Impossibilty of hidden variables (Bohm, 1951)

[atyy]

Bohm writes in his 1951 book "Quantum Theory" (p623): "We conclude then that no theory of mechanically determined hidden variables can lead to all the results of quantum theory". He bases his argument on the uncertainty principle. Presumably the argument is not correct, since Bohm himself later provided the first known hidden variable account of non-relativistic quantum theory?

 

[jfizzix]

If I had to guess (so take it for what it's worth), I think Bohm might be saying that non-contextual hidden variables cannot describe quantum theory, but that other local hidden variables might do so.

A non-contextual hidden variable theory is one where the hidden variables are objectively determined, and independent of one's measurement strategy. These models have been disproven in part by Gleason's theorem.

However, there are models of hidden variables where the hidden variables are determined in the context of one's measurement strategy. In other words, if you include the measurement device in the description of your measurements, a model of hidden variables exists that could describe the measurement outcomes. I expect that this is what Bohm provided.

 

[atyy]

Yes, I wonder whether Bohm knew about the non-contextuality qualification when writing his 1951 statement. Or did he mean it without qualification, and somehow later realized he had made a mistake, when he discovered Bohmian Mechanics?

 

[jfizzix]

I think it was only later that the term "contextuality" was used explicitly, but I couldn't say exactly when it started to become a common term. The earliest mention of it I know of is Abner Shimony's 1984 paper:
"Contextual Hidden Variables Theories and Bell's Inequalities".

Bohm may have been referring to the same thing by another name, but I couldn't say for sure.

 

[bhobba]

Yes, I wonder whether Bohm knew about the non-contextuality qualification when writing his 1951 statement. Or did he mean it without qualification, and somehow later realized he had made a mistake, when he discovered Bohmian Mechanics?

The whole thing is tied up with and incorrect proof given by the highly influential (and with good reason - he was one of the greatest to ever live - in many peoples top ten of all time) mathematician Von-Neumann in his book - Mathematical Foundations Of QM. Its not that the proof itself is incorrect - as you would expect from a mathematician of his stature - but the assumption that went into it (it was an assumption on the addition of statistical averages that didn't apply to hidden variables because they can be non-contextual as was later sorted out by Gleason with his famous theorem).

There were people like Grete Hermann that spotted the error - but were ignored:
http://arxiv.org/ftp/arxiv/papers/0812/0812.3986.pdf

Its a bit of a sad history really.

Thanks
Bill

 

[atyy]

There were people like Grete Hermann that spotted the error - but were ignored:
http://arxiv.org/ftp/arxiv/papers/0812/0812.3986.pdf

Here my interest in asking the question is to what extent the error got into the textbooks. For example. Landau and Lifshitz do almost make the error, but maybe not because what they say is that position and momentum cannot simultaneously exist at all times - which is in general true (with some exceptions).

Another famous textbook by Messiah correctly says that hidden variables cannot be ruled out, but he will go with Copenhagen since it is simpler and no experiments distinguish the two interpretations at that time. Messiah's book was published in 1958, so I do also wonder why he made the correct statement. Did he

1) like Grete Hermann (and others like Einstein, according to anecdotes) correctly reject von Neumann's proof because of the hidden assumption of non-contextuality?
2) incorrectly accept the EPR argument that quantum mechanics must be incomplete?
3) correctly accept the possibility of hidden variables because he knew about Bohmian Mechanics which Bohm discovered in 1952 after Bohm's textbook but before Messiah's?

The version of Landau and Lifshitz I have access to is the 3rd English edition, 1977. It looks like their first English edition is 1958, the same year as Messiah's. I don't know when the original Russian text was published.

Its a bit of a sad history really.

Well, despite his error, it still shows von Neumann's enormous good taste in actually trying to investigate the problem, and do it by a theorem.

I guess the sad part is Grete Hermann being ignored. It would be very interesting to know how Bohm came to the wrong conclusion in his book of 1951, and then managed to realize his error by 1952.

 

[TrickyDicky]

So to be clear, both Gleason's and Kochen-Specker theorems only rule out non-contextual hidden variables theories?

 

[bhobba]

So to be clear, both Gleason's and Kochen-Specker theorems only rule out non-contextual hidden variables theories?

