New clocked EPR Simulation with 100% detection.

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

Re: New clocked EPR Simulation with 100% detection.

Postby gill1109 » Mon Mar 03, 2014 12:19 pm

minkwe wrote:I'm also happy that in the same article (talk), you agreed with me that no "loophole"-free experiment will ever be done.

I'll leave that up to others to interpret whether you implied Pitowsky was deliberately trying to hide something. In anycase, my use of the term was in exactly similar context. You can replace Pitowsky (1989) with Gill and obtain my statement almost exactly. Were you being discourteous, impolite to Pitowsky?


1) I did not state that I believed that no loophole free experiment will ever be done. I stated that it was a logical possibility and that this possibility moreover had some scientific support.

2) No, seen in context I was not being discourteous or impolite to Pitowsky. You however were being extremely discourteous and impolite to me. Downright rude. In fact you very clearly violated the rules of the forum:

1. Impolite behavior is NOT to be tolerated

4. No flaming

5. No derogatory personal comments about anyone; stick to the physics

10. And... the most important rule; Have Fun!

(OK if you don't understand half what I write - but don't read it and don't respond to it, then).

PS I just studied the long set of rules as well as the short set of rules:

b. Members should post in a way that is respectful of other users. Flaming or abusing users in any way will not be tolerated and will lead to a warning.

c. Members are asked to not act as “back seat moderators”. If members note an issue which contravenes something in this policy document they are welcome to bring it to the attention of a member of the Moderator Team. Please use the “Report this Post” feature to report posts. Do not respond to such topics yourself. Members who constantly “act” as moderators may be warned.

I see I am presently contravening rule c. My apologies to all.
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Re: New clocked EPR Simulation with 100% detection.

Postby minkwe » Mon Mar 03, 2014 2:09 pm

Heinera wrote:Couple of quick questions for Michel:

Are the latest developments of your model still updated in the github sources? (https://github.com/minkwe/epr-clocked)

And, if you are familiar with the papers of De Raedt et al., what is your opinion on your model vs theirs?

Hi Heinera,
The model posted on Github matches the QM correlations while violating the CHSH and at the same time with 100% detection. I can make the model violate the CHSH even more but of course it won't match QM. If that is the one you are referring to then no haven't posted it.

I am aware of the work of De Raedt et al. but my model is not the same as theirs, although their model accomplishes the same thing. They do have more than one model though, my model does not use deterministic learning machines. The main point is that once you understand the error in Bell's theorem, it is not very difficult to come up with a variety of models which defeat it and the error is
the mathematical mistake of substituting correlations calculated from disjoint sets into an inequality derived from a single set.
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Re: New clocked EPR Simulation with 100% detection.

Postby minkwe » Mon Mar 03, 2014 4:12 pm

minkwe wrote:QM is a theory. Do you believe the predictions of QM violate the CHSH or not? If yes, how do you arrive at that violation? What QM calculations lead you to believe that the predictions of QM violate the CHSH?

This is what I'm asking?


Interesting paper: http://arxiv.org/pdf/quant-ph/0006014v3.pdf
Thus, before initiating Bell’s analysis, one has to choose explicitly one interpretation and stick to it. Unfortunately,
this is not what has been done. It will be shown here that the discrepancy exhibited by Bell’s Theorem is due to a meaningless comparison between strongly objective and weakly objective results, which means comparing the numerical value of the CHSH function for two systems, one having Nf degrees of freedom, the other 4Nf.
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Re: New clocked EPR Simulation with 100% detection.

Postby minkwe » Mon Mar 03, 2014 4:15 pm

gill1109 wrote:Your source is not perfect, it also emits unpaired particles. Ask any experimenter which source they would prefer to have.

Oh, so you believe that photons exist prior to being measured? (Realism anyone?) :D

gill1109 wrote:http://arxiv.org/pdf/1207.5103.pdf

The paper argues that Bell's theorem (and its experimental con firmation) should lead us
to relinquish not locality, but realism, as a universal physical principle.
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Re: New clocked EPR Simulation with 100% detection.

