# What does this example say about the applicability of Bell's inequalities?

#### billschnieder

Yes. In your 'proof' the inequality applies to averages from the same series of $\{a_i,b_i,c_i\}$, where the average is defined as arithmetic mean of all elements in the series, even though you did not explicitly state it. It does not allow you to pick different subsets to calculate <ab>, <ac>, and <bc>. But of course, since you did not articulate your proof, you have missed this. If, instead of handwaving, you actually try to write out the steps, this is as far as you can get.
Interesting you throw that accusation given that you do exactly the same thing when analyzing the EPR experiment. Note: this example was designed to reveal precisely this kind of misunderstanding. Now it is you making the argument which you have repeatedly rejected without understanding. I'm happy you are getting the point, which you have repeatedly refused to understand when I made it. Now you are forced to make the argument yourself when faced with an obviously local and realistic example which violates the inequalities.
Bell's inequality, on the other hand, applies to expectation values. It is a high time you learn the difference between the two.
Really DK? I thought you knew better than to make such a ridiculous claim:
Wikipedia said:
The expected value may be intuitively understood by the law of large numbers: the expected value, when it exists, is almost surely the limit of the sample mean as sample size grows to infinity. More informally, it can be interpreted as the long-run average of the results of many independent repetitions of an experiment (e.g. a dice roll).
...
In quantum mechanics, the expectation value is the predicted mean value of the result (measurement) of an experiment.
Now even a cave man can understand that <ab> is the expectation value of paired product of outcomes a*b for a pair of dice thrown a very large number of times, just like in the OP example. You need to learn about expectation values, einstein. I did not hear you complaining that Aspect, or Weihs, etc calculated averages from their experiments not expectation values. Such a suggestion will be laughed at, or rather cried at.

#### billschnieder

This example that the OP gives is very good in showing the problems you're driven into when considering the results of mutually exclusive experiments, as done in the quantum case as well.
Thanks. I'm happy the point got across.

But still, im not sure yet if the freedom of choice is enough to assure that including results of exclusive experiments is consistent and doesn't lead to absurd results.
One first thought on this problem is to try to consider a classical experiment (using hidden varibles), where given freedom of measurement choice we can still violate Bell's inequality. If it turns out that this isn't possible, then we can safely conclude that there's something strange about quantum mechanics :). But if it is possible then we have a serious problem...
This has been done by the group of Hans De Raedt. See http://arxiv.org/abs/1112.2629 However, many people still do not understand their result and simply wave it off. The OP was meant as way to re-cast their results in a manner that is simple enough to highlight the just the major issues while eliminating the peripheral stuff which often obstructs understanding of the major issues.
My personal opinion is that it's not possible, but i'll give it a little more thought these days.
If you haven't already. Please check out the above article from De Raedt.

#### Delta Kilo

Interesting you throw that accusation given that you do exactly the same thing when analyzing the EPR experiment.
Ha! I knew it would come to that! I didn't even mention EPR, did I? It was obvious from the very first post that you don't have a genuine question to ask, that this is yet another silly attempt at sneak attack on Bell's inequalities.

Now even a cave man can understand that <ab> is the expectation value of paired product of outcomes a*b for a pair of dice thrown a very large number of times, just like in the OP example.
No, this is not always the case, and it is specifically not true in your example. Having a large sample is not enough, sample selection procedure has to be unbiased. I can give you plenty of examples where biased sampling procedure will give you all sorts of different average values from the same random sequence. But I'm afraid this is too much for a caveman.

Bill, I do not get your line of reasoning at all. You present your own 'proof' and then you present a counterexample which invalidates your proof. Then you somehow drag EPR into discussion, and then you blame Bell for your own stuff-ups, while at the same time refusing to pay attention to his "vital assumption". Please stop that.

#### ThomasT

... sample selection procedure has to be unbiased.
Aren't the sample selection procedures in bill's coin experiment and in Bell tests both biased, ie., both outcome dependent?

#### ThomasT

How come?
The inapplicability of the inequality to the coin experiment seems obvious. I remember you phrasing this in a succinct way in one of your posts (in another thread), but I forgot exactly how it goes.

billschnieder said:
How come the inequalities which were supposed to be valid for the "coin-toss" experiment as demonstrated earlier in the OP, get violated by the experiment?
The inequality is based on three simultaneously existing values. The experiment can only generate two values at a time.

billschnieder said:
... we assume the inability to measure all three simultaneously is inconsequential.
I take this to be your vital assumption. That is, this is the assumption that is contradicted via the violation of the inequality by the coin-toss test.

I also take it that this is what you consider to be the effective cause of BI violation in Bell tests. Which would mean that what Bell stated as being the vital assumption was not the vital assumption, and the locality (or independence) condition encoded in Bell's formulation is precluded from being the effective cause of BI violation.

