To those who refer to Bohm's mechanics!

All the QM is about what we can measure. Bohm supposed that there exists a level below what we can measure. QM formulas don't contradict the existence of such a level, they don't refer to 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. He accepted the QM formalism and its conclusions entirely. But he believed in a subquantal level, and added formulas for that. These formulas are bound to lead to the same predictions on measurement results, as the QM.

However, Partha Gose indicated an experiment showing that the Bohmian velocity conflicts with the experiment – for more details, one can find his articles in quant-ph. I also indicated such an experiment - it is bound to appear in Journal of Modern Physics, the abstract appears on my profile page.

But these articles just prove that a particular formula in Bohm's formalism, the Bohmian velocity, is wrong. The idea of a particle guided by the wave-function, is more general, and it wasn't disproved. All the more, the idea of a subquantal level wasn't proved or disproved.

Sofia,

I see that you moved here from your former question on « Is the locality assumption necessary in Bell's inequality? », to which I gave an answer a few moments ago. So, although not an expert in Bohmian QM, I’d answer to this new question in line with the former one. As experiments in the years 1990 - 2000 (Aspect, Zeilinger, etc…) showed that Bell’s inequalities were violated, there are no « hidden variables ». To my knowledge, Bohmian QM is a.o. adding position in the formalism, which could be seen as putting an « hidden variable » (compared to the standard Copenhagen formalism) into light. This would at first sight be in discredit of this theory.

However, I don’t know all subtle details of Bohmian QM nor of Aspect and Zeilinger’s experiments.

So, please find herewith some information on work by Prof. Jean Bricmont of the University of Louvain (Belgium). He is for already a long time known as a supporter of Bohmian QM.

He just published a book on “Making Sense of Quantum Mechanics” at Springer (2016). See enclosed link :

http://www.springer.com/gp/book/9783319258874

 I also join some documents in English from him which could be interesting to you (there are also in French, if you have translation means …).

http://www.springer.com/gp/book/9783319258874

Dear Guilbert,

First of all thanks for articles, but to put it in short I am at a loss: with Bricmont 2011 I disagree, and Bricmont 2012 told me nothing new. I am sorry that you didn't notice in my first comment, Bohm's formalism was already disproved, first by Ghose, and cca. 16 years later, by myself. There are experiments with which Bohm's formula for velocity clashes.

On the other hand, if Bricmont can explain how an object can be at oncle in two places, I would be VERY interested to see. Unfortunately, from my house I have no access to the Springer articles. Can't you tell me the main idea of Bricmont? I would be very curious on that.

Third thing: to your attention, all the experiments until today dealing with hidden variables, suceeded to rule out ONLY local hidden variables. Zeilinger hoped to rule out non-local hidden variables, but was strongly criticized and proved wrong by two smart and lovely Swiss physicists, Colbeck and Renner. (Who says that geniuses cannot do mistakes?)

With best wishes,

Sofia

Dear Sofia,

Thank you for your answer and the last information on Zeilinger and the Swiss physicists. Concerning the disproval of Bohm’s formalism by Ghose and you, I actually noticed your first « comment », but (probably wrongly) interpreted it as not too bad for Bohm because of the positive turn of the last paragraph (« But these articles just prove that a particular formula in Bohm's formalism, the Bohmian velocity, is wrong etc…..»). Concerning more recent information on Bricmont, I’ll check the possible.

Regards

Dear Guibert,

You understood well. Indeed, I don't feel enough satisfied with just disproving Bohm's formula of velocity.

By the way, I wonder why, in 16 years from Ghose's first proof, the Bohmians didn't suggest a better formula. The fact that keep silence seems strange to me. Ghose's proof (experimentally implemented by Brida) should have worried them a lot.

At present, I am indeed trying to see whether a proof is possible which would rule out the very idea of a particle guided by the wave-function, with no specific assumption about velocity.

Of course, the idea of "realism" is much more general than the Bohmian particle.

(Let me tell you something in addition. Did you ever hear of the "Free will theorem" of Conway and Koshen? It is a very interesting proof. It attacks a more general class of hidden variables than local hidden variables. They prove that if such a class of hidden variables exists, we, the human beings, are mere robots that act according to pre-determined instructions, i.e. our decisions are not free. But the proof is very difficult.)

Well, indeed, if you can get that article of Bricmont, I would read it gladly.

Best regards!

Dear Sofia,

The realism in physics is to work from experiment. If we believe that the photon is a particle the double slits experiments at low flux of photons give a way to have a doubt on the wave approach see: “Interferences and periodicity”, on my ResearchGate site. Now we have to understand why the wave function seems a good approach?

