what does non locality exactly mean for you Sofia. The meaning or interpretation of non locality (not the fact which is proven) is still debatable

Dina,

The term non-locality, as we use it when we speak of quantum mechanics, means as follows: an event that happens "here" influences an event that happens "there", however, the difference in time between them is not enough long for allowing some information-carriers to pass between the two places, e.g. photons or other particles.

See also the note in the end of my question.

Thanks,

Dear Sofia: the derivation of Bell's inequalities from the existence of a joint probability distribution function is a mathematical proof and requires no hypothesis. In particular, it does not depend on any kind of locality.

However, the fact that there does exist a joint probability distribution function is often justified, in Bell's setup, by a locality assumption: since the two measurements are taken at large distances, we assume that there is no way for the detectors to communicate their settings. But if there were, there would be no way to prove that there exists a joint probability distribution function for the results. In fact, it is easy to construct a model in which any QM correlation is attained, if we allow the measurement of a particle property at A to depend, not only on the particle's state and the the instrument setting at A, but also on the setting at B.

That Bell intended "non-locality" to mean the same as "Einstein-causality" (i.e., no interaction faster than the speed of light) was made obvious in one of his papers in which he illustrated the issue in terms of light cones.  

Further, in his derivation of "the" inequality he explicitly considered CORRELATED events but then did not use the correct formula for a joint probability---pointed out first by Edwin Jaynes.  

All the details are explicated, inter alia, in various of my papers.

Dear François,

Thanks for your reply. I have some comments to it, please see: 

==> the fact that there does exist a joint probability distribution function is often justified, in Bell's setup, by a locality assumption:

So, this is a futile justification. My question is if it can be removed. You see, by introducing futile assumptions, one blocks the way to, eventually, more general conclusions.

==> we assume that there is no way for the detectors to communicate their settings.

Not only! By locality, we also assume that the particles don't communicate among themselves conveying data about type settings, and deciding together about responses to be produced.

==> But if there were, there would be no way to prove that there exists a joint probability distribution function for the results.

Why not? Nonlocal factors can't obey a statistics? A statistics is obtained from a very big number of individual cases.

==> In fact, it is easy to construct a model in which any QM correlation is attained, if we allow the measurement of a particle property at A to depend, not only on the particle's state and the the instrument setting at A, but also on the setting at B.

I am not sure about this. You see, if for a type of experiment we build a model, e.g. for Bell-type experiments, but the model can't justify other types of experiments, e.g. GHZ-type, Mermin square type, etc., etc., the model isn't good.

In all, my impression is that Bell needed the locality assumption for other reasons. In just adding probabilities algebraically, the locality is not needed. It's elsewhere that it is needed. But where?

Best wishes from me!

A. Kracklauer,

The question is not what Bell meant by non-locality, but why he excluded it.

Neither is it asked here how he obtained his inequality. To obtain the inequality is almost trivial, it's simple manipulation with the equalities (1), (2) and (3). The question is whether the locality assumption is necessary, or may be removed.

If this assumption can be removed, I repeat, if, the conclusions can be more general than Bell's conclusions.

Dear Sofía:

The point is, that it is not a priori obvious that there exists a joint probability distribution of the results in all possible settings. The problem is that, if A1 and A2 are the two settings at A, and B1, B2 at B, then we can measure at any time one of the four

A1 B1

A1 B2

A2 B1

A2 B2

but never both. So if there is communication, we cannot, using such measurements, determine a joint probability distribution.

Of course, standard QM states emphatically that there is no joint probability distribution. The locality leads, using ``realism'' assumptions, to the existence of a jpdf, which itself clearly implies Bell's inequalities, which are themselves contradicted by experiment. You are right in saying that no locality is needed to derive Bell's inequalities from the existence of a joint probability distribution function. It is to make the existence of such a distribution function plausible that Bell invoked locality.

``This completely undermines Bell's proof.'' There are two aspects to Bell. One is an, admittedly straightforward, but surely correct, computation, which shows that anything having a jpdf must satisfy certain inequalities.

Another part, equally undoubted, shows that using quantum mechanics, we can obtain results that violate this inequality. From this you deduce that it is not possible to describe quantum mechanical results assuming a jpdf.

In cases where no communication between detectors is possible, this is felt by some to be surprising, but on this subject opinions may well be divided. On the rest, they emphatically should not.