Postby FrediFizzx » Mon Mar 03, 2014 8:12 pm

minkwe wrote: Interesting paper: http://arxiv.org/pdf/quant-ph/0006014v3.pdf


Yes, very interesting and I believe 100 percent accurate. All the quantum experiments that are for a "so called" test of Bell don't really test Bell at all. All they do is confirm that quantum theory predictions seem to be correct. Bell's theorem is true for linear probabilities; as soon as you apply non-linear probabilities to it, it falls apart.
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Re: New clocked EPR Simulation with 100% detection.

Postby gill1109 » Tue Mar 04, 2014 9:48 am

Giullaume Adenier (in his Vaxjo conference paper http://arxiv.org/pdf/quant-ph/0006014v3.pdf) is following the Copenhagen interpretation, in the form: there is no sense in thinking about what you would have seen, if you had measured a different observable from the one which you actually did choose to measure. Luigi Accardi is the same. Adenier's conclusion is exactly the same as what John Bell (in his Bertlemann's socks paper) suggested that Niels Bohr's would have been: "I told you so!". (No sense can come of it. And it is irrelevant).

Everything hinges on what one means by locality and realism but essentially Adenier is actually *agreeing* with Bell: QM is incompatible with local realism; Adenier is perfectly happy with this. He keeps locality and, following Bohr, rejects realism. Adenier rejects "counterfactual definiteness" (so does Michel Fodje). Bell's personal preference was to keep realism - counterfactual definiteness - but to abandon locality. Bell was always careful though to distinguish between the logical possibilities (there are at least five) and his own intuitive preference - based of course on much knowledge and many years of experience and thought.

Michel asked me if I believe that photons exist prior to being measured? Well the answer is that I too believe that the predictions of QM are incompatible with counterfactual definiteness. I too prefer to keep locality and to abandon counterfactual definiteness.

On the other hand, simulation experiments on ordinary computers definitely are compatible with counterfactual definiteness. As was the whole of classical physics, prior to quantum mechanics.
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Re: New clocked EPR Simulation with 100% detection.

Postby minkwe » Tue Mar 04, 2014 12:53 pm

gill1109 wrote:Adenier rejects "counterfactual definiteness" (so does Michel Fodje).

This is false. I believe counterfactual definiteness is an essential component of modal logic which can not be abandoned without abandoning logic itself. I have repeatedly stated that you can not substitute actual correlations measured on a different distinct set of particles into an inequality which expects counterfactual correlations from a single set of particles. If you interpret that to mean I reject "counterfactual definiteness" then it is unfortunate (see below).

Adenier clearly states that the wrong inequality is being used. Anyone can read his paper and discern that for themselves:

Adenier wrote:It is demonstrated that once this meaning is determined, no discrepancy appears between local
realistic theories and quantum mechanics: the discrepancy in Bell’s Theorem is due only to a meaningless comparison between a local realistic inequality written within the strongly objective interpretation (thus relevant to a single set of particle pairs) and a quantum mechanical prediction derived from a weakly objective interpretation (thus relevant to several different sets of particle
pairs

...
which means comparing the numerical value of the CHSH function for two systems, one having Nf degrees of freedom, the other 4Nf.


Adenier is saying exactly what I've been saying all along. You can't use predictions and measurements from disjoint sets in an inequality derived for a single set. It is clearly explained that QM does not violate the CHSH. Adenier proves it. That is why I asked the question if anyone is still left who claims that QM violates the CHSH, they should show the calculation.

Michel asked me if I believe that photons exist prior to being measured? Well the answer is that I too believe that the predictions of QM are incompatible with counterfactual definiteness.

But you didn't really answer the question. There are three possible answers (a) Yes, photons exist prior to measurement, (b) No, photons do not exist prior to measurement (c) I don't know. Your answer above is none of them.
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Re: New clocked EPR Simulation with 100% detection.

Postby minkwe » Tue Mar 04, 2014 12:59 pm

I too prefer to keep locality and to abandon counterfactual definiteness.

My opinion is that anyone who makes such a claim does not understand what counterfactual definiteness means.

Counterfactual definiteness, means counterfactual statements have definite truth values. A counterfactual statement is a conditional statement in which the first clause is a past tense subjunctive statement expressing something contrary to fact. Counterfactual statements must be conditional statements. Every prediction is a conditional statement, with the conditioning elements being the specific experimental context. You have predictions in both classical and quantum mechanics. Every prediction for an experiment which ended up not being performed, and is no longer possible to perform is a counterfactual prediction. Counterfactual definiteness simply means those statements continue to have the same truth values, irrespective of whether the conditional clause is contrary to actuality or not. To abandon counterfactual definiteness means as soon as it is no longer possible to perform the experiment, the prediction which was true in the past ceases to be true. This is a logical error. To say that QM is incompatible with counterfactual definiteness is a logical error.
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Re: New clocked EPR Simulation with 100% detection.