Kochen-Specker is a simple corollary to Gleason, but Gleason is notoriously difficult to prove so a direct proof was devised.
http://kof.physto.se/cond_mat_page/theses/helena-master.pdf

What Gleason say is if you assume non-contextuality then Borns rule follows (yes I know some other assumptions like the strong principle of superposition is required but that the main one) - no escaping it and you can't have properties having definite values at all times - specifically with Born's Rule you can't define a 0 and 1 only map on the Hilbert space. However hidden variable theories do not have to be non-contextual.

Thanks
Bill

 

[OCR]

A bit more about von Neumann's proof...

In 2010, Jeffrey Bub published an argument that Bell (and, thus, also Hermann) had misconstrued von Neumann's proof, claiming that it does not attempt to prove the absolute impossibility of hidden variables, and that it is actually not flawed, after all.

von Neumann’s ‘No Hidden Variables’ Proof: A Re-Appraisal...
http://arxiv.org/pdf/1006.0499.pdf

Grete Hermann... http://en.wikipedia.org/wiki/Grete_Hermann

 

[bhobba]

I know Von Neumanns proof from studying his text.

IMHO there was no misconstruing. He gave an operational definition of expected outcomes that easily showed it must be additive. However it didn't apply to hidden variables as a number of counter examples published by Bell and others showed - indeed Bohmian Mechanics is a counter example.

Thanks
Bill

 

[TrickyDicky]

Bohm writes in his 1951 book "Quantum Theory" (p623): "We conclude then that no theory of mechanically determined hidden variables can lead to all the results of quantum theory". He bases his argument on the uncertainty principle. Presumably the argument is not correct, since Bohm himself later provided the first known hidden variable account of non-relativistic quantum theory?

He wrote "mechanically determined hidden variables". Is it posible that even though the formal distinction between contextual and non-contextual had not been made at the time he was actually referring to non-contextual theories with that qualifier?
I mean if by "mechanically determined" he was referring to classical type theories, which were a few years later excluded by Bell's theorem, one can wonder if there is an equivalence between local hidden variables and non-contextual hidden variables theories.

 

[atyy]

He wrote "mechanically determined hidden variables". Is it posible that even though the formal distinction between contextual and non-contextual had not been made at the time he was actually referring to non-contextual theories with that qualifier?

I thought that just meant "deterministic" in the sense that dBB is deterministic with all variability being put in the initial conditions.

 

[bohm2]

Doesn't "machanical" just mean action by "contact mechancs" (or local causality). .So when he writes "no theory of mechanically determined hidden variables can lead to all the results of quantum theory", doesn't he just mean that no local hidden variables can lead to all the results of QT?

 

[TrickyDicky]

Doesn't "machanical" just mean action by "contact mechancs" (or local causality). .So when he writes "no theory of mechanically determined hidden variables can lead to all the results of quantum theory", doesn't he just mean that no local hidden variables can lead to all the results of QT?

That was basically my point, as I commented in the second part of my post.

 

[TrickyDicky]

I thought that just meant "deterministic" in the sense that dBB is deterministic with all variability being put in the initial conditions.

I don't think that could be the case, not in any dBB sense. He would have been ruling out his own interpretation which l'm pretty sure he already had in mind(remember dBB is a modification of de Broglie's own 1920s pilot wave theory) by 1951.

 

[Demystifier]

I have read the relevant parts of the Bohm's 1951 book again and concluded that his arguments against hidden variables were totally incoherent.
(And I suspect that in 1952 and later he would agree with that qualification.)

 

[atyy]

I don't think that could be the case, not in any dBB sense. He would have been ruling out his own interpretation which l'm pretty sure he already had in mind(remember dBB is a modification of de Broglie's own 1920s pilot wave theory) by 1951.

But de Broglie I think rejected his own theory, which is why the first solution of the measurement problem is (to my knowledge) due to Bohm. In his 1952 paper, Bohm does cite de Broglie, and also mentions problems that others (including de Broglie) pointed out with the de Broglie theory, but then goes on to say that he (Bohm) will show that all the problems are not problems.

However, the book is 1951 and Bohmian Mechanics is 1952, so that seems rather close. Did he make a breakthrough between 1952 and 1952, or was the book finished somewhat earlier than its date of publication, as is usually the case?