As to what is proper to Bell, it seems that the realisation that a jpdf implies certain inequalities goes back to George Boole, but Bell's rediscovery thereof was surely independent. That the inequalities can be violated in QM is definitely Bell's discovery.

Dear François

==> The point is, that it is not a priori obvious that there exists a joint probability distribution of the results in all possible settings.

Let's not modify my question. Bell assumed that a probability P(A, B, C) exists. I don't argue about THIS assumption of his, but about the locality assumption.

If you want to speak of the CHSH inequality, then, the authors of that inequality assumed that the probability P(A1, A2; B1, B2) exists. They also assumed locality. It's about the locality assumption that I ask, not about the existence of the 4-variable probability.

==> It is to make the existence of such a distribution function plausible that Bell invoked locality. 

It's not clear to me what you say. Please be more explicit.

You see, Bohm's mechanics is very plausible, and also implies the existence of a 4-variable distribution P(A1, A2; B1, B2). And it is a nonlocal interpretation. In a two-particle system, the Bohmian velocity of each particle is a function of the positions of both particles, even if the particles ar distant from one another.

My best wishes! 

Charles,

I don't understand what you say:

==> since the results of both measurements at the time of the measurements cannot be known even in principle, a joint probability cannot be said to exist at that time.

The quantum mechanics gives us the amplitudes of probability and you can calculate  with it whatever 2-particle joint probabilities.

 ==> It tells us that a classical view is incorrect.

Who tells us that and what is the classical view? The violation of Bell's inequalities tells us that the nature works with amplitudes of probabilities, which are complex. The calculus with positive probabilities is inapropriate. Bell added or subtracted positive joint probabilities. The nature adds or subtracts complex joint amplitudes, and if we want probabilities we have to raise the result to absolute square.

Anyway, how Bell worked is not how the nature works. But, again, my question is why Bell needed locality.

I am trying to explain the logic of Bell:

He says: *if* there is a joint probability distribution function, *then* these inequalities must hold.

That is algebra, and has nothing to do with locality.

Then he says: in QM some correlations do not obey these inequalities. That is simple calculation and also has nothing to do with locality.

Therefore QM cannot be described by Jpdf's.

However, if the measurements are far apart, then the non-existence of a jpdf seems to contradict locality. Locality is *only* an argument to justify the existence of a jpdf. If there is no locality, in particular if the instrument settings can be instantly communicated, and if the result of an experiment at A can depend on the settings at B, then there is no difficulty in violating Bell's inequalities, because there is no jpdf depending only on the local instrument settings.

Bohm's mechanics is a case in point: it violates Bell's inequalities, yet it is classical. Hence Bohm's mechanics does not allow for a jpdf depending only on local settings, which is indeed the statement that Bohmian mechanics is nonlocal.

Bell's logic is the question: what consequences does the very existence of a meta theory with more variables but free of all QM-weirdness have on conventional QM when the extra variables are averaged out?  Unfortunately he writes a formula for  joint probabilities that is incorrect at any level and so then draws erroneous conclusions and infests all subsequent discussion with endless confusion!

Dear Francois,

I understand what you explain (although it took some effort from me - this is not criticism.)

Let me try to formulate what you explain equivalently, but more directly, and please correct me if I misunderstood you: the locality assumption is not necessary when manipulating with the probabilities of the (supposed) distribution, but when comparing their consequences with the experiment.

Now, the settings of an experiment which measures A1 and B1, are different from the settings when measuring A1 and B2. Then, if the probabilities are non-local, who says that the 4-variable probabilities in these two different experiments should be the same?

Our 2-variable measurements provide 2-variable probabilities. For getting 4-variable probabilities we have to construct them. For example, we have to take the probabilities P(A1, B1) provided by the experiment, and split each one of them for obtaining P(A1, A2; B1, B2). Who says that doing this splitting for al the four combinations of measurements, A1&B1, A1&B2, A2&B1, A2&B2, one should get the same 4-variable probabilities? The violation of the CHSH inequalities shows that we can't get the same distribution.

By assuming locality, i.e. A1 and A2 take values independently of what measurement is done on the other particle, and so B1 and B2, Bell yes could construct a unique distribution. 

Now, just please tell me if you agree with me,

And best wishes! 

 A. Kracklauer,

If you want people to react to what you say, you have to tell us what you think is wrong in Bell's formula? Just to indicate articles, won't help, people don't read articles just because you say "read my articles". Everybody is busy.

