## Evidence that QM does not violate Bell's inequalities

Foundations of physics and/or philosophy of physics, and in particular, posts on unresolved or controversial issues

### Re: Evidence that QM does not violate Bell's inequalities

Guest wrote:There is dependency between the terms: it is *assumed* that Phi = phi_1 & phi_2 & ... & phi_N is impossible.

Yes, since it is "supposed" that you have P = 0 earlier in that section. However, the dependency should be better expressed mathematically in eq. (1).

Guest wrote:To give an example: suppose a local hidden variables model is true in the Bell-CHSH set-up. Define X_1 and X_2 to be the outcomes which Alice would have observed, had she used either of her two settings 1 or 2 (outcomes +/- 1 in the conventional scenario), define Y_1 and Y_2 to be the outcomes which Bob would have observed, had he used either of his two settings 1 or 2 (outcomes +/- 1 in the conventional scenario).

Notice that (since these four variables are restricted to being equal to +/- 1) it is impossible that X_1 = Y_1 & X_1 != Y_2 & Y_2 != X_2 & X_2 != Y_1. For instance if X_1 = Y_1 = +1, then Y_2 would have to be -1, X_2 would have to be +1, and Y_1 would have to be -1 ... a logical contradiction. Similarly in the other case X_1 = Y_1 = -1.

It follows that Prob(X_1 = Y_1) + Prob(X_1 != Y_2) + Prob(Y_2 != X_2) + Prob(X_2 != Y_1) <= 3.

The point is that these variables X_1, X_2, Y_1, Y_2 exist according to a local hidden variables theory, but quantum mechanics says nothing about them at all. In QM we don't assume they exist at all.

That is fine. No problem there.

Guest wrote:Quantum mechanics does predict the value of Prob(Alice's outcome = Bob's outcome | Alice uses setting i and Bob uses setting j) for each i, j = 1, 2. And experiment allows us to measure the value of Prob(Alice's outcome = Bob's outcome | Alice uses setting i and Bob uses setting j).

So in an experiment with many trials with each of the four pairs of settings we can get to see (up to statistical error) the values of Prob(Alice's outcome = Bob's outcome | Alice uses setting 1 and Bob uses setting 1), Prob(Alice's outcome != Bob's outcome | Alice uses setting 1 and Bob uses setting 2), Prob(Alice's outcome != Bob's outcome | Alice uses setting 2 and Bob uses setting 2), Prob(Alice's outcome != Bob's outcome | Alice uses setting 2 and Bob uses setting 1).

And QM allows the sum of these four probabilities to exceed 3. In fact, QM allows 1 + 2 sqrt 3 = 3.4 approx

What you fail to realize is that the QM experiments use the inequality,

$\left |\sum_{i}E_{i} \right | \leq N$ (independent terms)

$\left |\sum_{i}E_{i} \right | \leq N -2$ (with dependent terms)

So they don't "violate" the Bell-CHSH inequality for LHV. It is mathematically impossible for anything to violate it.
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### Re: Evidence that QM does not violate Bell's inequalities

FrediFizzx wrote:What you fail to realize is that the QM experiments use the inequality,

$\left |\sum_{i}E_{i} \right | \leq N$ (independent terms)

$\left |\sum_{i}E_{i} \right | \leq N -2$ (with dependent terms)

So they don't "violate" the Bell-CHSH inequality for LHV. It is mathematically impossible for anything to violate it.

Yes, this is the key (albeit phenomenological) point, which Michel has also stressed on these pages many times. In actual QM experiments counterfactually possible alternatives are inevitably replaced with actual alternatives, which amounts to surreptitiously replacing dependent terms with independent terms, as you point out.

--------

PS: In any case this is all now an academic exercise, because we now have this clear-cut counterexample to Bell's theorem: viewtopic.php?f=6&t=188&p=5155#p5145.
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### Re: Evidence that QM does not violate Bell's inequalities

Fred,
Interesting discussion. I think you put your finger already on Hardy's problem right from Equation (1):
$\left |\sum_{i}E_{i} \right | \leq N$ (independent terms)
$\left |\sum_{i}E_{i} \right | \leq N -2$ (with dependent terms)

Guest makes the same error, because he/she argues that:
Guest wrote:There is dependency between the terms: it is *assumed* that Phi = phi_1 & phi_2 & ... & phi_N is impossible.