I have read the relevant parts of the Bohm's 1951 book again and concluded that his arguments against hidden variables were totally incoherent.
(And I suspect that in 1952 and later he would agree with that qualification.)

That's what I suspect too. Is there any history as to how he came to realize his mistake? I mean, from my point of view, the 1952 paper is a big breakthrough. Bell clearly thought it was, and as late as the early 1960s, we have Feynman's wonderful lectures making the same mistake that particle trajectories are not possible. Although the book and paper are so close in publication date that it seems he must have had some inkling of the 1952 development by 1951, it seems such a big breakthrough that I cannot imagine he would have written such wrong or at best ambiguous and misleading statements in his book.

 

[TrickyDicky]

I have read the relevant parts of the Bohm's 1951 book again and concluded that his arguments against hidden variables were totally incoherent.
(And I suspect that in 1952 and later he would agree with that qualification.)

That might well be the case, but we only have the sentence in the OP to judge here. That Bohm was incoherent about QM right until the very moment he saw the light and published his dBB interpretation is a possibility, it is hard to say , I can't really contribute to that debate due to my ignorance about BM and Bohm's writings.

 

[atyy]

I found a number of interesting stories on the history of BM online. They are from sources with good reputations, but I don't know the evidence behind these particular bits.

"David Bohm wrote a quantum mechanics book and also gave a proof that hidden variables theory were impossible. Einstein pointed out a flaw in the argument. Bohm responded with Bohmian mechanics, a hidden variables theory that agrees perfectly with quantum mechanical predictions. His theory was not well-received. David Bohm moved on." http://www.mathematik.uni-muenchen.de/~bohmmech/BohmHome/aboutus_members.html

"It was Einstein who explained to David Bohm at Princeton in 1951 why orthodox quantum mechanics is inacceptable. Therefore and because of his earlier studies of "hidden" variables, Einstein must be counted as a grandfather of Bohmian mechanics. However, he did not like Bohmian mechanics and did not support Bohm's proposal in 1952, probably because Bohmian Mechanics is nonlocal and "too simple"." http://www.mathematik.uni-muenchen.de/~bohmmech/BohmHome/whatisbm_history.html

So Einstein read the 1951 book, told Bohm the argument was flawed (hopefully not using EPR, since that argument is wrong), and that lead Bohm to BM?

 

[bohm2]

Not sure what it means except for some type of "wholeness/holism", but this is what Bohm's co-worker Hiley wrote:

The very term, “Bohmian Mechanics”, lies at the root of much confusion concerning the direction that Bohm’s own thinking took after he first published his two seminal papers in 1952. While I quite understand the wish to give credit to Bohm for his pioneering work, the linking of Bohm’s name with the term ‘mechanics’ has led many to believe that Bohm himself was motivated to find a classical order based on a deterministic mechanics from which the quantum formalism would emerge. That was never his intention. Indeed the content of his book “Quantum Theory” published in 1951, which gives an exhaustive account of the orthodox view of the theory, already sows the seeds of how radical a change Bohm thinks is needed in order to begin to understand the structure that underlies the quantum formalism. In that book he sees the need to go beyond mechanical ideas. In the section headed ‘The need for a nonmechanical description’, he writes,

...the entire universe must, in a very accurate level, be regarded as a single indivisible unit in which separate parts appear as idealisations permissible only on a classical level of accuracy of the description. This means that the view of the world as being analogous to a huge machine, the predominant view from the sixteenth to nineteenth century, is now shown to be only approximately correct. The underlying structure of matter, however, is not mechanical [7].​

In a footnote to this quote he writes “This means that the term ‘quantum mechanics’ is very much a misnomer. It should, perhaps, be called ‘quantum nonmechanics’.”

In Hiley, "Some Remarks on the Evolution of Bohm's. Proposals for an Alternative to Standard Quantum.", 2010.

Anyway, this seems more philosophy than physics because I don't understand what "non-mechanical", means in physical terms either than going against local causality (e.g. non-locality).