You have to explain, in short, the main idea in those articles. If people consider that idea interesting, they would read your articles.

Best wishes,

Sofia

Charles,

==> The probability for an experiment we cannot do (e.g. simultaneous measurement of position and momentum) is a meaningless idea.

You do injustice to de Broglie and Bohm. They were not stupid. They thought that, while the limitations of our experiments don't allow simultaneous precise measurements of position and linear momentum, these value though co-exist with some probabilities.

The fact that the standard QM has a different approach, it matter of interpretation. Only the experiment, if there exists such a one, can tell us which approach is correct.

Can you indicate such an experiment? If not, each approach has the chance to be correct.

Charles,

It doesn't go like that. Can you indicate an experiment that shows that Bohm's assumption about positions and linear momenta is incorrect? Your argument,

==> There are many experiments which show that the mathematical structure of quantum mechanics is correct, and hence that ideas which contradict the mathematical structure of quantum mechanics are incorrect.

is not sharp. If you want to tell me that 1+1 = 2, please don't go around. Don't tell me that 1+1 s not equal to 1, neither to 3, nor to 4, etc. Tell me that it is equal to 2. So, if there are so many experiments, then please indicate one of them, that contradicts Bohm's assumption, clearly.

With kind regards,

Sofia

Sofia:  

Bell's mistake:  he wrote P(a,b)=/int P(a,l)P(b,l) dl.  He should have used:

P(a,b)=int P(a|b,l)P(b|l) dl.  The consequences are complex enough to burn bneedlessly  

``I start from the position that probability describes a state of knowledge. I am then already not able to write down a jpdf for events outside the light cone''

I find this hard to understand. Assume one has two observers, spatially separated, writing down, say each of the two chiselling on a slab of marble the results he observes. The the two slabs are sent to be compared. In my opinion, if you can write a jpdf for the combined results of the two marble slabs once they are together, this involves that you can say the same thing of the original marble slabs, since the results written on them presumably were not affected either by the transport or the analysis. So the jpdf obtained from the collated results should be interpretable as a jpdf of the original results.

I feel I must be misunderstanding you.

Good argument, Charles

Dear Charles,

As in other cases we depart from the question, and I don't quite like that.

Now, in referring to the Bohmian mechanics you go too much quickly and say many things, s.t. I find difficult to follow you. So, I will refer only to the block of sentences

==> momentum is defined in quantum mechanics by a linear superposition of position states. It is then a theorem that Bohm's assumption is incorrect. You can't define momentum two different ways at the same time, and you cannot simultaneously claim that momentum is conjugate to position, so that you can prove the uncertainty relation, and that it is not conjugate to position because position is a hidden variable.

Momentum eigenstates are linear superposition of position eigenstates. Which theorem you see in this?

Now, linear momentum operator doesn't commute with position operator. According to QM, they have to respect uncertainty relations. But these relations refer to what we can get if we measure. All the QM is about what we can measure. Bohm just supposed that there exists a level below what we can measure. QM formulas don't contradict the existence of such a level, they ignore such a level. The Copenhagen approach is that that the wave-function reflects what we can know, what we can measure, not what exists. 

Bohm had a different approach. But he accepted the QM formalism and its conclusions entirely.

Of course, if you can point to an experiment that leads to a formula, resulting from Bohm's mechanics, that is in conflict to a quantum formula, the situation changes.

Now, I stop here my contribution to this talk which is not about what the question asked.

Charles,

I move the answer to my new question "The "realism" hypothesis in QM. Do we have an experiment that disproves it?"

If I remember well some older readings (I hope my memories are OK, as I’ve no time to re-check all this now, apologies … !), Bell’s inequalities were a.o. designed to allow to give an answer to the EPR (for « Einstein-Podolsky-Rosen ») article (Einstein, A., Podolsky, B. and Rosen, N. « Can quantum mechanical description of physical reality be considered complete ? », Phys. Rev., 47 : 777-780, 1935). In this article, it is alluded to a thought experiment to show that QM is incomplete. The idea was that two particles having met and being thus intricated would - according to QM - form a single system and know from each other’s response to any further measurement. And this instantaneously although unable to communicate at a speed higher than the speed of light. This would mean the existence of « hidden variables » that are not taken into account by QM. Thus QM would be incomplete.