Postby gill1109 » Tue Mar 04, 2014 10:51 pm

minkwe wrote:
I too prefer to keep locality and to abandon counterfactual definiteness.

My opinion is that anyone who makes such a claim does not understand what counterfactual definiteness means.

Counterfactual definiteness, means counterfactual statements have definite truth values. A counterfactual statement is a conditional statement in which the first clause is a past tense subjunctive statement expressing something contrary to fact. Counterfactual statements must be conditional statements. Every prediction is a conditional statement, with the conditioning elements being the specific experimental context. You have predictions in both classical and quantum mechanics. Every prediction for an experiment which ended up not being performed, and is no longer possible to perform is a counterfactual prediction. Counterfactual definiteness simply means those statements continue to have the same truth values, irrespective of whether the conditional clause is contrary to actuality or not. To abandon counterfactual definiteness means as soon as it is no longer possible to perform the experiment, the prediction which was true in the past ceases to be true. This is a logical error. To say that QM is incompatible with counterfactual definiteness is a logical error.

In this context, counterfactual definiteness has a more subtle meaning. It refers to mathematical models, not to reality. It is a technical term concerning mathematical structures used to model physical phenomena, not a term from philosophy or metaphysics.

It's easiest to explain with an example. I'll talk in terms of computer simulations instead of mathematical models, but a computer simulation model is also a mathematical model.

Consider your first computer simulation model, the one with discrete time emissions and detections. Let's add a save / restore /set random seed facility to the first line of the code in the source program. Settings will be fixed outside the programs, so there is no randomness in the station programs. Let' take N = 1. Alice and Bob will each supply one setting. Run the source programme, saving the seed at the start, and let's do spin 1, Alice angle is 0 degrees, Bob's is 22.5 degrees. Alice and Bob each get one outcome +1, 0 or -1. Call Alice's outcome AliceOutcome1

Now run the program again this time setting the seed, at the start, to the same initial seed which was saved last time. Alice angle is 45 degrees, Bob's is 22.5. Alice's outcome can be different from what it was last time, Bob's is the same. Call Alice's outcome AliceOutcome2

Now run the program once more, setting the seed, at the start, to the same initial seed as last times. This time, Alice tosses a coin and uses angle 0 when the outcome is heads, and 45 when it's tails. Bob sticks to 22.5 degrees.

Alice will see the outcome AliceOutcome1 if she get's heads, and AliceOutcome2 if she gets tails. We notice that she observes one of the two outcomes, but the other one, the one whe would have got if her coin had fallen the other way, is also well-defined.

And if I didn't save the random seed? I can still imagine doing it, and I can still state that the outcome which Alice would have got if she had got the other coin toss result is defined.
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Re: New clocked EPR Simulation with 100% detection.

Postby minkwe » Wed Mar 05, 2014 7:46 am

gill1109 wrote:In this context, counterfactual definiteness has a more subtle meaning. It refers to mathematical models, not to reality. It is a technical term concerning mathematical structures used to model physical phenomena, not a term from philosophy or metaphysics.

Science without basic understanding of philosophy and logic is mumbo jumbo. The scientific method is based on philosophy. When people make claims such as "realism must be abandoned" or "counterfactual definiteness must be abandoned" or "locality must be abandoned", they are in fact making metaphysical claims. Often, I have found that accusations of "philosophy" and "metaphysics" are used when people want to ignore logic.


It's easiest to explain with an example. I'll talk in terms of computer simulations instead of mathematical models, but a computer simulation model is also a mathematical model.
...
Let' take N = 1. Alice and Bob will each supply one setting. Run the source programme, saving the seed at the start, and let's do spin 1, Alice angle is 0 degrees, Bob's is 22.5 degrees. Alice and Bob each get one outcome +1, 0 or -1. Call Alice's outcome AliceOutcome1

Now run the program again this time setting the seed, at the start, to the same initial seed which was saved last time. Alice angle is 45 degrees, Bob's is 22.5. Alice's outcome can be different from what it was last time, Bob's is the same. Call Alice's outcome AliceOutcome2

Now run the program once more, setting the seed, at the start, to the same initial seed as last times. This time, Alice tosses a coin and uses angle 0 when the outcome is heads, and 45 when it's tails. Bob sticks to 22.5 degrees.