Let us now consider the hypothesis of Louis de Broglie of a wave associated with the electron which has led to the discovery of the wave equations. It leads to extend the notion of continuous to the scale of the interactions between the constituents of the atom. Thus the continuous appears to us always intimately linked to the discontinuous. But it is necessary to keep in mind that the point is a mathematical concept that has no volume and hence no physical reality. The continuous subsequently appears a convenience but one as to keep in mind that material reality remains the discontinuous. It was in noting that light comes to us from atoms, therefore emitted from a finite set of atoms, that Einstein was brought to propose the hypothesis of the photon. Come back then to the symmetry between the motion of a mobile and the propagation of a wave which led de Broglie to associate a wave to the electron; It is also possible to associate a flow of material particles in the wave, for example of light, thus joining the hypothesis of the photon of Einstein. However if the number of photons becomes small, then the support of the continuum which is the wave can no longer interpret interference; one has then to consider the stocking of the photons where the interferences are observed. See: “The wave and the quantum state” on my RG site.

Yours, Xavier

Dear Sofia, I can answer your question with an interpretation “within the classical mechanics” within my theory, where I perform analysis of the “A.3 Experimental Test of Bell's Inequalities Using Time-Varying Analyzers Dr. Alain Aspect in 1982.” On page No. 207 of the “The Three-dimensional Complex Space Theory”. See: http://dx.doi.org/10.5539/apr.v4n2p190 or https://www.researchgate.net/publication/282359307_TCS_Theory_-_Space_properties_quarks_and_particles-2?ev=prf_pub

Data TCS Theory - Space properties quarks and particles-2

Observer A puts a pair of gloves in two boxes and sends one box to each of two observers B and C. Since A knows which glove s/he put in which box Is there any doubt as to the physical definiteness of the state of each glove? Of course not. Now suppose observer A sets up the production of a pair of entangled particles, and sends them off to B and C. Unlike the gloves s/he does not know which particle went where. The information as to which is which is not available anywhere in the universe. Now suppose A peeked at the particles before they left. Then that information would be available before B and/or C detected it, but known only to A. Simple logic tells us that B and C must confirm what A already knew. Since the information available to B and C however cannot depend on whether or not A peeked, the particle states must also be definite regardless of whether A peeked. The difference between the glove example and the QM particle example lies purely in the knowledge available to A. In both cases the individual states are definite prior to detection. Non-locality is a consequence of (a) an observer's limited information and (b) their imposition of a space-time frame of reference.

Dear Sofia,

On « Springer’s article » by J. Bricmont, I cannot give a view. This is because it is in fact a new book (entitled « Making Sense of Quantum Mechanics » and published by Springer in 2016 – see link in a former post), not an article. So the book has first to be bought - or consulted in university libraries having bought it (but it cannot be freely diffused anyway …) - to know the content of the chapter entitled « The de Broglie – Bohm Theory » (pp. 129 – 197).

The only thing I can do for the present is to enclose an older article from J. Bricmont which is freely available and which I think correctly summarizes his main ideas as they are probably still unchanged today (see enclosed article : Bricmont_meaningWF.pdf)

I can also quote hereafter an interesting comment on the issue taken from a chat. The comment was made in French, so what follows is a free translation (by me) of it into English :

« Jean Bricmont is professor of theoretical physics at the University of Louvain in Belgium. He is an established « bohmian ».

It is correct to say that the theory of Bohm - which should rather be called « theory of de Broglie-Bohm » - assumes that there exist definite positions for the particles. These positions are solutions of equations of motion very different from the equations of Newton. These differential equations make use of a « quantum potential » which fills the space and is calculated from the wave function. When the system involves two or several particles, this quantum potential makes that the particles have an instantaneous influence on each other. It is then thanks to this non-locality that it is possible to introduce « hidden » variables without contradicting the violation of Bell inequalities, as in standard QM.

In fact, it is possible to show that the theory of Bohm exactly predicts the same probabilities as standard QM at any time in the future, on the condition that the probability distributions of these « hidden variables » comply with Born’s postulate at the initial time. Some people go even beyond : Detlef Dürr, from the University of Munich, showed that these initial distributions are « typical » in the sense of statistical physics. In the theory, the quantum evolution is fully deterministic. The probabilities only appear because one cannot experimentally control all initial values (see the book "Bohmian mechanics" by D.Dürr and S.Teufel, published by Springer). This is the reason why Dürr states that Bohmian mechanics outstrips standard QM because it demonstrates what is only a postulate in standard QM. This is however arguable as Bohmian mechanics introduces a new postulate, that of the quantum potential equation.