Bell’s inequalities should allow to test this. In case of existing hidden variables, measurements (of spin or say schematically +1 or -1) on couples of particles by 2 detectors which can be switched onto 3 positions, would give only 8 possible results. This is fairly general in probability and applies to any population of couples of individuals of which one analyses 3 dichotomical properties (here the 3 positions of the detectors). There is no need to assume locality.

Bell thus designed his inequalities to allow experimental distinguishing. Are these inequalities not violated, EPR is right and QM is incomplete indeed. Are they violated, QM wins and there are no « hidden variables ».

Further experiments in the years 1990 - 2000 (Aspect, Zeilinger, etc…) showed that QM is right.

Charles, you already answered, I already answered, etc.

It's not that I don't accept mathematical proof, I accept if it is conclusive. Bohm did not provide a formula for linear momentum, different from QM. Also, he didn't say that one can have a state which is simultaneously an eigenstate of linear momentum operator, and of position. You attribute to Bohm things that he didn't say, and do not result from his formalism. In particular, I hope that you don't take the Bohmian velocities as equal to quantum linear momentum divided by mass. These two concepts have nothing in common.

Now, a conclusive proof against Bohm's mechanics is like Ghose's proof: experiment, QM formula, BM formula, and showing that the two formulas disagree. 

However, if you want to end our talk by saying that I can prove nothing - well, I am an aged person and I won't disturb your pleasure in saying such things. Also, you disregarded my advice to move the conversation to a more appropriate site. This is a mistake, if you want a post to be read, you shouldn't place it at an inapropriate site.

I understand that you are displeased by that I disagree with you, and I would be glad if I could do otherwise.

Sofia

Charles,

At the point where you resorted to insults, I stop whatever communication with you.

As an addition to my former post (in order to be more accurate) : the « assumption of locality » comes from the EPR article because Einstein, Podolsky and Rosen considered evident that no communication could take place at a speed higher than the speed of light. So, in established absence of hidden variables (theorems), a violation of Bell inequalities could be interpreted as showing evidence of non-locality.

The evidence of non-locality being instantaneous doesn´t violate the speed of light maximum

Dina,

EPR assumes locality, so violation of Bell inequalities can be seen as proof of non-locality at QM level.   

@ Charles: we had this discussion about Bohm before. You insist on misunderstanding what he did. It is unfortunate that your theorem (as proved in your paper) is quite unclear as to what you assume of a hidden variable theory. You say it should have dispersion-free states. But dispersion of what?

A clear discussion, for instance, of Bell's hidden variable theory for a spin 1/2 would be illuminating.

But we should probably open a new thread for this, since this whole issue is entirely off thread, interesting though it is.

Guibert:

Bell did not call his inequality a "theorem," correctly so. Nothing acausal/nonlocal is seen in experimental tests as soon correlation is attributed to a "prior cause."

@ A. Kracklauer: How does ``attributing correlation to prior cause'' (whatever that actually means, it might be a kindness to the less well educated among us to explain in greater detail) make it impossible to describe measurements of distant essentially simultaneous events using a joint probability distribution function?

Because the connection between the existence of a jpdf and Bell's inequalities is in fact a theorem.

Let us be clear: it is impossible to ``refute'' a theorem, at least if the theorem was correctly proved. I am not sure what Bohm claimed, but Bell certainly never stated that Bohm refutes von Neumann. What he rather states is that there can be interesting hidden variable theories to which von Neumann's theorem does not apply, because they do not satisfy the hypotheses that von Neumann makes for a hidden variable theory.

Bell's example, I think, is illustrative: I do not know what you mean by saying that ``you specify the variable after the measurement result''. The way I understand Bell's example is simply that, whenever you prepare a ``pure'' quantum state having positive spin in the z direction, what you in fact do, the best you can do using accessible techniques, is to create a pure spin, which is a randomly chosen point on the northern hemisphere. There simply are no techniques (available to us) to create a pure spin state, but these nevertheless are assumed to exist.

In case you are tempted to say that this is philosophical nonsense, I would argue that a microstate in classical statistical mechanics---that is, a state in which all the molecules' positions and velocities are accurately known, is also a technological impossibility, yet the existence of such states is routinely taken for granted in statistical mechanics.

Similarly, whenever you measure a spin, say sx, then you get a positive answer if the ``true'' spin is on the hemisphere of the sx=1 pole on the Bloch sphere, and negative otherwise. The true spin is always the same, it is just our rules for measuring or creating it that cause the uncertainty.