 

[atyy]

Here is a late interview with Bohm. It pretty much seems that like what Demystifier said, the arguments in the 1951 book are incoherent, and Bohm himself felt that after a number of discussion with Einstein about his book.

http://www.aip.org/history/ohilist/4513.html
Interview with Dr. David Bohm
By Lillian Hoddeson
At the home of the Bohms, Edgware, London
May 8, 1981

"Well, I had several conversations with Einstein. After writing this book on quantum mechanics, which I wrote to try to understand it (based on my graduate course), I sent a copy to various scientists including Einstein. He wanted to discuss it with me, and we discussed it. He felt that the book was as good as you could present the ordinary point-of-view, but he still didn’t accept it. So we discussed it for a while, and meanwhile I myself had been feeling that it wasn’t all that clear, and that therefore these two things together made me feel that the interpretation of quantum mechanics was not satisfactory. So I began to think about it, and I produced another interpretation, which came out in two papers in Phys. Rev, in 1952, two papers, using a particle and a wave, the causal interpretation I called it. And I discussed all those things with Einstein; we also had correspondence afterwards when I was in Brazil."

 

[TrickyDicky]

Here is a late interview with Bohm. It pretty much seems that like what Demystifier said, the arguments in the 1951 book are incoherent, and Bohm himself felt that after a number of discussion with Einstein

Maybe from the current mainstream view it seems incoherent but the quotes Bohm2 posted from Hiley suggests a different interpretation, he was not looking for a deterministic theory. Perhaps the main mistake with hidden variables theories is to frame them in terms of determinism- indeterminism as there are option outside that false dichotomy.

 

[atyy]

Maybe from the current mainstream view it seems incoherent but the quotes Bohm2 posted from Hiley suggests a different interpretation, he was not looking for a deterministic theory. Perhaps the main mistake with hidden variables theories is to frame them in terms of determinism- indeterminism as there are option outside that false dichotomy.

From the point of view of realistic theories, determinism-indeterminism is a false dichotomy - but if we give up realism (whatever that means) then it is not so clear. So the real question is realism, so that determinism-indeterminism can indeed be a false dichotomy.

What is realism? Realism just means that the theory completely obeys classical probability, as given by Kolmogorov's axioms. The achievement of Bohmian Mechanics is to show that quantum mechanics can be embedded in a theory that obeys Kolmogorov's axioms. In contrast, in a minimal Copenhagen-like interpretation, quantum mechanics is an interface between the quantum state which does not obey Kolmogorov's axioms, and measurement outcomes which do obey Kolmogorov's axioms.

 

[TrickyDicky]

From the point of view of realistic theories, determinism-indeterminism is a false dichotomy - but if we give up realism (whatever that means) then it is not so clear. So the real question is realism, so that determinism-indeterminism can indeed be a false dichotomy.

What is realism? Realism just means that the theory completely obeys classical probability, as given by Kolmogorov's axioms. The achievement of Bohmian Mechanics is to show that quantum mechanics can be embedded in a theory that obeys Kolmogorov's axioms. In contrast, in a minimal Copenhagen-like interpretation, quantum mechanics is an interface between the quantum state which does not obey Kolmogorov's axioms, and measurement outcomes which do obey Kolmogorov's axioms.

In the end we judge theories by how well they predict measurement outcomes, so by the Born rule the physical interpretation of QM is realist according to your definition. BM shows that you can keep that to be the case even if one takes seriously the wave function, quite a feat.

 

[Demystifier]

What is realism? Realism just means that the theory completely obeys classical probability, as given by Kolmogorov's axioms.

This is quite an unusual definition of realism. Have you seen that definition somewhere else, or is it your own definition?

 

[atyy]

This is quite an unusual definition of realism. Have you seen that definition somewhere else, or is it your own definition?

No, I haven't seen it anywhere else. The usual definition of realism is that things should exist independently of any observer. What I was thinking (now maybe I'm not sure this is right) is that in quantum mechanics the pure states are not extremal points of a simplex. In Kolmogorov's axioms, there should be a space of elementary events and a sigma algebra of combinations of events to which probability can be consistently assigned. I have assumed the sigma algebra over the elementary events gives rise to a state space that is a simplex (but I am not sure if that is necessarily true), and that that is the reason quantum mechanics does not fit into classical probability, or as bhobba likes to say - improper mixtures are not "ignorance interpretable". Then I have further assumed that there is no classical probability theory that will have an observer problem as quantum mechanics has. This is all rather informal, so it'd be interesting to know whether it's really right or not.