Alice will see the outcome AliceOutcome1 if she get's heads, and AliceOutcome2 if she gets tails. We notice that she observes one of the two outcomes, but the other one, the one whe would have got if her coin had fallen the other way, is also well-defined.


Let us translate your "explanation" into clear "philosophical" and "metaphysical" terms to show you exactly what you are failing to understand:

Monday: We generate *ONE* particle pair which we send to Alice and Bob, one each. They will measure on Wednesday. A particle can only be measured once.
Tuesday: Richard makes predictions about what they Alice and Bob might observe. His predictions are:
a) If Alice measures at 0 degrees her outcome will be AliceOutcome1.
b) If Alice measures at 45 degrees her outcome will be AliceOutcome2

Wednesday: Alice picks her angle randomly using a method of her choice. She measures at 0 degrees, and indeed observes AliceOutcome1 confirming Richards prediction (a).
Thursday: Michel believes in counterfactual definiteness and tells Richard that although his prediction (b) was counterfactual since it now can never be tested, the particle having been destroyed on Wednesday, the prediction is still valid and true. But Richard does not believe in counterfactual definiteness so claims that his prediction (b) is untenable because what Alice would have gotten had she measured at angle 45 degrees is not well defined.

Analysis of Richards error: (On Thurday)
a) IF Alice measures at 0 degrees her outcome will be AliceOutcome1.
b) IF Alice measures at 45 degrees her outcome will be AliceOutcome2

The antecedent (conditioning clause) of the above statements is what determines whether they are counterfactual or not. The antecedent does not determine the truth value of the statement as a whole. Each of (a) and (b) are conditional statement. In logic, these statements can be written as

if p then q

This statement can be true, whether or not the antecedent is true or false. The statement can also be true when the consequent is either true or false. That is because the statement captures a relationship between the truth values of the antecedent and the consequent, not the separate truth values of each. The statement is saying, when P is true, then Q must also be true. if P is false, then the statement will be counterfactual. It will be equivalent to saying "Had P been True, Q would have also been true", or "Had Alice measured at 45 degrees, she would have observe AliceOutcome 2". Accepting counterfactual definiteness, means that you accept that the truth value of a conditional statement such as those above, does not change when the antecedent becomes false and the conditional statement becomes counterfactual.

It means Richards predictions are just as true on Tuesday as they are on Thursday, irrespective of what Alice Does. It means Alice by choosing to measure at 0 degrees can not go back into the past to change the truth value of Richard's predictions.

Therefore Richards error was to think that only the antecedent determines the truth value of a conditional statement.

All mathematical and physical theorems are based on this basic logical structure. It can not be escaped.
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Re: New clocked EPR Simulation with 100% detection.

Postby minkwe » Wed Mar 05, 2014 8:53 am

Continuing...

Now let's say on Tuesday, Richard did not just make the predictions, he actually derived a mathematical expression containing both Alice and Bob's predictions using the following reasoning:

AliceOutcome1*BobOutcome1 + AliceOutcome1*BobOutcome2 + AliceOutcome2*BobOutcome1 - AliceOutcome2*BobOutcome2 <= 2

Which can be factored as:

AliceOutcome1(BobOutcome1 + BobOutcome2) + AliceOutcome2(BobOutcome1 - BobOutcome2) <= 2

He reasoned that since each outcome can only be -1 or +1, then one of (BobOutcome1 + BobOutcome2) or (BobOutcome1 - BobOutcome2) must be zero and the other 2, which means the upper bound of the expression must be 2 or -2.

If (BobOutcome1 + BobOutcome2) is 0, then (BobOutcome1 - BobOutcome2) must be 2 or -2, and if (BobOutcome1 - BobOutcome2) is 0 then (BobOutcome1 + BobOutcome2) must be 2 or -2. This is the core of the expression. This statement can only be made for a single particle. If Outcome1 is from one particle and Outcome2 is from a different particle, then the statement is false and the inequality so derived does not apply.