Bohm's approach is considerably messier, but it works similarly

Dear Leyvraz:

Sarcasim won't save Bell!  "Prior cause" is a BASIC concept in probability theory.  Read all about it in any text.  BTW, formal logiciens will tell you that it is impossible to have a "theorem" in Physics theory, lose palaver notwithstanding.

I see here a lot of talk about Bell vs. von Neumann. QM does not admit dispersion-free quantum states. This is well-know. But neither Bohm, nor Bell, ever claimed that such quantum states exist. They definitely referred to the possibility of a sub-quantal structure which would not contradict the QM.

None of them claimed that one can produce, by a measurement (or preparation) procedure, a dispersion-free, statistic ensemble of particles. Indeed, when we measure a certain observable A of some quantum system, all the observables whose operators don't commute with Ȃ, remain in an undetermined states.

Now, PLEASE, EVERYBODY, move this talk of yours to another site. I can recommend my other question: "The "realism" hypothesis in QM; do we have an experiment that disproves it?" Different people may be interested in issues about realism in QM, and if you place your talk at a wrong site, those people cannot know.

@ Kracklauer: `` "Prior cause" is a BASIC concept in probability theory. Read all about it in any text. ''

I have read a large number of probability texts (Feller, Bernoulli, de Moivre, Grimmett) and have yet to read anything on ``prior cause''. So if you could give a more specific reference than ``just see anywhere'' it might be helpful.

But in ay case, you fail remotely to address the question (Quand un philosophe vous répond, on ne sait plus ce qu'on lui avait demandé): my question was, how any concept of prior cause affects the possibility of having a joint probability distribution function.

``formal logiciens will tell you that it is impossible to have a "theorem" in Physics theory, lose palaver notwithstanding''

I fully agree: physics is an experimental science, so theorems are out of place. However, a physicist may well derive mathematically a theorem. That is just what Bell did. In fact, I have found out that George Boole in fact found out about these inequalities a lot before Bell, though of course he was not in a position to appreciate their connection to quantum measurement. Perhaps George Boole is on your list of people qualified to prove theorems?

In any case, Bell's (or Boole's) inequality is in fact a theorem for any set of data for which a joint probability distribution exists. Until you then explain what you r ``prior cause'' means and how it is relevant, your post will remain a prototypical example of arrogant and ignorant pomposity.

Dear Sofia,

So sorry to be so late on answering your question. I think, though,

that it has already sufficiently been answered by Leyvraz: the

locality assumption is unnecessary because the Bell inequalities

can be derived from the existence of a quadrivariate probability

distribution, which does not need any assumption of locality. So,

from this point of view you are completely free to keep

entertaining Bohm´s hidden variables theory (which, as you may

remember, I do not like for methodological reasons).

Ongoing discussion may be caused by a question different from the

one you posed, viz. Is nonlocality necessary for violation of

Bell's inequality? The answer to this question can already be found

in Bohr´s 1935 answer to the EPR paper, where he states that ``The

last remarks apply equally well to the special problem treated by

Einstein, Podolsky and Rosen, ... which does not actually involve

any greater intricacies than the simple examples discussed

above.'', the ``simple examples discussed above'' referring to

Heisenberg's thought experiments illustrating the latter's

uncertainty principle. Indeed, violation of the Bell inequalities

can be explained by Heisenberg disturbance just as well as by the

spooky actions at a distance Einstein thought to be necessary for

sticking to the completeness of quantum mechanics. It seems to me

that Heisenberg disturbance is a local affair since it is regarding

two observables of the same object.

Dear Willem: Heisenberg disturbance is indeed a local affair: it involves the uncontrolled action of a measuring device on the measuring system. But such local uncontrolled reactions would rather tend to diminish correlations, whereas they are too large. In fact, any correlations arising from local effects should satisfy Bell's inequalities.

In fact, it is precisely because the information as to what is being measured on one side cannot propagate in time to influence the measurement on the other side, that we have difficulties. Indeed, just a few lines below your quote, Bohr says:

``Of course there is in a case like that just considered no question of a mechanical disturbance of the system under investigation during the last critical stage of the measuring procedure.''

So things are not so simple, and I believe Bell did essentially show that any classical point of view---that is, any interpretation of quantum mechanics resting mainly on classical probability---must be nonlocal.