 

[TrickyDicky]

No, I haven't seen it anywhere else. The usual definition of realism is that things should exist independently of any observer. What I was thinking (now maybe I'm not sure this is right) is that in quantum mechanics the pure states are not extremal points of a simplex. In Kolmogorov's axioms, there should be a space of elementary events and a sigma algebra of combinations of events to which probability can be consistently assigned. I have assumed the sigma algebra over the elementary events gives rise to a state space that is a simplex (but I am not sure if that is necessarily true), and that that is the reason quantum mechanics does not fit into classical probability, or as bhobba likes to say - improper mixtures are not "ignorance interpretable". Then I have further assumed that there is no classical probability theory that will have an observer problem as quantum mechanics has. This is all rather informal, so it'd be interesting to know whether it's really right or not.

I don't think it works, not for Bohmian mechanics anyway where the guiding wave and the trajectories are not observable so it is not realist in many senses. Realism is a really ambiguous and complex concept anyway, that almost anyone working with it has a different idea of what it is, so I'm very skeptical it can help to clarify anything, unless one uses some form of naive realism, which is the basis of empirical sciences so everyone is sme way or another obliged to follow. In its more radical form could be what Heisenberg seeked as a basis of the new theory in his seminal 1925 paper starting QM, in his words:"A basis founded exclusively upon relationships between quantities which in principle are observable". Sadly it took less than a year for the founders to give up that program, when Schrodinger came along with the wave function and introduced the state vector, something far from the exclusive quantities Heisenberg was seeking.

 

[write4u]

Not sure what it means except for some type of "wholeness/holism", but this is what Bohm's co-worker Hiley wrote:In Hiley, "Some Remarks on the Evolution of Bohm's. Proposals for an Alternative to Standard Quantum.", 2010.

Anyway, this seems more philosophy than physics because I don't understand what "non-mechanical", means in physical terms either than going against local causality (e.g. non-locality).

Question: are waves mechanical functions, and if they are, can they differ from physical mechanics. I am thinking of the different behaviors of particle/wave duality?

 

[bhobba]

Question: are waves mechanical functions, and if they are, can they differ from physical mechanics. I am thinking of the different behaviors of particle/wave duality?

Can you perhaps elucidate what you mean by mechanical function?

In BM its a potential.

Thanks
Bill

 

[DrChinese]

The usual definition of realism is that things should exist independently of any observer.

Nice wording.

 

[bohm2]

Question: are waves mechanical functions, and if they are, can they differ from physical mechanics. I am thinking of the different behaviors of particle/wave duality?

I interpret Bohm to be using "mechanical" to mean contiguous local action:

The mechanical philosophy was a philosophy of nature, popular in the seventeenth century, that sought to explain all natural phenomena in terms of matter and motion without recourse to any kind of action at a distance (cause and effect without any physical contact).

http://www.encyclopedia.com/doc/1G2-3424300461.html

And any realist interpretation of QM necessitates going against this view, which seems counterintuitive as Newton pointed out:

It is inconceivable that inanimate brute matter should, without the mediation of something else which is not material, operate upon and affect other matter without mutual contact...so that one body may act upon another at a distance through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it.

 

[write4u]

Can you perhaps elucidate what you mean by mechanical function?

In BM its a potential.

Thanks
Bill

Sorry, let me rephrase.
I should have asked if waves are QM functions. As a fan of BM I want to accept that in BM waves are a potential. After all, every action is preceded by potential and the Implicate.

However, using the definition of potential in its most fundamental form as: "that which may become reality", it seems to me that a wave is an action in reality regardless if it is observable or not, and while it is preceded by potential, it is a function in reality as demonstrated by the particle/wave duality in the double slit experiment..

I do understand that we have dubbed this wave function as a "probability wave" (a potential), eventually determining where the particle may become observable, but that does not explain the properties of the wave function itself, which is clearly present and mechanically influential on the photon in reality, as demonstrated by its interference patterns.