However, on Thursday, in order to prove his believe that counterfactual definiteness must be wrong, Richard, knowing that it is no longer possible to measure the particles, decides to take a different pair of particles and measure them at the angles at which Alice and Bob did not measure but could have. He expects (erroneously) that if counterfactual definiteness was correct, then he should be able to substitute those results into the original inequality and obtain the same results. However, as we've already seen, he is mistaken, the first pair of particles are correlated with each other, but neither of them is correlated with any of new pairs now measured on Thursday. Uncorrelated particles can not impose constraints on the values of each other like correlated particles can (cf bold statement above). Averaging over many disjoint uncorrelated sets of particles still does not cause them to impose constraints on each other.
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Re: New clocked EPR Simulation with 100% detection.

Postby Heinera » Wed Mar 05, 2014 9:32 am

minkwe wrote:He reasoned that since each outcome can only be -1 or +1, then one of (BobOutcome1 + BobOutcome2) or (BobOutcome1 - BobOutcome2) must be zero and the other 2, which means the upper bound of the expression must be 2 or -2.

If (BobOutcome1 + BobOutcome2) is 0, then (BobOutcome1 - BobOutcome2) must be 2 or -2, and if (BobOutcome1 - BobOutcome2) is 0 then (BobOutcome1 + BobOutcome2) must be 2 or -2. This is the core of the expression. This statement can only be made for a single particle. If Outcome1 is from one particle and Outcome2 is from a different particle, then the statement is false and the inequality so derived does not apply.


I am not sure what you mean here. Do you claim that this inequality only holds when Outcome1 = Outcome2?
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Re: New clocked EPR Simulation with 100% detection.

Postby gill1109 » Wed Mar 05, 2014 11:21 am

Michel, I told you what *I* meant by the term "counterfactual definiteness" in the context of Bell's theorem. QM is a mathematical theory. Many possible mathematial theories exist which "allow" counterfactual definiteness. Which means: the theory can be augmented so that outcomes of all possible measurements are defined simultaneously. Theories with local hidden variables, for instance. A(a, lambda) is simultaneously defined for all a, not just for the single value of a chosen by the experimenter in a particular run. Bell's theorem states that no local hidden variables theory can exactly reproduce QM predictions (which are probabilistic) when one spin of each of *one* pair of particles in the singlet state are measured perfectly. In fact the theorem states that local hidden variables can't even get close.

I showed you how counterfactual definiteness is also satisfied by your simulation models, which are based on local hidden variables.

I don't think the notion of counterfactual definiteness as discussed by philosophers (who play endless word games) is relevant here. I am talking about mathematics and I'm using some elementary mathematics to deduce properties of various classes of computer simulation models. For instance, I apply Chernof's theorem to find probability bounds for the correlations computed by your programs, where the probability aspect refers to the random choices of sequences of settings. Everything else is completely deterministic.
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Re: New clocked EPR Simulation with 100% detection.

Postby minkwe » Wed Mar 05, 2014 11:26 am

Heinera wrote:
minkwe wrote:He reasoned that since each outcome can only be -1 or +1, then one of (BobOutcome1 + BobOutcome2) or (BobOutcome1 - BobOutcome2) must be zero and the other 2, which means the upper bound of the expression must be 2 or -2.

If (BobOutcome1 + BobOutcome2) is 0, then (BobOutcome1 - BobOutcome2) must be 2 or -2, and if (BobOutcome1 - BobOutcome2) is 0 then (BobOutcome1 + BobOutcome2) must be 2 or -2. This is the core of the expression. This statement can only be made for a single particle. If Outcome1 is from one particle and Outcome2 is from a different particle, then the statement is false and the inequality so derived does not apply.


I am not sure what you mean here. Do you claim that this inequality only holds when Outcome1 = Outcome2?


No. I mean that you can not expect Outcome1 from one particle to restrict Outcome2 from a different particle in the same way you would expect Outcome1 from one particle to restrict Outcome2 from the same particle.

When anyone says:

If (BobOutcome1 + BobOutcome2) is 0, then (BobOutcome1 - BobOutcome2) must be 2 or -2, and if (BobOutcome1 - BobOutcome2) is 0 then (BobOutcome1 + BobOutcome2) must be 2 or -2.