Bell inequalities can be formulated without encoding a locality or independence assumption. So, for now I suppose I agree with your analysis and assessment -- until somebody explains it better.

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#### rlduncan

Bill, I do not get your line of reasoning at all. You present your own 'proof' and then you present a counterexample which invalidates your proof. Then you somehow drag EPR into discussion, and then you blame Bell for your own stuff-ups, while at the same time refusing to pay attention to his "vital assumption". Please stop that.
Doesn’t Bell do the exactly the same. That is, Bell presented his own proof and then he used quantum predictions as a counterexample to disprove it. Then concluded the locality assumption was impossible or false.

Could you convincingly explain what assumption Bill made that is impossible or false?

#### DrChinese

Science Advisor
Gold Member
Could you convincingly explain what assumption Bill made that is impossible or false?
This was already done, and virtually anyone should be able to see that Bill's example is not apropos. The below reasoning would be cited in one form or another in any response to Bill's "question". I am just sorry that Bill's deception has caused you confusion.

4. The root rule is not the CHSH inequality. The root requirements are:
i) the possibility of any permutation must be within the range of 0 to 1 (realism);
ii) the outcome cannot change based on what the observers choose to look at (locality or separability or whatever you want to call it).

In your example, i) is satisfied but ii) is not. Note that QM predicts values outside the range of i). You can see that negative probabilities are such a prediction at:

http://drchinese.com/David/Bell_Theorem_Negative_Probabilities.htm

To convince yourself that your example, if properly respecting ii), would not violate any type of Bell inequality, just write down a set of data points for your a/b/c (we have had this discussion previously of course). To make things work out for you, I will make it simple: I will always select a for one of the two, and will randomly pick between b and c. That way, you can respect ii) (since the outcome b does not change). Below are the only 2 permutations:

a b c
+ - -
- + +

This has <ab>=-1, <ac>=-1, <bc>=+1, and the inequality is not violated (as it was when requirement i was violated). QED.

#### DrChinese

Science Advisor
Gold Member
This has been done by the group of Hans De Raedt. See http://arxiv.org/abs/1112.2629 However, many people still do not understand their result and simply wave it off. The OP was meant as way to re-cast their results in a manner that is simple enough to highlight the just the major issues while eliminating the peripheral stuff which often obstructs understanding of the major issues.
You pretend to ask "why" when it is obvious you are not asking a question at all. You are trying to TELL us something which again, is non-standard physics and represents your personal theories.

So to answer the title question and wrap things up: This example has NO connection to Bell and is not applicable in any way. To show you how inapplicable it is, let's morph it to this example, which is exactly equivalent. There is a bag, and in it are 3 marbles. Some are red and some are green. We reach in and get 2 out, always 1 red and 1 green. By your [sarcastic adjective omitted] reasoning, this too violates the CHSH inequality but is local and realistic. I hope it is clear that this is EXACTLY the ORIGINAL EPR paradox and was considered explicitly by Bell and rejected over 40 years ago.

I'm sorry Bill, but you are approaching childishness here and yet another new low. If it were up to me (and it is not), I would shut this thread down now that it is completely clear what your true purpose is. This is not really the place for debate on your personal beliefs. I will definitely report you if you continue this charade.

#### billschnieder

You pretend to ask "why" when it is obvious you are not asking a question at all.
I'm clearly asking a question. The inequality is valid and yet it is violated, there is a reason for it and that is the question. To discuss that reason. And you do understand the question from your responses so far, although you do not like the question because it reveals your misunderstanding. That is hardly grounds to close a thread because DrC does not like it.

You are trying to TELL us something which again, is non-standard physics and represents your personal theories.[/b]
Everything in the openning post is standard physics. The inequality proven in the OP post is Bell's inequality and the treatment of data from the experiment in the OP is very similar to how data is treated in EPR experiments. It is funny that you are willing to spend time discussing in threads about an unpublished "Herbet's proof" and your own personal proofs from your non-peer-reviewed website, and it is OK for you to refer other readers to your non-peer-reviewed personal theories about a nonsensical idea such as "Negative Probabilities" but as soon as I start discussing valid published peer-reviewed material which you don't like, you start throwing suggestions to moderators to lock the thread.