But unfortunately, not realize that in the actual experiment , the 'impossible' *assumption* obviously fails. So the apparent "violation" should be interpreted as a failure of the "impossible" assumption, which is immediately recognized to be false as soon as you consider the physics of an actual experiment or QM prediction.

Guest also says:
Guest wrote:To give an example: suppose a local hidden variables model is true in the Bell-CHSH set-up. Define X_1 and X_2 to be the outcomes which Alice would have observed, had she used either of her two settings 1 or 2 (outcomes +/- 1 in the conventional scenario), define Y_1 and Y_2 to be the outcomes which Bob would have observed, had he used either of his two settings 1 or 2 (outcomes +/- 1 in the conventional scenario).

The underlined statement above represents counterfactual outcomes, which are completely absent in the QM predictions and Experimental results. So we arrive again at the stumbling block at which all Bell followers continue to fall. The recipe is as follows:

1 - Derive an inequality based on counterfactual outcomes (or impossible to measure dependent terms)
2 - Calculate QM predictions for non-counterfactual outcomes (or possible to measure independent terms)
3 - Assume that the terms in (1) and (2) are the same as each other
4 - Substitute the terms predicted from (2) into the inequality from (1) to obtain a "violation"
5 - Perform an experiment to measure the terms from (2) and confirm that the predictions are true, therefore "violation" of (1).
6 - Conclude that the "violations" from (4) and (5) imply that the assumptions required to obtain (1) are untenable.

Every Bell-type argument follows this recipe, and can be debunked simply by finding the point at which assumption (3) and step (4) are performed. Hardy's "Curious observation" is one of such.

Here is one curious observatioin about Hardy's conclusion. He says:

Hardy wrote:The correlation polytopes of Pitowsky [41], which have a lineage going back to Boole’s ‘conditions of possible experience’ [42], should also be mentioned. Although this line of thought is certainly in a kindred spirit, Boole’s conditions are arithmetical in nature; while the central theme of the present paper is that complete sets of Bell inequalities can be defined in terms of purely logical consistency conditions.

So Boole derived the inequalities assuming only "arithmetic" therefore their "violation" points to the violation of arithmetic, nothing physical.
Hardy derived his inequalities assuming only "logical consistency" therefore their "violation" points to the violation of logical consistency, nothing physical.

What is astounding is that Bell's follows continue to refuse to draw the only obvious conclusion. It is an elephant in the room -- where has the arithmetic error been made? Where is the logical inconsistency? We've been saying it over and over on this forum as Joy points out:

Joy Christian wrote:Yes, this is the key (albeit phenomenological) point, which Michel has also stressed on these pages many times. In actual QM experiments counterfactually possible alternatives are inevitably replaced with actual alternatives, which amounts to surreptitiously replacing dependent terms with independent terms, as you point out.
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### Re: Evidence that QM does not violate Bell's inequalities

minkwe wrote:What is astounding is that Bell's followers continue to refuse to draw the only obvious conclusion. It is an elephant in the room -- where has the arithmetic error been made? Where is the logical inconsistency? We've been saying it over and over on this forum as Joy points out:

Joy Christian wrote:Yes, this is the key (albeit phenomenological) point, which Michel has also stressed on these pages many times. In actual QM experiments counterfactually possible alternatives are inevitably replaced with actual alternatives, which amounts to surreptitiously replacing dependent terms with independent terms, as you point out.

Thanks guys. Well... Gill has sent emails about this part of the thread to the authors of the paper under current discussion. We will see if they can or want to defend their position here. Probably not though would be my guess.
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### Re: Evidence that QM does not violate Bell's inequalities

Ok, so moving on with this paper we know that eq. (1) is OK as long as we remember that it has dependent terms. Thanks to Guest for showing how that works. Then we arrive at Proposition III.1 "Any possibilistically contextual model violates a logical Bell/CHSH inequality."

Hmm... since I think it is mathematically impossible for anything to violate a logical Bell/CHSH inequality, I doubt very much that this proposition can be true. Perhaps Guest would like to try to explain how it could be true? Or anyone?
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### Re: Evidence that QM does not violate Bell's inequalities

FrediFizzx wrote:Ok, so moving on with this paper we know that eq. (1) is OK as long as we remember that it has dependent terms. Thanks to Guest for showing how that works. Then we arrive at Proposition III.1 "Any possibilistically contextual model violates a logical Bell/CHSH inequality."