(…)

The major problem when one wishes to take this theory seriously is that the quantum potential creates a kind of absolute simultaneity. In fact, it defines a privileged « foliation » of space-time, which is in plain contradiction with Lorentz invariance, and thus with Special Relativity. It is on that fact that it hurts. Nobody really formulated a relativistic theory of Bohm allowing to make all the calculations which are performed in relativistic quantum theory. This is not a priori impossible if the foliation defined by the quantum potential depends on the wave function: in this case, it could endorse the status of a particular solution non-distinguishable from other possibilities determining other foliations. (…). But, to my knowledge, such a theory has never been formulated.

For these reasons, but also because this theory doesn’t introduce anything really new in our knowledge of physical processes, a majority of physicists don’t adopt it, maybe in line with Occam’s razor.

On these subjects, I recommend reading the books of Roland Omnès and Frank Laloë. »

One could add that Bohmian supporters could also try to correct the formula for velocity as you suggest it.

Concerning Bricmont’s article, you might already be aware of most of the content of it, but I nevertheless send it in case you would encounter any useful hint in it and for the other potentially interested followers.

On my side, not being an expert in Bohmian mechanics, I won’t take position for or against. I just wish to follow the thread for the light it could throw on the fundaments of QM.

To be noted : J. Bricmont is on RG, though not very active as it looks like. However he would most probably answer your questions for specific enlightment via his RG page.

https://www.researchgate.net/profile/Jean_Bricmont

Dear Guibert,

Many thanks for kindly quoting from Bricmont. I am very glad when instead of telling me "read my article", or "read that article", people explain the main idea, even if it takes a good couple of lines.

Now, Bohm's mechanics was disproved, I mean, at least the Bohmian velocity formula as I said in other comments of mine. First, P. Ghose disproved that formula, in the years 2000-2009, and now I provided an additional proof. It displeases me a lot that the Bohmians keep silence of Ghose's article (my one is very new, it is about to appear soon.) I wrote a letter to Dellef Dürr, but he never answered me. (Since I am terribly busy now, I can't engage in writing to additional acquaintences, but I intend to do that as soon I have more time.)

But, you told me that Bricmont said that he can explain how an object can be in two places at once. How you know of this saying of him? Where did you see that? I can't ask Bricmont about a saying that I don't know where it appeared.

With best wishes,

Sofia

Sofia D. Wechsler, What I remember in relation to Ghose is that this has been refuted already long ago, a simple search gives http://arxiv.org/abs/quant-ph/0108038v1 but afair there has been more.  

 Charles, de Broglie-Bohm theory is, of course, consistent, and your personal attack against Bohm disqualifies only yourself.  

Dear Sofia,

I can't remember having told that Bricmont said he could explain how an object can be in two places at once. Was it in this thread or another one ? Anyway, I don't think Bricmont ever said anything like this (at least to my knowledge). It must have been that one of my sentences in a former post gave the impression of such a claim (as a native French speaking, my English is far from perfect !), but I assure you that you can consider it to be false.

Kind regards      

Mathematics exists everywhere in nature.  It is always discovered and never invented.  The only thing we invent is the notation.  

I think that mathematical laws can be found in nature if you look for them, but they are just a "part of" nature, nature being bigger and not man-made. Mathematical laws would be a subset of nature.

This looks to be the recreation time in this thread :=)

“The most incomprehensible thing about the world is that it is at all comprehensible.” (A. Einstein)

Nature is structured. As making part of nature, our brain is structured.

Making philosophy / logic is inventing coherent descriptions of structures.

Making mathematics is making philosophy / logic in the frame of a specific language called mathematics.

Making science is discovering structures in nature.

Sometimes, invented coherent descriptions of structures match natural structures. They are then called models and/or theories (in function of their extent), involve laws and hold as long as they are not contradicted by experiment and / or observation.

An example is natural selection.

When the models and / or theories use the specific language of mathematics to describe the discovered structures in nature, they are called physical.

Examples are Newton’s mechanics, Einstein’s General Relativity Theory, Standard Quantum Mechanics and Bohmian Mechanics.

I think there is as much logic in nature laws as in nature and as in mental (conscious ?) reasoning. Otherwise nature as we know it could never exist. Without logic, nothing could become structured and nature would be pure chaos, entropy.

Nature doesn't change it's mind -- or conspire to confuse us -- just because of an observer's lack of information.

In mathematics, every natural number has a successor.  That's not true in physical reality, there is always one number that has no successor, even if it is very large.  A mathematical model can only be an approximation, therefore it has certainly no philosophical meaning.

We must be able to count objects exactly, but that's only an assumption.  For example, our models can describe the interaction of two universes, but there is only one.  How can these models be exact for fewer particles, while in the extreme case the very notion of number isn't even defined, since there is no number of universes?  All that we can say is that the models are validated within the experimental errors, and that's not a philosophical statement.

