

The bridge between mathematics and reality is causing us all the trouble here.

The bridge is causing you a lot of problems as I've documented many times, including your recent confusion about "weakly objective" vs "strongly objective". You are now trying hard to run away from it.

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.

Unfortunately it is now apparent that some statisticians do not understand how to apply probability theory to physics. A failure of their educational system for sure. Statistics without a solid foundation of probability theory leads you to what we are seeing here, such as the proliferation of paradoxes due to misapplication of probability being interpreted as mystical properties of nature.

http://bayes.wustl.edu/etj/prob/book.pdf

http://www.amazon.com/Probability-Theor ... 0521592712

Chapters 9 "Repeatitive experiments: probability and frequency" and 10 "Physics of random experiments" are particularly relevent here.

- minkwe
**Posts:**1441**Joined:**Sat Feb 08, 2014 10:22 am

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
**Posts:**1441**Joined:**Sat Feb 08, 2014 10:22 am

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

I am looking forward to your incisive comments / queries in the new thread.

- gill1109
- Mathematical Statistician
**Posts:**2812**Joined:**Tue Feb 04, 2014 10:39 pm**Location:**Leiden

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.

The shortest proof I know is this one

https://en.wikipedia.org/wiki/Tsirelson's_bound#Tsirelson_bound_for_the_CHSH_inequality

I would be surprised if you can beat that ...

- gill1109
- Mathematical Statistician
**Posts:**2812**Joined:**Tue Feb 04, 2014 10:39 pm**Location:**Leiden

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.

Yes this is a wonderful book, I know it well.

Of course Jaynes was a true Bayesian "We have developed probability theory as a generalized logic of plausible inference which should apply, in principle, to any situation where we do not have enough information to permit deductive reasoning. We have seen it applied successfully in simple prototype examples of nearly all the current problems of inference, including sampling theory, hypothesis testing, and parameter estimation."

- gill1109
- Mathematical Statistician
**Posts:**2812**Joined:**Tue Feb 04, 2014 10:39 pm**Location:**Leiden

I see there is a lot of misunderstanding about the equation

Part of the problem is writing the integral using the notation approriate when lambda is an element of Euclidean space an rho(lambda) a probability density function. A modern mathematician would write

where P is a probability measure on a measurable space.

But anyway, this key equation is not a *definition* but a theorem, though a rather basic and easy theorem, belonging to the theory of local hidden variables.

E(a, b) stands for the mean value of products of outcomes of measurements of spin in the directions a and b of infinitely many similarly prepared pairs of particles. ("State" = "preparation").

The integral on the right hand side is the result of (1) assuming a local hidden variables model and (2) the law of large numbers.

The local hidden variables theory says that preparing a new pair of particles and measuring a and b is like: picking lambda at random according to the probability measure P; getting to see the values A(a, lambda) and B(b, lambda).

Given functions A and B and a probability measure the mathematician is free to study a new composed function such as

A(a, lambda)B(b, lambda) - A(a, lambda)B(b', lambda) + ... + ... and integrate over lambda with respect to the probsbility measure P. Because this new function is everywhere -2 or +2, its average lies in between those bounds.

There is no suggestion anywhere of measuring different things at the sane time. There are som functions, there is a trivial logical bound, there is some calculus and writing an integral of a sum as a sum of integrals.

No voodoo, just plain model + calculus. If you believe the model represents reality, then model deductions should fit too. If they don't fit, the model is inappropriate.

It's all rather simple as long as one careful distinguishes physical reality from mathematical models of parts of it.

- E(a, b) = int A(a, lambda) B(b, lambda) rho(lambda) d lambda.

Part of the problem is writing the integral using the notation approriate when lambda is an element of Euclidean space an rho(lambda) a probability density function. A modern mathematician would write

- E(a, b) = int A(a, lambda) B(b, lambda) dP(lambda)

where P is a probability measure on a measurable space.

But anyway, this key equation is not a *definition* but a theorem, though a rather basic and easy theorem, belonging to the theory of local hidden variables.

E(a, b) stands for the mean value of products of outcomes of measurements of spin in the directions a and b of infinitely many similarly prepared pairs of particles. ("State" = "preparation").

The integral on the right hand side is the result of (1) assuming a local hidden variables model and (2) the law of large numbers.

The local hidden variables theory says that preparing a new pair of particles and measuring a and b is like: picking lambda at random according to the probability measure P; getting to see the values A(a, lambda) and B(b, lambda).

Given functions A and B and a probability measure the mathematician is free to study a new composed function such as

A(a, lambda)B(b, lambda) - A(a, lambda)B(b', lambda) + ... + ... and integrate over lambda with respect to the probsbility measure P. Because this new function is everywhere -2 or +2, its average lies in between those bounds.

There is no suggestion anywhere of measuring different things at the sane time. There are som functions, there is a trivial logical bound, there is some calculus and writing an integral of a sum as a sum of integrals.

No voodoo, just plain model + calculus. If you believe the model represents reality, then model deductions should fit too. If they don't fit, the model is inappropriate.

It's all rather simple as long as one careful distinguishes physical reality from mathematical models of parts of it.

- gill1109
- Mathematical Statistician
**Posts:**2812**Joined:**Tue Feb 04, 2014 10:39 pm**Location:**Leiden

About Joy's experiment:

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.

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.

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.

- Heinera
**Posts:**917**Joined:**Thu Feb 06, 2014 1:50 am

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.

(1) Contrary to your claim, I am not Michel's "QM teacher."

(2) Contrary to Gill's claim, I am not Michel's "hero."

(3) Contrary to Gill's claim, I am not Michel's "boss."

(4) Contrary to Gill's claim, I did not pay Michel, or anyone else, to write simulations, or do anything else for me.

(5) Michel is an independent scholar of considerable talents and skills, and has his own mind, own views, and own knowledge, independent of my views or my model.

(6) Some of our views agree and some of them do not. Your and Gill's attempts to provoke friction between us or our views are pathetic (to say the least).

(7) My teacher and grand-teacher of QM were Abner Shimony and Eugene Wigner. So blame them, if you must, for any deficiencies in my knowledge of QM.

(8) As for my proposed experiment, you and Gill should really read the two relevant papers before going about spewing nonsense about my work all over the internet.

- Joy Christian
- Research Physicist
**Posts:**2793**Joined:**Wed Feb 05, 2014 4:49 am**Location:**Oxford, United Kingdom

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