They are in fact saying that BobOutcome1 in (BobOutcome1 + BobOutcome2) is the same as BobOutcome1 in (BobOutcome1 - BobOutcome2) (aka, the same particle). Calculating (BobOutcome1 + BobOutcome2) from one particle and (BobOutcome1 - BobOutcome2) from a completely different particle is a mathematical error.

In other words, Say Outcome1 is the result at 0 degrees, and Outcome2 is the result at 180 degrees, then it follows that for the same particle, Outcome1 is (minus)-Outcome2. So we can say if Outcome1 is +1, then Outcome2 must be -1. This statement only applies to that one particle because knowing Outcome1, we have to apply the symmetry constraints from Outcome1 to Outcome2.

If we instead take a new particle, Outcome1 from the first particle can not impose any constraints on Outcome2 from the new particle. So if Outcome1 from the first particle is +1, Outcome2 from the second particle can be either +1 or -1. Therefore in an expression which is supposed to encapsulate the constraints between outcomes from a single set (Bell's inequalities), it is not allowed to substitute, willy-nilly outcomes from different sets. Because those outcomes from different sets should not be expected to have the same relationships (constraints) between them that counter-factual outcomes from a single set do.
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Re: New clocked EPR Simulation with 100% detection.

Postby gill1109 » Wed Mar 05, 2014 11:32 am

minkwe wrote:When anyone says:

If (BobOutcome1 + BobOutcome2) is 0, then (BobOutcome1 - BobOutcome2) must be 2 or -2, and if (BobOutcome1 - BobOutcome2) is 0 then (BobOutcome1 + BobOutcome2) must be 2 or -2.

They are in fact saying that BobOutcome1 in (BobOutcome1 + BobOutcome2) is the same as BobOutcome1 in (BobOutcome1 - BobOutcome2) (aka, the same particle). Calculating (BobOutcome1 + BobOutcome2) from one particle and (BobOutcome1 - BobOutcome2) from a completely different particle is a mathematical error.

That's right. We're talking about the same particle. Because of local hidden variables, both BobOutcome1 and BobOutcome2 are well defined. Bob tosses a coin and gets to observe just one of the two.
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Re: New clocked EPR Simulation with 100% detection.

Postby Heinera » Wed Mar 05, 2014 11:52 am

minkwe wrote:
Heinera wrote:
minkwe wrote:He reasoned that since each outcome can only be -1 or +1, then one of (BobOutcome1 + BobOutcome2) or (BobOutcome1 - BobOutcome2) must be zero and the other 2, which means the upper bound of the expression must be 2 or -2.

If (BobOutcome1 + BobOutcome2) is 0, then (BobOutcome1 - BobOutcome2) must be 2 or -2, and if (BobOutcome1 - BobOutcome2) is 0 then (BobOutcome1 + BobOutcome2) must be 2 or -2. This is the core of the expression. This statement can only be made for a single particle. If Outcome1 is from one particle and Outcome2 is from a different particle, then the statement is false and the inequality so derived does not apply.


I am not sure what you mean here. Do you claim that this inequality only holds when Outcome1 = Outcome2?

When anyone says:

If (BobOutcome1 + BobOutcome2) is 0, then (BobOutcome1 - BobOutcome2) must be 2 or -2, and if (BobOutcome1 - BobOutcome2) is 0 then (BobOutcome1 + BobOutcome2) must be 2 or -2.

They are in fact saying that BobOutcome1 in (BobOutcome1 + BobOutcome2) is the same as BobOutcome1 in (BobOutcome1 - BobOutcome2) (aka, the same particle). Calculating (BobOutcome1 + BobOutcome2) from one particle and (BobOutcome1 - BobOutcome2) from a completely different particle is a mathematical error.
.


But they are of course not calculating (BobOutcome1 + BobOutcome2) and (BobOutcome1 - BobOutcome2) from completely different particles. BobOutcome1 in the first expression is the same as BobOutcome1 in the second expression, and ditto for BobOutcome2. So I'm still struggling to get your point here.
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Re: New clocked EPR Simulation with 100% detection.

Postby minkwe » Wed Mar 05, 2014 12:03 pm

gill1109 wrote:Michel, I told you what *I* meant by the term "counterfactual definiteness" in the context of Bell's theorem.