Hmm... since I think it is mathematically impossible for anything to violate a logical Bell/CHSH inequality, I doubt very much that this proposition can be true. Perhaps Guest would like to try to explain how it could be true? Or anyone?

Fred. The proposition is "true", so long as you ignore the illegal substitution of incompatible terms, and then keep in mind that by "violation" he means deviation from dependence. Proposition III is equivalent to the statement that terms which maximally "violate" a Bell ineqiality are maximally statistically independent.

We know this is obvious because the terms in the inequalities are dependent. The difference is, we understand that there is no mystery in the fact that the experimentally measured, and QM predicted terms are statistically independent.

The errors were already made at step (3) and (4). Everything else follows if you grant him that.
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### Re: Evidence that QM does not violate Bell's inequalities

***
For non-experts reading this and wondering what Fred, Michel, and I are talking about, the following easy to follow reply by me to a friend's query may help (edited):
The real issue with all Bell-test experiments is not experimental, but conceptual. There is a fatal conceptual error in these experiments, and it cannot be fixed, ever, unless we can make repeated measurements on the same pair of particles. In the original EPR paper as well as in Bell's work there is this assumption of "counterfactual definiteness." What this means is that, "had we measured spin along this direction instead of that direction, we would have obtained this result instead of that result." Now the problem with this is that it is physically impossible to measure the spin in two different directions, even successively, let alone simultaneously. Once the spin of a particle is measured, that particle is either destroyed or depolarized. So in the actual experiments they inevitably measure the spins of an altogether different pair of particles (those next in line at the source, so to speak) and then compare. In conclusion, in my opinion the entire Bell's theorem saga is a scandal of epic proportions.
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### Re: Evidence that QM does not violate Bell's inequalities

It seems they violated Bell's inequality with classical light.

https://www.osapublishing.org/optica/fu ... &id=321243

At the end they talk about extending the equality to classical things, but not once did they say the inequality might be wrong from the get go.
Guest

### Re: Evidence that QM does not violate Bell's inequalities

Guest wrote:It seems they violated Bell's inequality with classical light.

https://www.osapublishing.org/optica/fu ... &id=321243

At the end they talk about extending the equality to classical things, but not once did they say the inequality might be wrong from the get go.

Wonderful. They do say a reinterpretation of the "violation" is called for. It is about time. I am not familiar with the journal, but it does look respectable.

Let us hope that this is just a beginning of the correction process (which started a long time ago but is being actively suppressed by the Bell enthusiasts).
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### Re: Evidence that QM does not violate Bell's inequalities

Guest wrote:It seems they violated Bell's inequality with classical light.

https://www.osapublishing.org/optica/fu ... &id=321243

At the end they talk about extending the equality to classical things, but not once did they say the inequality might be wrong from the get go.

viewtopic.php?f=6&t=68&p=3165&hilit=Classical+Shimony+Wolf+States#p3165

Of course the Bell-CHSH inequality is correct (Bell's theory is wrong). However, they didn't actually violate Bell-CHSH since it is mathematically impossible to do so. Their "violation" is by the same method as quantum experiments "violate" it by "shifting the goal posts" using a different inequality that has independent terms. As shown previously in this thread.

Here is the arXiv link to the paper,

http://arxiv.org/abs/1506.01305

You can see it has text overlap with,

http://arxiv.org/abs/1406.3338
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### Re: Evidence that QM does not violate Bell's inequalities

Joy Christian wrote:
Guest wrote:It seems they violated Bell's inequality with classical light.

https://www.osapublishing.org/optica/fu ... &id=321243

At the end they talk about extending the equality to classical things, but not once did they say the inequality might be wrong from the get go.

Wonderful. They do say a reinterpretation of the "violation" is called for. It is about time. I am not familiar with the journal, but it does look respectable.

Let us hope that this is just a beginning of the correction process (which started a long time ago but is being actively suppressed by the Bell enthusiasts).