Charles:

How do you define an "object"? There is a judgment that must be made about what we are counting that is ours alone, not part of nature. No two balls are exactly the same. Even two electrons have different locations or different momenta. Counting "objects" always depends on a selection of defining characteristics that ignores the differences.

Bob, I was quoting Charles. You have merely repeated my point.

Dear Bob Skiles,

There is so much talk in discussing this question of mine that I lost the possibility to understand who answers to whom. Maybe your last post is an answer to somebody. But, anyway, to your attention: my question about realism is not restricted to local realism, it mainly refers to NON-local factors that may, eventually, influence the result of a measurement.

Best wishes,

Sofia

Charles, von Neumann's theorem has not been criticized for being wrong, it is not, but for making unreasonable assumptions.  So, no, dBB theory is indeed not a counterexample to von Neumann's theorem, it is simply a realistic and causal theory which makes, in quantum equilibrium, the same predictions as QT.  Which is what matters.  Not if it fulfills all assumptions made by von Neumann. The one who ignores theorems is you - namely you ignore a well-known equivalence theorem with nonsensical claims that dBB theory is somehow inconsistent.  

It is, of course, contextual.  But the conclusions you make from this are .... simply absurd. 

I don't think it is even in principle possible to disprove realism experimentally.  The aim of science is to study reality.  So, this would have to be a proof that science is meaningless. 

Actually there is, of course, no reason at all to doubt.  There are reasonable realistic and causal interpretations.  The situation is much worse for fundamental relativistic symmetry.  Some weak relativistic symmetry restricted to observables is unproblematic, not anything beyond this is dead. 

Charles, sorry, but this is nonsense.  And, no, I do not dissociate myself from Bohm's position, because dBB theory is a counter example to what was claimed to be the result of von Neumann, and what you seem to believe is the result, namely that there can be no hidden variable theories equivalent to quantum theory.  

Bohm's equivalence theorem is, of course, about all possible quantum measurements. For the subset of position measurements this was already known long before by de Broglie, who was at that time unable to prove the equivalence for all measurements.  

And your primitive attempt to distort what I have said disqualifies you already completely. 

Charles, read Bell's paper, it is about something completely different. Namely, "the formal proof of von Neumann does not justify his informal conclusion".  

Then, read Bohm's paper, and understand the meaning of phrases like "Let us now consider an observation designed to measure an arbitrary (hermitian) "observable" Q, associated with an electron". 

What makes a theory contextual is that it is not about "measurements", but about the results of interactions which depend not only on the "system", but also on the "measurement device".   And there is nothing which pops in and out of existence. All parts have the same type of "hidden variables" (in fact not so hidden, because what we observe in the real world are these "hidden" variables of macroscopic objects), namely trajectories in configuration space.  

Anyway, learn the theories and read the papers you criticize before criticizing them.

As an outsider (and independent) thinker trying to grasp the fundaments of Quantum Mechanics (QM), I must conclude from the discussion till now that all Standard QM (SQM = Copenhagen QM) rules out the realism hypothesis. This is particularly clear from the excellent example of Charles Francis with Bertlmann’s socks (to explain entanglement). If we look at one sock to see if it is red (= to measure its redness/greenness), if it is red, we know the other is green and if it is green we know the other is red. Similarly, if we look at one sock to see if it is blue (= to measure its blueness/orangeness), if it is blue the other is orange and if it is orange the other is blue. Now, if we have “measured” it is red, and “measure” it again just afterwards to check if it is still red, we find that indeed it is still red. But if after having “measured” it to be red we “measure” it again just afterwards, to check if it is blue, i.e. we measure its blueness/orangeness instead of its redness/greenness, we will find that it is either blue or orange. But this will not change the colour of the second sock, because the colours are no longer entangled. So the only “reality” you get is one which depends on what you measure and when. There is no place for subquantal parameters which would fully determine reality outside measurement. So Copenhagen interpretation obviously rules out the realism hypothesis. And if you stick to SQM you never will accept this hypothesis : there are no hidden local (but also non-local) parameters, there is no existing reality outside measurement, etc.

What bothers me is the ambiguities that seem to have accompanied SQM since the beginning.

Take for instance following quotation from Werner Heisenberg : « We can no longer speak of the behavior of the particle independently of the process of observation. » (1958)

In fact this sentence could receive 2 completely different interpretations :

1)      The particle does not exist with a defined behavior if it is not observed. Therefore « we can no longer speak of the behavior of the particle independently of the process of observation »

2)      The particle exists but its behavior will definitely be influenced by the process of measurement of its physical characteristics. Therefore « we can no longer speak of the behavior of the particle independently of the process of observation »

Interpretation 1) is positivist (typical SQM) and interpretation 2) rather realist (recognizing that we don’t know the totality of the influences of the process of measurement on the behavior of the particle).