I don't think you did. You *implied* that counterfactual definiteness means: "the [outcome] she would have got if her coin had fallen the other way, is also well-defined."

Which means you believe rejecting counterfactual definiteness means "the [outcome] she would have got if her coin had fallen the other way, is not well-defined." This is clearly what I'm arguing against. If this is not what you mean, then you haven't explained what you mean very well. Using your definition of counterfactual definiteness, the idea of "rejecting it" defies logic.

Which means: the theory can be augmented so that outcomes of all possible measurements are defined simultaneously.

This is another key misunderstanding on your part. If a mathematical theory is accurate and consistent, then all it's predictions are well defined at all times. The suggestion that the predictions of a mathematical theory can be defined at some times and not defined at other, simply because somebody decided to measure at a different angle, defies logic.

Theories with local hidden varriables, for instance. A(a, lambda) is simultaneously defined for all a, not just for the single value of a chosen by the experimenter in a particular run.

Exactly, because A(a, lambda) is not simply an outcome. It is a conditional prediction, conditioned on both the setting "a" and all the hidden parameters "lambda". To say A(a,lambda) = +1 is similar to saying "If Alice measures at setting 'a' when hidden parameters 'lambda' are in play, then she will obtain +1". If the particle no longer exists and Alice did not measure at angle 'a', or the hidden parameters 'lambda' were not in play, then the prediction is counterfactual. You can have as many of those predictions as you like for as many settings and lambda combinations as you like. If you theory is mathematical consistent and accurate, those predictions will be true at all times, counterfactual or not. If you are trying to suggest that for some theories, those predictions are true and well defined at one moment and all of a sudden, because Alice chooses 22.5 degrees instead of another angle, all the other predictions become undefined, then such a claim is illogical. This is what I'm arguing.

Bell's theorem states that no local hidden variables theory can exactly reproduce QM predictions (which are probabilistic) when one spin of each of *one* pair of particles in the singlet state are measured perfectly.

I have already explained why this claim is nonsensical. It is based on calculating QM predictions, not from one pair of particles, but from 4 different distinct sets of particles, and using them in the CHSH as if they are the same results which would have been obtained had the same pair of particles been measured instead of the 4. Adenier's paper which I reference above goes into clear detail why this is wrong. I have explained very clearly many different ways why this is wrong. That is why I asked you to show the calculation by which you make the claim that QM violates the CHSH.

I showed you how counterfactual definiteness is also satisfied by your simulation models.

You modified the simulation such that already measured particles were recovered (by saving random number) seeds, and remeasured at different angles. I already told you that was meaningless because the QM predictions you are using to discredit counterfactual definiteness are not calculated for such a scenario. AND the experimental results you are using to discredit counterfactual definiteness are not done in such a manner, nor can they ever be.

I don't think the notion of counterfactual definiteness as discussed by philosophers (who play endless word games) is relevant here.

Unless you can point to the specific "word games" being played here, I would suggest that anyone avoiding to discuss the philosophical and logical issues of their claims is the one playing games.

I am talking about mathematics and I'm using some elementary mathematics to deduce properties of various classes of computer simulation models.

And I have used some elementary mathematics and logic to show that you are mistaken. For example, I have pointed out that it is impossible in logic or mathematics to violate the CHSH. I have also pointed out that the QM calculation being used to justify Bell's theorem is wrong (See Adenier's paper for details). I do not believe you have any clear mathematical responses to these.
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Re: New clocked EPR Simulation with 100% detection.

Postby minkwe » Wed Mar 05, 2014 12:27 pm

Heinera wrote:But they are of course not calculating (BobOutcome1 + BobOutcome2) and (BobOutcome1 - BobOutcome2) from completely different particles. BobOutcome1 in the first expression is the same as BobOutcome1 in the second expression, and ditto for BobOutcome2. So I'm still struggeling to get your point here.

Who do you mean by they? Let's analyze various possibilities:

They = EPR-experimentalists:
* They measure <AB> from one set of particles {1} at angles (a,b) == <A1B1>
* They measure <AB'> from another set of particles {2} at angles (a,b') == <A2B2'>
* They measure <A'B> from yet another set of particles {3} at angles (a',b) == <A3'B3>
* They measure <A'B'> from yet another set of particles {4} at angles (a',b') == <A4'B4'>

They use their calculated expectation values and calculate an expression of the form:
<A1B1> + <A2B2'> + <A3'B3> - <A4'B4'> <= ?
What did they expect to find on the RHS??