Dear Leyvras,

Thanks for your comments. However, they are asking for quite a few answers, which would go far beyond the present thread and probably would annoy Sofia. Therefore I would prefer to either discuss in private, or start a new thread on a question which in my view would have to be discussed, viz. ``Is there any justification for application of the Bell c.q. BCHS inequalities to measurements like those performed by Aspect?'' I have not been able to find one.

Everyone gets in a tangle over the Bell-Kochen-Specker notions. The problem ultimately lies in that little symbol, i generally taken to be the scalar square root of -1. This is purely imaginary. There are however real objects with geometrical significance such as bivectors which square to -1. Joy Christian has shown that using i as being the unit bivector allows the oreintation of the bivector to act as a hidden variable so demolishes Bell's theorem. Furthermore he shows that Bell made a topological mismatch in the derivation of his inequallity. Joy Christian is published on arXiv because like me he is blacklisted by the journals. Look Joy up on arXiv and read his work. He does a very good demolishion job on the authodoxy.

Dear Levraz:

A "prior cause" is an event in the intersection of the past cones of two subsequent events---measurements by Alice and Bob, say.  In Stat. & Prob. texts often little note if taken of this concept as for all correlated events (except `spooky´ QM ones) it is implicit that such prior events "caused"  correlation.   

Boole may have proved some theorem pertaining to number sets, but Bell did not.  He did not denote his result as a "theorem."  Far as I know, John Clauser did that later. Bell's  non theorem (inequality derivation) presumes to encode "locality" with a formula that tacitly actually encodes statistical independence or zero-correlation between the measurements involving vonNeuman's projection process on ambiguous and unreal states (i.e., the sum of mutually exclusive entities, e.g., the so called 'singlet' state)  ["Dog's breakfast" of incompatible notions!].   Bell's specific math error is an incorrect formula for a correlation coefficient, which is the product of a conditional-probability with an absolute-probability, not two functionally similar (really undefined) terms "A" and "B" in customary notation.  

BTW, all test experiments of Bell-type inequalities have been event-wise simulated without nonlocal interaction but still get the observed violation.  Full story takes too much bandwidth for this venue; see my pubs.

``Bell's specific math error is an incorrect formula for a correlation coefficient, which is the product of a conditional-probability with an absolute-probability, not two functionally similar (really undefined) terms "A" and "B" in customary notation.''

I do not believe there is a ``math error'' by Bell, but rather an interpretation error, by yourself: when two measurements take  place and they depend on common causes, which Bell denotes by lambda, then if the two measurements take place in such a way that they cannot influence each other (because of locality), then

Probability of A&B given lambda = (Probability of A given lambda) multiplied by (Probability of B given lambda)

where lambda represents the set of all common causes and the measurements apart from lambda are independent, as they occur ``simultaneously'', in other words within a spacelike separation.

As for Boole, I have no quarrel with naming the theorem after Bell. My point was that a similar point had been made by a ``true blue'' mathematician before Bell, so denying the title of theorem on the quaint reason that Bell was a physicist is thereby unjustified. Bell himself did call his result a theorem at least in later work. In any case, it is a theorem.

 Leyvraz:

"One can lead a mule to water, but can't make him drink"

Were your viewpoint on Bell correct, it should be impossible to classically simulate the relevant experiments.  But there they are, waiting for you to study them!

Your understanding of Bell's rendition of a joint probability fails to see its ambiguity---which explains why it, as Bell and you write it, cannot be found in any of the texts on Prob.&Stat. you claim to have read!

The appearance of a parameter of the opposite station in a CONDITIONAL probability does not imply nonlocality as Bell took it.  It is in fact exactly that formulation that is used in ALL applications except by Bell for QM.

BTW, my points here are clues, not full blow arguments.  Bandwidth  & duplication. All my papers are available on the Net. If you are serious ....

It is, of course, possible to perform simulations of quantum processes...because, self-evidently, simulations are not limited to local processes: there is nothing to stop the simulator from letting the outcome at A depend arbitrarily from the outcome at B and viceversa. Bell himself makes the point about simulation.

However, in the real world, what is called locality prohibits the process whereby an actual value is measured at A to depend in any manner from the corresponding process at B except through what you call the common causes lambda.

A question concerning the fact that one station's parameter should appear in the other's: which should it be? The answer that it should be ``the one that is measured first'' will clearly not do, since for spacelike separations, which happens first is a question, the answer of which depends on the reference frame.