The views discussed here are published in the following articles which apparently you are unware of:
EPL, 87 (2009) 60007, http://arxiv.org/abs/0907.0767
J. Comp. Theor. Nanosci. 8, 1011 - 1039 (2011), http://arxiv.org/abs/0901.2546
Optics Communications 170 (1999) 55-60 http://arxiv.org/abs/quant-ph/0101094
Optics Communications 170 (1999) 61-66 http://arxiv.org/abs/quant-ph/0101087
So to answer the title question and wrap things up: This example has NO connection to Bell and is not applicable in any way.
You are wrong, it has a connection. You do not argue that Bell's inequality should not apply to three coins in the manner described in the first part of the OP because you know that it should. In fact, you have often used similar arguments to push your unpublished so-called "DrC Challenge". In any case, feel free to wrap up yourself. We will do just fine without your whining.
To show you how inapplicable it is, let's morph it to this example, which is exactly equivalent. There is a bag, and in it are 3 marbles. Some are red and some are green. We reach in and get 2 out, always 1 red and 1 green. By your [sarcastic adjective omitted] reasoning, this too violates the CHSH inequality but is local and realistic.
That makes no sense, especially as I've made no such argument.
I'm sorry Bill, but you are approaching childishness here and yet another new low.
That's a funny accussation coming from someone who throws a tantrum whenever their beliefs are challenged.
If it were up to me (and it is not), I would shut this thread down now that it is completely clear what your true purpose is. This is not really the place for debate on your personal beliefs. I will definitely report you if you continue this charade.
Be my guest. In fact it would more useful if you please direct all your off-topic complains about the thread to the moderators rather than littering the thread with unfounded accusations. I will definitely report you if you continue to disrupt the discussion with your accussations. It is very clear what your purpose is. You want to shutdown any discussion that goes against your personal beliefs. Why are you so afraid?

#### billschnieder

No, this is not always the case, and it is specifically not true in your example. Having a large sample is not enough, sample selection procedure has to be unbiased.
So why don't you tell us what the correct expectation value for the product of the "ab" outcome will be for the experiment described in OP, if not <ab>???? Did you even think about this at all?
I can give you plenty of examples where biased sampling procedure will give you all sorts of different average values from the same random sequence.
We have an example already, and you are claiming that the expectation value is wrong. Provide the correct answer.
Bill, I do not get your line of reasoning at all. You present your own 'proof' and then you present a counterexample which invalidates your proof. Then you somehow drag EPR into discussion, and then you blame Bell for your own stuff-ups, while at the same time refusing to pay attention to his "vital assumption". Please stop that.
I asked you earlier to show where your so-called "vital assumption" was required to obtain the inequality in the OP. By your own admission you did not understand it so please stop throwing accusations about stuff you do not understand.

#### billschnieder

The inequality is based on three simultaneously existing values. The experiment can only generate two values at a time.
Hi ThomasT,
You are right. Clearly, the experiment in the OP violates the inequality in the OP therefore either one of the assumptions required to obtain the inequality or one of the assumptions used to generate terms from the experiment is wrong.

I take this to be your vital assumption. That is, this is the assumption that is contradicted via the violation of the inequality by the coin-toss test.
The experimenters mistakenly thought that expectation values obtained from just pairs of coins would be valid terms. However a simple inspection reveals that

a*b=-1, a*c=-1, b*c=-1

can only occur if the individual outcomes change with time. Let us start with a=-1, b=1 we get ab=-1, in order to get ac = -1 it means "c" must be +1 but b is already +1 so bc can not be -1 at the same time. The scenario is impossible if we have all three outcomes at the same time. However if each coin is dynamic with the values changing, it is possible to obtain the scenario, just as in the OP experiment. Therefore, in this case, the cause of the violation is the assumption that pairs taken at different times from a dynamic system are appropriate substitutes for the LHS of the inequality. Note that if we include the bias of the unmeasured coin from the OP for each toss into a list of triples of outcomes such as:

a b c
+ - -
- + +
...
etc

and the from this list we calculate <ab>, <ac>, <bc>, the inequality will not be violated. It is now obvious why the so-called "DrC challenge" misses the point completely.

I also take it that this is what you consider to be the effective cause of BI violation in Bell tests. Which would mean that what Bell stated as being the vital assumption was not the vital assumption, and the locality (or independence) condition encoded in Bell's formulation is precluded from being the effective cause of BI violation.
Yes, this is the argument made by De Raedt and Sica in the articles cited above.

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#### morrobay

Gold Member
The experimenters mistakenly thought that expectation values obtained from just pairs of coins would be valid terms. However a simple inspection reveals that

a*b=-1, a*c=-1, b*c=-1

can only occur if the individual outcomes change with time.
So I take the outcomes changing with time as a hidden variable, based on sin (t)
In the other Bells Inequalities with entangled states are there also outcome time rate of changes ?

#### DrChinese

Science Advisor
Gold Member
So I take the outcomes changing with time as a hidden variable, based on sin (t)
In the other Bells Inequalities with entangled states are there also outcome time rate of changes ?
This is a red herring that has nothing to do with anything. It is just a way of generating a random number. This has absolutely nothing to do with physics, much less quantum physics, much less Bell. It is equivalent to a card game. Imagine shuffling a deck and seeing whether you get red or black cards. Same thing.

This is all just a trick to make things seem like there is a physical underpinning. I am sorry, you have been snookered.

#### jtbell

Mentor
Time out, pending a decision by the Mentors (moderators).

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