They = Gill/Bell theorem believers:
* They calculate a QM prediction for C(a,b) = -cos(a1b1) which can be measured on a single set {1}
* They calculate a prediction for C(a,b') = -cos(a2b'2) which necessarily must be for a distinct set {2} of particles from the first.
* They calculate a prediction for C(a',b'') = -cos(a3'b3'') which necessarily must be for a distinct set {3} of particles from the others.
* They calculate a prediction for C(a',b') = -cos(a4'b4') which necessarily must be for a distinct set {4} of particles from the others.
(numbers added to reflect the fact that each QM prediction requires a distinct experimental arrangement to measure and therefore requires a distinct set of particles)
They plug those expectation values into an expression of the form:
-cos(ab) - cos(ab') -cos(a'b') + -cos(a'b') <= ?
What did they expect to find on the RHS??

They = CHSH:
A, A', B, B' represent possible outcomes at angles (a,a',b,b') respectively for a single set of particles.
Since for each particle in the set,

AB + AB' + A'B - A'B' <= ?
Since the A in the first two terms is the same A, and the A' in the last two terms is the same A', we can factor them out.
A(B + B') + A'(B - B') <= ?
Since the B and B' within the two terms are the same, and each can only be +1 or -1, we can therefore say:

if B + B' = 0, then B-B' must be either 2 or -2 and vice versa. Therefore they expect to see 2 in the RHS. Extending to averages, the same restrictions apply and they would expect to see
<A1B1> + <A1B1'> + <A1'B1> - <A1'B1'> <= 2

In other words, since we are dealing with a single particle, the outcome when that particle is measured at angle B' is correlated with the outcomes when that particle is measured at angle B. This will not be true if we were dealing with two different particles like in the QM case or the EPR experiment case.

Still struggling?
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Re: New clocked EPR Simulation with 100% detection.

Postby minkwe » Wed Mar 05, 2014 12:36 pm

gill1109 wrote:That's right. We're talking about the same particle. Because of local hidden variables, both BobOutcome1 and BobOutcome2 are well defined. Bob tosses a coin and gets to observe just one of the two.

http://arxiv.org/pdf/quant-ph/0312035v2.pdf
The problem here is that the ensemble on which the correlations are evaluated changes with the settings, while the original Bell inequality requires that they stay the same. In effect,the Bell inequality only holds on the common part of the four different ensembles

Translation: the CHSH and Bell inequalities are not valid for disjoint ensembles, and when using 4 ensembles, the CHSH will only be valid for the parts of the 4 that are common between all 4. I'm not saying anything new here, this is pretty standard stuff.

The only remaining question is: Are the 4 ensembles in EPR-experiments disjoint or not? Are the 4 correlations from QM disjoint or not. I say they are. Adenier agrees. You say (to the extend you have said anything to this question) they are not?
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Re: New clocked EPR Simulation with 100% detection.

Postby minkwe » Wed Mar 05, 2014 12:41 pm

I forgot to answer the questions:
They = EPR-experimentalists:
...
<A1B1> + <A2B2'> + <A3'B3> - <A4'B4'> <= ?
What did they expect to find on the RHS??

They expected to find 2 as the upper bound. Unfortunately, they are mistaken, according to mathematics and logic, they should have been expecting an upper bound of 4 not 2. By using 2, they have assumed that the sets on which the expectation values do not matter, so that they can ignore the subscripts and do the factorization

A1(B2 + B2') + A3'(B3 - B4') <= ?

Assuming that A1 = A2 and A3' = A4'. That is the only way to expect 2 on the RHS. But this also means they expect the outcomes on one particle at one setting to be correlated with the outcomes of a different particle from a different pair at a different setting. This is "absurd".

They = Gill/Bell theorem believers:
...
They plug those expectation values into an expression of the form:
-cos(ab) - cos(ab') -cos(a'b') + -cos(a'b') <= ?
What did they expect to find on the RHS??

They expected to find an upper bound of 2. Unfortunately, they are wrong, the upper bound should be 4 not 2. The same absurdity applies.
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