Yeah, I am glad they got this published. Thanks to our Guest poster for providing the link. Notice that they had to change the title from "Violation of Bell's Inequalities with Classical Shimony-Wolf States: Theory and Experiment" to "Shifting the Quantum-Classical Boundary: Theory and Experiment for Statistically Classical Optical Fields".

This is similar to the kind of experiment that I was proposing on your blog.

http://libertesphilosophica.info/blog/e ... comment-15

Of course their proposition about classical entanglement is wrong but they probably had to "toe the mainstream line" to get it published. Or they probably do believe in classical entanglement. We have to fix that somehow.
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### Re: Evidence that QM does not violate Bell's inequalities

FrediFizzx wrote:Of course their proposition about classical entanglement is wrong but they probably had to "toe the mainstream line" to get it published. Or they probably do believe in classical entanglement. We have to fix that somehow.

Yes, they are still thinking -- or being forced to think -- in terms of some kind of "classical entanglement", whatever that means. The ideological bias in the community for "entanglement" is too strong, as we have already witnessed in the context of my work. For example, many people have a violent kneejerk reaction to the title and subtitle of my book rather than its full content (which almost no one has bothered to read beyond its gross misrepresentations by ignoramuses like Gill and Aaronson).
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### Re: Evidence that QM does not violate Bell's inequalities

Joy Christian wrote:
FrediFizzx wrote:Of course their proposition about classical entanglement is wrong but they probably had to "toe the mainstream line" to get it published. Or they probably do believe in classical entanglement. We have to fix that somehow.

Yes, they are still thinking -- or being forced to think -- in terms of some kind of "classical entanglement", whatever that means. The ideological bias in the community for "entanglement" is too strong, as we have already witnessed in the context of my work. For example, many people have a violent kneejerk reaction to the title and subtitle of my book rather than its full content (which almost no one has bothered to read beyond its gross misrepresentations by ignoramuses like Gill and Aaronson).

Well... a lot of self brainwashing has been going on for over 50 years. It is going to take awhile to unravel it. This experiment is a step forward. Things are progressing. Slower than we would like but still progressing.
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### Re: Evidence that QM does not violate Bell's inequalities

Hi Fred!

Just my two cents: the way I understand it, to say that it's impossible to construct a LHV that reproduces the QM singlet correlations means that it's not possible to complete the following R code and get correct results.

Code: Select all
rm(list = ls())N <- 10^5lambda <- numeric(N)# create any vector lambda you like hereA <- function(a, lambda) { # angle a will be in degrees  # insert you code here}B <- function(b, lambda) { # angle b will be in degrees  # insert your code here}# don't change anything after this pointfor (a in runif(2, 0, 360)) {  for (b in runif(2, 0, 360)) {    cat("(a, b) = (", a, ", ", b, ")\n", sep = "")    cat("LHV: ", mean(A(a, lambda)*B(b, lambda)), "\n")    cat("QM: ", -cos((a-b)*pi/180), "\n\n")  }}

In this code, it's not possible to use information about the detectors' angles when you create the vector of hidden variables lambda, and it's also not possible to use information about the other detector's angle in the functions A and B, because the values of those angles are only defined within the scope of the two nested for loops. If you need help with R's syntax, it will be a pleasure to help.

And to the irrealists/nonlocalists who love this kind of result, my question is: are you worried at all about the perfect anti-correlations when a=b? In my opinion, you should.
Guest

### Re: Evidence that QM does not violate Bell's inequalities

Guest wrote:Hi Fred!

Just my two cents: the way I understand it, to say that it's impossible to construct a LHV that reproduces the QM singlet correlations means that it's not possible to complete the following R code and get correct results.

Code: Select all
rm(list = ls())N <- 10^5lambda <- numeric(N)# create any vector lambda you like hereA <- function(a, lambda) { # angle a will be in degrees  # insert you code here}B <- function(b, lambda) { # angle b will be in degrees  # insert your code here}# don't change anything after this pointfor (a in runif(2, 0, 360)) {  for (b in runif(2, 0, 360)) {    cat("(a, b) = (", a, ", ", b, ")\n", sep = "")    cat("LHV: ", mean(A(a, lambda)*B(b, lambda)), "\n")    cat("QM: ", -cos((a-b)*pi/180), "\n\n")  }}

In this code, it's not possible to use information about the detectors' angles when you create the vector of hidden variables lambda, and it's also not possible to use information about the other detector's angle in the functions A and B, because the values of those angles are only defined within the scope of the two nested for loops. If you need help with R's syntax, it will be a pleasure to help.