So, if I were to try and identify a wave function, I would suggest that a wave function HAS potential but IS NOT potential in and of itself. But if a wave is not mechanical action in itself, but is an expression of potential in reality, then what category can we place the wave function in? Could there be a third scientific but (as yet) undefined force at work?

Am I overthinking this?

p.s. I read somewhere that Bohm himself mentioned that the term Bohmian "Mechanics" was actually a misnomer, probably for the very reason you mentioned above.

 

[bhobba]

However, using the definition of potential in its most fundamental form as: "that which may become reality", it seems to me that a wave is an action in reality regardless if it is observable or not, and while it is preceded by potential, it is a function in reality as demonstrated by the particle/wave duality in the double slit experiment.

The meaning here is not philosophical, but the meaning you will find in physics texts on mechanics that determines the force a particle experiences.

I do understand that we have dubbed this wave function as a "probability wave" (a potential), eventually determining where the particle may become observable, but that does not explain the properties of the wave function itself, which is clearly present and mechanically influential on the photon in reality, as demonstrated by its interference patterns.

You are thinking in terms of the wave-particle duality which isn't actually true - its one of a number of myths about QM:
http://arxiv.org/pdf/quant-ph/0609163v2.pdf

So, if I were to try and identify a wave function, I would suggest that a wave function HAS potential but IS NOT potential in and of itself. But if a wave is not mechanical action in itself, but is an expression of potential in reality, then what category can we place the wave function in? Could there be a third scientific but (as yet) undefined force at work?

I think you are getting caught up too much in semantics. A wave-function has a very precise meaning in the theory - its the expansion of a pure state in terms of the position observable, but to explain that unfortunately requires a reasonable acquaintance with linear algebra. If you have that its not too hard. The fundamental axiom of QM is the outcomes of observations are described by a resolution of the identity Ei. If we associate the value yi with outcome i then we can form the Hermitian operator O= Σyi Ei called the observation's observable. By the spectral theorem a hermitian operator can be uniquely decomposed into the yi and Ei. From the Ei we can get an orthonormal basis |bi>. A representation of a state |u> in terms of the basis |bi> from an observable O is the representation of the state in terms of that observable.

Am I overthinking this?

Its a bit hard to dissect this stuff without delving into its technical detail.

Thanks
Bill

 

[metacristi]

I don't think it works, not for Bohmian mechanics anyway where the guiding wave and the trajectories are not observable so it is not realist in many senses. Realism is a really ambiguous and complex concept anyway, that almost anyone working with it has a different idea of what it is, so I'm very skeptical it can help to clarify anything, unless one uses some form of naive realism, which is the basis of empirical sciences so everyone is sme way or another obliged to follow. In its more radical form could be what Heisenberg seeked as a basis of the new theory in his seminal 1925 paper starting QM, in his words:"A basis founded exclusively upon relationships between quantities which in principle are observable". Sadly it took less than a year for the founders to give up that program, when Schrodinger came along with the wave function and introduced the state vector, something far from the exclusive quantities Heisenberg was seeking.

In the book 'The undivided Universe. An Ontological interpretation of QM' (written together with Hiley) Bohm (chapter 1) writes in non equivocal terms about his goals at this level, namely to provide an ontology to QM.

That is to say, it seems, as indeed Bohr [3] and Heisenberg [4] have implied, that quantum theory is concerned only with our
knowledge of reality and especially of how to predict and control the behaviour of this reality, at least as far as this may be possible. Or to put it in more philosophical terms, it may be said that quantum theory is primarily directed towards epistemology which is the study that focuses on the question of how we obtain our knowledge (and possibly on what we can do with it). It follows from this that quantum mechanics can say little or nothing about reality itself. In philosophical terminology, it does not give what can be called an ontology for a quantum system. Ontology is concerned primarily with that which is and only secondarily with how we obtain our knowledge about this (in the sense, for example, that the process of observation would be treated as an interaction between the observed system and the observing apparatus regarded as existing together in a way that does not depend significantly on whether these are known or not). We have chosen as the subtitle of our book “An Ontological Interpretation of Quantum Theory” because it gives the clearest and most accurate description of what the book is about. The original papers in which the ideas were first proposed were entitled “An Interpretation in Terms of Hidden Variables” [5] and later they were referred to as a “Causal Interpretation” [6]. However, we now feel that these terms are too restrictive. First of all, our variables are not actually hidden. For example, we introduce the concept that the electron is a particle with well-defined position and momentum that is, however, profoundly affected by a wave that always accompanies it (see chapter 3). Far from being hidden, this particle is generally what is most directly manifested in an observation. The only point is that its properties cannot be observed with complete precision (within the limits set by the uncertainty principle). Nor is this sort of theory necessarily causal. For, as shown in chapter 9, we can also have a stochastic version of our ontological interpretation. The question of determinism is therefore a secondary one, while the primary question is whether we can have an adequate conception of the reality of a quantum system, be this causal or be it stochastic or be it of any other nature.