Finally, to ``The appearance of a parameter of the opposite station in a CONDITIONAL probability does not imply nonlocality as Bell took it.'' I would answer that this is a very strange statement. It would be more correct to say that this is how Bell, in Einstein's footsteps, *defines* nonlocality. You are, of course, free to argue that this is not a sensible definition of nonlocality. However, so far, neither in your comments nor in those papers of yours I have, in fact, looked at, have I found any hint of this.

Seems your readings, if any, of my papers were very superficial

Leyvraz:  The referred simulations generate detections using only information sent to a detector, and no info pertaining  to or sent to the other detector.  There is no interaction between the detectors at all!  Just what is propagated to them from the prior cause (in the back light cone of both).

Bell's arguments do not require SR, indeed were not formulated to be invariant or whatever.  Not relevant anyway, the formula (or Bayes' Ansatz) for coincident probabilities can be stated either way---just one must be a conditional probability (with partner's parameter), the other an absolute probability.  Works everywhere, even where Bell thought it doesn't!  

It is true that Bell sought to redefine nonlocality, and thought he was encoding locality, but inadvertently encoded statistical independence (noncorrelation) in stead, as is implicit in the subsequent algebraic manipulations to derive his inequality. Result: it is valid only for uncorrelated pairs but tested with correlated pairs.

Pitch your prejudices; have a cold beer, and reread the papers slowly with focus.

``It is true that Bell sought to redefine nonlocality, and thought he was encoding locality, but inadvertently encoded statistical independence (noncorrelation) in stead, as is implicit in the subsequent algebraic manipulations to derive his inequality. Result: it is valid only for uncorrelated pairs but tested with correlated pairs.''

Saying that Bell sought to ``encode'' locality would seem to suggest that he thought his inequality was a necessary and sufficient condition for locality, which I have nowhere seen stated. Rather, locality implies that the two detections are, in fact, independent apart from common causes, as you call them, thereby leading to Bell's inequality. As far as I have understood your papers, you do not seem to clearly understand what is at stake in locality. The point is, that the two processes taking place *simultaneously* at A and B, each leading from the same common cause to a given result, should, indeed, be statistically independent. If you can give a physical picture where this is not so, it would be interesting. Hence the equation I wrote a few posts ago.

Try to understand Bell's papers. They are certainly clearer than yours. You recommend focus: I fear that does not help when the original image is hopelessly blurred

Of course, Bell is clearer for those locked into Bell-think!  Novelty, especially when its consequence will be hyper embarrassment, is always rejected; until it isn't.  Per Planck, this requires even the internment of the current generation.

You will never find clear statements of how one makes a mistake.  Virtually always there are unarticulated assumptions involved.  It took me ~30 years to sort out just the central points in Bell's (plus many 2nd order commentators) stories although convinced the whole time that there is something seriously wrong.     

Since you have publicly committed yourself to the rectitude of Bell-type analysis, one can only expect jujitsu style defensive rationalization.  If you'r happy with the fundamental  mystical aspect of "entanglement,"  so be it.  

If an argument is simple, like Bell's original paper, or Mermin's explanations, it should  be possible to show the presence of a mistake in simple terms. Above all, if what you claim is a mathematical mistake, as appears to be the case, then it is enough to show where the mistake was made. This should be extremely straightforward, yet all your papers are basically full of complex and unclear concepts, instead of simply addressing whatever it is which you consider to be wrong.

As for mysticism, I see none: I admit to not understanding how correlations violating Bell's inequality can arise. It seems as though we should either renounce locality---something I am most reluctant to do---or radically review the way we think of correlations as arising from common causes via probabilistic processes, the way you seem to like to have it. No mysticism there, just an unwillingness to bow to dogmatic obscurantism.

Leyvraz:  In fact at least I find my papers as straightforward as the issue permits.  The math error is exactly where I have pointed to it: in Bell's rendition of a joint probability. To see and comprehend the error it is useful to compare Bell's expression with the form found in Feller, for example, and then trace through the algebra leading to the BI, with both forms.  Bell's form, since both "A" & "B" are functionally symmetric, seems to work; Feller's (Bayes') obviously doesn't---except when the two are uncorrelated.

BTW, what you have denoted as the "way" I like a joint probabilities, is shared with (actually taken from)  ALL authors of pure math Prob.&Stat. texts.  Bell & followers are the outliers.