Similarly, let’s take an example in the present thread. I understand from part of the discussion that Bohm’s theory can be seen as not being a counterexample to von Neumann's theorem but that it does not fulfill all assumptions made by von Neumann (unreasonable assumptions are ruled out). On another hand, Bohm himself would have seen (and Bohmians would still see) his Bohmian mechanics as being a counterexample to von Neumann’s theorem, but no sensible criticisms against “unreasonable assumptions” by von Neumann would have been made neither by Bohm nor by Bell. So Bohmian mechanics and von Neumann’s theorem disagree in a way but don’t disagree in another way depending on the observer. Or, better said, they disagree on point A and agree on point B for observer X while they agree on point A and disagree on point B for observer Y.

This kind of ambiguities and subtle variations of interpretations is typical of many writings and discussions on QM and renders it extremely difficult to grasp its fundaments. In spite of this, QM has obtained fantastic results. Why then can it not be coined in a vocabulary understandable by everybody in the same manner ? Probably, because the world described by QM is so different from the intuitive everyday world we know, that the full vocabulary for it doesn’t exist yet …..  

Conclusion : So, Sofia, as an answer to your question, one could say that the whole SQM - which has proven very powerful and has given fantastic results - disproves the “realism” hypothesis. However, because of existing ambiguities in the present structure of this SQM theory - and its relationships to sister theories - one cannot presently rule out that the “realism” hypothesis would prove to be nevertheless correct in the future.

Charles,

I did not want to talk with you because of your impolite remarks, but I can't stop my revolt.

DO YOU CALL JOHN BELL, AN IDIOT?

How do you dare? What is this kind of language? You may criticize whomever you want, but keep a civilized way of talking.

I also criticized Bell (from another point of view), though, with the due respect which is normal in a scientific polemic.

I require from you to CORRECT YOUR POST. Please do it, or, else, withdraw from my question! I don't admit the site of my question to be transformed into a garbage basket.

It seem time to stop discussion with Charles.  Let's note that he repeats primitive and aggressive  personal attacks against established scientists and names peer-reviewed and often cited papers "inconsistent and mathematically inept".  This is a type of behavior is typical for people whose "arguments" are unable to survive a civilized discussion and usual peer-review. 

Charles,

I am not against whatever criticism you want to do. Just, please talk civilizedly. Bell was not on RG. If he would have participated to one question of mine, and use an impolite language, I would have required from him to withdraw from my site. Absolutely!!!

You are on my site here. Be polite! There are other words that can express criticism, severe as the criticism may be, and still civilized. You are not here to punish Bell for an impoliteness, by using another impoliteness.

I stronly protest against talking rudely.

                           *******************

Now, to physics. You say that Bell refuted the equality

(1) = + .

Of course he did, though, for dispersion-free subquantal states. One dispersion-free subquantal state corresponds to a well defined value of the hidden variable λ. The value obtained for an operator Ȃ is given by the function

(2) A = f(MA,λ),

where MA reflects the setting of the apparatus. Of course that a value produced for the operator (Ȃ+B̂) in some trial of the experiment, doesn't have to be equal to the the sum of the values produced for the operators Ȃ and B̂. Bell even gave an example with noncommuting operators Ȃ = σ̑x and B̂=σ̑ y . The operators σ̑ x , σ̑ y , and (σ̑ x + σ̑ y ), are non-commuting, they require three different orientations of the apparatus, therefore they can't be measured together. Thus the arguments in the function f in (2) are different. Even λ may differ. 

As Bell said, the propert (1) "is a quite peculiar property of the quantum mechanical state, not to be expected a priori".

Then what's your problem?

Guibert, it seems you have been confused by Charles Francis. The Copenhagen interpretation is certainly not a realistic one, many of its proponents have bee positivists, but this does not mean at all that it would rule out realism.  

Then, there are known hidden variable theories.  They contain hidden causal but not Einstein-causal influences, and are realistic, dBB theory is even deterministic.  The equivalence of dBB theory and SQM is also a proven theorem.  

About von Neumann's theorem, nor Bohm nor the proponents of dBB theory think that von Neumann's theorem is formally wrong. It makes assumptions about hidden variable theories which dBB theory does not fulfill, so that there is no conflict at all.  The only conflict one can see here is a conflict with a sloppy informal summary of von Neumann's theorem as excluding hidden variables completely.  

Ilja,

Ok, I understand : thus dBB theory does not enter into the category of hidden variable theories corresponding to the assumptions made in von Neuman's theorem. So dBB does not contradict von Neuman's theorem. It is just out of its scope.  