I am afraid your code is too restrictive. It does not correspond to what Bell permitted to be a LHV model. In Bell's LHV framework "lambda" can be anything one likes, not just a "vector" or a tensor. In fact, in Bell's LHV framework A(a, lambda) is allowed to be any general function of a and lambda, and likewise for B(b, lambda).

To see how this can be accomplished in a manifestly local-realistic manner, please take a look at this R code and tell us why it is not a simulation of a LHV model.

The essential part of the code is very simple, and it reproduces the strong correlation in full compliance with all of the requirements of Bell for a LHV model:

Code: Select all
A = +sign(g(a,e,s))  # Alice's measurement results A(a, e, s) = +/-1          B = -sign(g(b,e,s))  # Bob's measurement results B(b, e, s) = -/+1        N = length((A*B)[A & B]) # Number of all possible events observed in S^3        corrs[i,j] = sum(A*B)/N  # Product moment correlation coefficient E(a, b)

Here Bell's hidden variable "lambda" is a pair (e, s), where e is like your "vector" and s is another scalar parameter.
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### Re: Evidence that QM does not violate Bell's inequalities

Guest wrote:And to the irrealists/nonlocalists who love this kind of result, my question is: are you worried at all about the perfect anti-correlations when a=b? In my opinion, you should.

This was why the CHSH-inequality got so popular; the perfect anti-correlation for a=b is hard to demonstrate experimentally, but the CHSH-inequality doesn't use that pair of settings.
Last edited by Heinera on Wed Aug 19, 2015 12:45 pm, edited 1 time in total.
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### Re: Evidence that QM does not violate Bell's inequalities

Heinera wrote:This was why the CHSH-inequality was developed; the perfect anti-correlation for a=b is hard to demonstrate experimentally, so the CHSH-inequality doesn't use that pair of settings.

False!

CHSH allows any pair of settings, including a = b.
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### Re: Evidence that QM does not violate Bell's inequalities

Joy Christian wrote:
Heinera wrote:This was why the CHSH-inequality was developed; the perfect anti-correlation for a=b is hard to demonstrate experimentally, so the CHSH-inequality doesn't use that pair of settings.

False!

CHSH allows any pair of settings, including a = b.

Yes, CHSH allows any pair of settings, but I don't think I have ever seen a = b used in an experiment. It is mute point though since Bell-CHSH is not really used for the QM experiments as described earlier in this thread.
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### Re: Evidence that QM does not violate Bell's inequalities

Joy Christian wrote:
Heinera wrote:This was why the CHSH-inequality was developed; the perfect anti-correlation for a=b is hard to demonstrate experimentally, so the CHSH-inequality doesn't use that pair of settings.

False!

CHSH allows any pair of settings, including a = b.

Yes, it allows any pair of settings, which means you can avoid a=b. In particular, you can choose settings where QM predicts a maximal violation of the inequality, and a=b is not one of them.
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### Re: Evidence that QM does not violate Bell's inequalities

You're right. The code must be slightly adapted for each LHV model. If each lambda is a pair (e,s), in which e=(e1,e2,e3) and s is a scalar, then we can use:

Code: Select all
rm(list = ls())N <- 10^4lambda <- matrix(nrow = N, ncol = 4)# for each line of the matrix lambda, the first three coordinates# will be e and the fourth coordinate will be sA <- function(a, lambda) { # angle a will be in degrees  e <- lambda[1:3]  s <- lambda[4]  # insert your code here}B <- function(b, lambda) { # angle b will be in degrees  e <- lambda[1:3]  s <- lambda[4]  # insert your code here}# don't change anything after this pointfor (a in runif(2, 0, 360)) {  for (b in runif(2, 0, 360)) {    cat("(a, b) = (", a, ", ", b, ")\n", sep = "")    cat("LHV: ",         mean(apply(lambda, 1, function(lambda) A(a, lambda)) *              apply(lambda, 1, function(lambda) B(b, lambda))), "\n")    cat("QM: ", -cos((a-b)*pi/180), "\n\n")  }}
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