Alternatively, Bell's error can be found in other consequences; one such can be seen dissected in Found. Phys. Lett 19(6) 625 (2006).  Maybe that one is straightforward enough for your taste. 

What you seem to regard as "simple," is really just familiar.  Bell's writing style is facile (Eng. sense) but ambiguous.  It took him ca. 6 years even to restrict his idea of nonlocality to "Einstein nonlocality" via Minkowski diagrams,  before that "radical correlations" were not excluded.      

If, for a practicing physicist, nonlocality is not mysticism, maybe you'r in the wrong trade!

I still fail to understand you: Bell uses essentially the formula I wrote a few posts ago

P(A&B given lambda) = P(A given lambda) times P(B given lambda)

when the processes yielding A and B from lambda are independent.

Is this what you object to?

Leyvraz: Bell uses it OK; but it is not appropriate for his intended application.  Either the A or B must be (or have the structure of) a conditional probability, which in the usual form contains a parameter of the other station and it is not counted unless that station too has made a detection.  (Seems Bell saw the presence of the parameter as an indication of nonlocal interaction.)  As this parameter is changed (or changes) the coincidences are tallied to determine the correlation as a function of  a,b (in Bell's notation). Bell's form, which he never actually uses to analyze data, but just manipulates algebraically in the abstract, does not accommodate his manipulations in actual usage, i.e., data analysis.

The issue of nonlocality actually cannot arise in Bell-test experiments without the vonNeumann collapsing wave-packet hypothesis.  Without this extra assumption it would be taken for granted that the cause of correlation is to be found in the intersection of the past light cones of both measurement stations.  Perhaps, even, this was Sofia's original point.

In any case, all the experiments can be understood without calling on nonlocality, entanglement, wave-collapse, or QM even, etc.  That's why there are numerous examples of classical phenomena and simulations to be found in the lit. 

Seems to me that you really do not want to understand. You are asking for a degree of spoon-feeding that goes way beyond what is expected of the readers of professional papers in Physics. This "social media" pingpong venue has different customs, I guess. 

Whether it I who do not understand, or you who are missing the point, is not necessary to debate here. If you replace one of the two terms by a conditional probability, you get a triviality, or a definition. Under these circumstances, indeed, no conclusion can be drawn. Bell's claim is that, if a theory has what he calls locality, then, since the two measurement processes take place at spatially separated positions and times, they must proceed independently. That allows to specialise from eq (9) of ``Are quantum ‘irreality’ and ‘nonlocality’ ineluctable?'' to eq (8) of the same.

As far as I can see, this is a definition of locality. Can you show how a local process could possibly contain an influence of the setting of an apparatus, which was decided on at a time and at a distance from the measurement at A which precludes communication even at the speed of light?

It is not that I do not want to understand, it is that, up to now, you have asked me to take on faith that your obscurity hides depth, instead of merely more obscurity. I am unwilling to do this.

Leyvraz:  I ask for NOTHING on faith!  I have often said: "the word "believe" should never be used wrt science," e.g., "do you believe in QM?"

It is your stubborn resistance (or fear of embarrassment) that's the prob. here.  

Bell clearly implied that the parameter found in a conditional probability is a symptom of nonlocality (or else he just didn't command probability math).  In fact nonlocality would enter through wave function collapse.  Confusing story!  Confused story tellers.

FYI: per rumor, Bell confessed to a confidant that he never actually systematically studied probability theory, but, just like many physicists, learnt what he does know "on the job."  (I'm neither the confidant nor rumor monger, however.)

The answer to your question is very very simple: prior cause.  BTW, it is not the setting itself that causes a detection in the distant detector, but the appropriate value of lambda to enable response to that setting.  The experimenter cannot ever control or even 'see' the value of lambda, only detections when both the detector is set to a given value and Nature has delivered a vulnerable-to-that-value entity to detect.  I.e., the presence of a outside parameter in an expression of a conditional probability does not indicate a causative interlink between measuring stations, it gives only a criterion for selecting data points for analysis of correlations.

The main issue is, do experimental tests as done prove that QM is nonlocal?  Since there are many (~25) examples of classical phenomena which yield the thought-to-be exclusively QM correlations as well as numerous simulations to various degrees of detail, the claim for QM (mystical) entanglement is spurious or false. 

I give up, Heraclitus.

I don't blame ya!  Hopeless cause!