Dear Sofia,

I would like to add one hint to the conversation, based only on experimental evidences shown in the attached picture. Reasoning or math is vain if it fails in front of evidence, meaning that there is something wrong in the line of reasoning (incorrect assumptions  or the problem ill posed).

The quantum entaglement is a phenomenon totally non local, and cannot be built up by entities travelling at any speed or any hidden local variable. The wave function is an entity which represents so far the only way to give account of such phenomenon and being as such it has to be considered a real entity. Either we conceive and accept that there is a "holism" in quantum mechanics behind these phenomena or we give up understanding such phenomena. No explanation can be given according to any theory involving finite speed of energy.

dBB theory produces determinist results for all "measurements".  von Neumann makes additional assumptions about relations between different "measurements" which cannot be done at the same time. 

Guibert:

That is not true. It does not follow from your preceding argument. What follows is that any underlying reality can be perceived differently by different observers. But we already know that from relativity theory.

What is more, any observer can deduce the nature of that underlying reality by a straightforward frame transformation. Simply transform to the rest frame and then rotate until the angular momentum ("spin" since in the rest frame) ) "component" is at its maximum (m=j). The resulting intrinsic information (i.e. "reality")  has no spatial or other observer-dependent properties. These are assigned by the observer when they transform to their frame from the intrinsic frame. What is more, that assignment is made when the observer sets up their apparatus, not at the time of measurement. The underlying (intrinsic) state then has a reality regardless of the frame the observer chooses. The observer's uncertainty about that reality is due to the fact that they don't know how to transform to the intrinsic frame until they measure the state in their own frame. 

Mike,

This quotation is not the result of a demonstration. It is just a short summary of what you get with the colours of Bertlmann’s socks as a metaphor of quantum measurement. It does not involve the observers nor any formalism. This is why the word « reality » is put into quotation marks. I used it as a wink to Sofia’s question but probably I shoudn’t have …

Charles,

You wrote : “Von Neumann asked can there be any other parameter outside of Hilbert space, which can lead to the same predictions as QM. He proved that there cannot. ……….. Fundamentally, that is why Bohmian mechanics cannot be consistent”. So the key point is that dBB uses positions of the particles as hidden variables in a separate equation (which leads to determinist results for all measurements) although the positions already are inside of Hilbert space ? And this renders the theory contextual ?

Ilja, and all the other friends,

The so-called equivalence between the QM and the dBB theory is incomplete.

Bohm thought that he proved such an equivalence, i.e. that his formalism predicts the same results for any experiment, as the QM.

Well, this is not true. QM predicts not only certain probability distributions encapsulated in the absolute square of the wave function. It also predicts 2nd order correlations, i.e. given that a particle was detected at some place r1, what is the probability to detect another particle at r2. This is the famous HB&T experiment.

Bohm didn't think, in his proof, of 2nd order correlations. As I mentioned in many other posts, Partha Ghose, an eminent Indian physicist, proved that Bohm's formalism make wrong predictions about the 2nd order correlations. Ghose proved that Bohm's formula for velocities of the Bohmian particles, is wrong.

Now, on the other hand, the failure of dBB, is not necessary a failure of the general idea of realism in QM. The fact that a velocity formula in dBB doesn't cope with the experiment, is not a general proof against realism. 

Dear Stefano,

Of course entanglements display non-locality. Now, "holism" is just a word, one has to explain what is the physical phenomenon that stays behind it.

This physical phenomenon is well-known to us - joint phases. We are aware of that, it lies under our nose, but we ignore it.

I explained these issues in my article "Is Qunntum Mechanics Nonlocal? The Violation of Bell's Inequalities . . . ", but I am aware that it is adifficult article.

So, I will explain the main idea below: when we create an entanglement, e.g.

|ψ> ~ eiθ|x>A |x>B + eiφ|y>A |y>B

we endow each coupling with a joint phase with respect to the vacuum. E.g. the coupling |x>A |x>B has the joint phase θ, and the coupling |y>A |y>B has the joint phase, φ. These phases are non-local physical quantities. Such a phase is common to both wave-packets it precedes, as if those wave-packets were at the same place. When passing through beam-splitters, the joint phase-factors (amplitudes) add up complexly, creating new joint phase-factors.

Sometimes, however, the joint amplitudes mutually cancel. For instance, assume that for the coupling |u>A |v>B the joint amplitude cancels up. Then, if for the particle A we catch the wave-packet |u>, for the particle B, at the output of the device (beam-splitter) that should produce the wave-packet |v>, all the contributions cancel out mutually.

These things are trivial. Here is the "holism".

@ Charles: Of course linearity implies the equality you display:

= +

It is true for all quantum states. But if you assume that quantum states are built up from different underlying states, then for *these* states it need not be reasonable at all to require this relation, since A+B is an observable altogether unrelates to either A or B when the two do not commute. I always understood that to be Bell's objection to von Neumann's proof. It is true that I have nowhere seen von Neumann's original proof.

In any case, the question is not whether von Neumann's theorem is correct. It is whether its intepretation, as precluding all interesting hidden variable theories, is correct. That cannot be proved easily, since one has to give a precise definition of what one means by a hidden variable theory.

At the very least, I believe Bell has clearly shown that, for a spin, it is possible to have a reasonable hidden variable theory. This is a counterexample to von Neumann, in the sense that a reasonable theory can be built which does not satisfy von Neumann's definitions (that follows from the fact that von Neumann's theorem does not, I believe, assume the Hilbert space to have dimension >=3).

As for Bohm, one should simply define what one means by a hidden variable theory. It will turn out that Bohm is one, it is deterministic, but has some strange features, among which is non-locality.

Charles,

you don't read what is written? Can't you understand that Bell spoke of results of SINGLE TRIALS in measurements, i.e. of single results and NOT of averages? Bell spoke of A, B, and A + B, as single values, not of , , and .

All the rest that you say,

==> "Bell nowhere addressed why we have the mathematical structure of quantum theory, . . . . .  In fact it is difficult to see that a basic change to Hilbert space is possible, . . .  "

 is alien to Bell. He didn't seek to change the Hilbert spaces, as you say there. He accepted the structure of QM completely. But in a SINGLE TRIAL of the experiment, one cannot even speak of a value of some observable A + B, if these A and B don't commute, because you can't measure them together.

Look at position and linear momentum. Measurement of position you do by letting the particle fall on a photographic plate. To measure linear momentum you insert a magnetic field or some diffraction grating.

So, what you talk about? Read what's written!

And stop being nervous, take it easy! We, all the rest of the users, we discuss the things calmly. What happens with you? Are you at war, is your life under threat?

von Neumann assumes that all variables have to be assigned to the system itself, instead of the interaction with the "measurement device", and that sums of non-commuting operators have to be described by sums of the corresponding hidden variables, despite the fact that the corresponding measurements have nothing to do with measuring above parts and computing their sum. These are nontrivial assumptions, they do not hold in dBB theory, which is, nonetheless, a deterministic and realistic theory, in a quite obvious way.

Mike, no, this has nothing to do with different observers and their confusion about who is at rest.  Of course, the results depend on what you measure, but whatever you "measure", the result depends in dBB theory also from the state of the "measurement device".  But all observers will agree about the result of the particular experiment. 

Sofia D. Wechsler, I disagree that Ghose has proven such a non-equivalence. He has made such claims, but they have been refuted.  One problem with such second order correlations is that if you measure position, you distort the wave function and cannot simply use the old wave function with the measured position as if it would be the Bohmian position.  One can argue that weak measurements can be used. But I doubt they really measure the position, and suspect they in fact measure $| \psi|^2$.

Ilja,

who refuted Ghose's claims?

For refuting someone's claims one has to know what's in the fellow's articles.

A terrible mistake that people do, it to assume that great physicists don't know elementary facts in physics. Well, Ghose, who is indeed an illustrious physicist, did not do such an unpardonable mistake as you think.

You have to know that the HB&T experiment does not refer to a single particle wave function, but a TWO-particle wave-function.

Well, you cannot measure position without measuring position, and by measuring position you don't distort anything related with the operator position, but with the linear momentum.

Next, 2nd order correlations are well-known in QM, it's not a confusion, and physicists working in QM are supposed to know what they are and how to use them. In particular Ghose knew. By the way, I proved by myself Ghose's result. Moreover, I provided an additiona proof, independent of Ghose's proof (my article is about to appear).

I wouldn't recommend Ghose's proof and conclusion, if I wouldn't know it wery well. And I repeat, 2nd order correlations are common topic in QM, and they regard 2-particle wave-functions.

Charles,

first of all, don't distort why I wrote. I didn't "fill my post with rude accusations". To ask somebody if he didn't read, has nothing rude in it. It happens to people to read not attentively. But you jump to accuse me of rudeness for covering your own insults. 

Let me remind these "polite" words of yours:

==> "You responded . . . showing only that you know absolutely precisely nothing about the mathematical structure of quantum mechanics. This is supposed to be a site for genuine researchers, not for people those like yourself who are not happy because they disagree with science."

And to call John Bell an IDIOT, is polite?

AS a general rule, it's top mistake to think that great thinkers were unable to understand QM. You'd better question yourself whether the misunderstanding isn't on YOUR side. But you preferred to insult, and that includes not only J. Bell, but also all his followers, a long line of brilliant physicists: Clauser, Horne, Shimony, Holt, Aspect and all his team, Rarity, Tapster, and their  team. They all agreed with Bell. All are IDIOTS?

HOW DO YOU DARE? To doubt is legitimate, to insult is forbidden.

No, here are Bell's own words, for everybody to see:

"His essential assumption (i.e. von Neumann's) is: Any linear combination of any two Hermitian operators represents an observable, and the same linear combination of expectation values is the expectation value of the combination. This is true for quantum mechanical states; it is required by von Neumann of the hypothetical dispersion free states too. In the two-dimensional example in Sec. II, the expectation value must then be a linear function of α and β. But for a dispersion free state (which has no statistical character) the expectation value of an observable must equal one of its eigenvalues. The eigenvalues (2) are certainly not linear in β."

Now, do you see what Bell wrote? I repeat his words, "for a dispersion free state (which has no statistical character) the expectation value of an observable must equal one of its eigenvalues." And I also explain again, a dispersion-free state corresponds to a single value of the hidden variable. Indeed, such a value produces one and only one of the eigenvalues of the quantum state. On the other hand, a statistical average is produced by the statistical collective of values of the hidden variable, i.e. by averaging over all the eigenvalues of the quantum state.

Prof. F Leyvraz explained you these things too.

But, since I am sure that you will add more insults, more distortions of what I said, or other bad things, I STOP THE TALK WITH YOU NOW.

Moreover, if you don't take back your insults at Bell, I require you to WITHDRAW FROM MY QUESTION.

Sophia, http://arxiv.org/abs/quant-ph/0108038 

The argumentation of Charles Francis becomes completely abstruse, given that he starts to deny that dBB theory is deterministic.  To find out if a theory is deterministic or not is trivial. All one has to do is to look at the equations, and the equations of dBB theory are obviously deterministic. 

And, as usual, he continues to falsify Bell claiming "He was not talking about individual measurements but about mean quantities".  To quote Bell: "There is no reason to demand it individually of the hypothetical dispersion free states, whose function is to reproduce the measurable peculiarities of quantum mechanics when averaged over".

My dear Ilja,

My name is not Sophia, but simply Sofia.

About Charles, as I said in my last post to him, I find his vocabulary unbearable.

Now, regrettably, it's true that John Bell wasn't a polite fellow. It is true that he said about von Neumann's proof that it is "silly", and also added "You may quote me on that: The proof of von Neumann is not merely false but foolish!"

If Bell (may rest in peace) would have tried to contribute to my question while using such expressions, I would have shown him the door. Also, Bell's impoliteness is not an example to follow, and I don't admit Charles' behavior.

As far as I understand, Bell claimed that von Neumann's proof was worthless. The proof regarded systems whose Hamiltonian is a sum of two non-commuting observables. Bell said "There is nothing to it." But such systems exist, von Neumann gave an example. Though, I won't get into their dispute (about physics - leaving aside Bell's vocabulary), because I don't examine such systems s.t. I don't need that proof. 

My best wishes,

Sofia

Dear friends,

I just want to share with you some more physical information that I have about that Bell-von Neumann dispute. Again, as I said in my former post, I consider Bell's style of speaking as unacceptable.

Von Neumann defined "dispersion-free" states in the following way: any physical quantity R in that state has to obey

(1) avg(R2) = (avg(R))2.

This definition is easily obeyed by the dispersion-free state with which worked Bell, and which was defined by (ψ, λ), where ψ is the wave-function and λ is the value of the hidden variable.

Up to this point it doesn't seem that there was any conflict between the two opponents. But von Neumann added a requirement for physical quantities:

(2) avg(aR + bS) = a avg(R) + b avg(S).

where R and S are two arbitrary physical quantities, and a, b, two constants. This requirement played an important role in von Neumann's proof that dispersion-free states don't exist.

It's this requirement that Bell strongly criticized, inclusively by giving a counter-example. Bell claimed that while this requirement is satisfied in quantum states, 

(3) = a + b,

i.e. when the average is taken over the quantum state, it should not be imposed for dispersion-free states when R and S are imcompatible physical quantities. He illustrated his claim with an example, which essentially says that in a dispersion-free state, is an eigenvalue of R, and is an eigenvalue of S; so, if R and S are incompatible, the equality (2) fails.

Ales, physics is a sufficiently complex field, and one first better learns and understands the thoughts of others before starting to develop own ideas. Dead or not, the question is if their arguments are correct or not, and this is what matters. 

And scientists have a good tradition, namely to attribute such ideas not to themselves, but to those who have had these ideas first.  Even if only in a slightly different form.