Determinism / indeterminism (usually framed in causality / acausality terms) is only a secondary problem and I tend to agree, indeed a real world could evolve very well deterministically overall (at the level of observed facts) yet still having some uncaused events. Even his idea of implicate order (which relegates matter - more generally the physical world, the explicate order - to a secondary status) is fully tenable notwithstanding its current metaphysical status. Personally I do not think that hidden variables scientific programs are a dead end but probably we need something stronger than Bohm's interpretation to tip the balance in its favour.

As about realism things are complicated indeed, (here is paper on this theme http://www.sagepub.com/upm-data/44131_1.pdf) but overall scientists (and philosophers) accept forms of indirect realism these days (critical and so on). Even Einstein seems to have been a supporter of some distinct kind of indirect realism (http://www3.nd.edu/~dhoward1/Was Einstein Really a Realist.pdf) although he was way more reticent than the current proponents of scientific realism (via taking seriously a more holistic version of Duhem's underdetermination argument, close to what Quine proposed). Personally I am sympathetic with arguments on this line (well more with later Quine), sophisticated scientific realism has the epistemological upper hand at the moment (especially via philosophical arguments in its favour) but we have always to be prepared for possible rational non trivial changes in ALL parts of what we accept today as knowledge (i'm afraid even idealism is still with us even if it does not deserve primary status at the moment).

 

[metacristi]

To conclude Bohm's pilot-wave interpretation is definitely realist in nature. It has some problems (for example it requires a reformulation of SR to admit the absolute simultaneity of all inertial systems, fully possible see for example Cushing 'Philosophical concepts in physics', chapter 23.4 and 16.3) but what interpretation is without problems?

Nothing fatal yet, remain to be seen. By the way one can find here (http://www.tcm.phy.cam.ac.uk/~mdt26/pilot_waves.html , go to 'Lectures and slides' on the rgiht) an introduction, of interest is also 'Quantum Theory at the Crossroads. Reconsidering the 1927 Solvay Conference' (http://arxiv.org/pdf/quant-ph/0609184.pdf) and Measure For Measure: Quantum Physics and Reality -- World Science Festival 2014 on youtube

()

 

[atyy]

To conclude Bohm's pilot-wave interpretation is definitely realist in nature. It has some problems (for example it requires a reformulation of SR to admit the absolute simultaneity of all inertial systems, fully possible see for example Cushing 'Philosophical concepts in physics') but what interpretation is without problems?

That's a rather subjective type of problem, because there is nothing to say that nature isn't like that - as is often said when explaining relativity or quantum mechanics - "nature doesn't care what we like"*. An objective definition of a problem would be lack of internal coherence or inconsistency or inability to predict known experimental results. Bohmian Mechanics does have an open objective problem: there is no known Bohmian version of chiral fermions interacting with non-Abelian gauge fields.

*unless ultrahardcore Copenhagen is right :)

 

[write4u]

[es,

The meaning here is not philosophical, but the meaning you will find in physics texts on mechanics that determines the force a particle experiences.

You are thinking in terms of the wave-particle duality which isn't actually true - its one of a number of myths about QM:
http://arxiv.org/pdf/quant-ph/0609163v2.pdf

I think you are getting caught up too much in semantics. A wave-function has a very precise meaning in the theory - its the expansion of a pure state in terms of the position observable, but to explain that unfortunately requires a reasonable acquaintance with linear algebra. If you have that its not too hard. The fundamental axiom of QM is the outcomes of observations are described by a resolution of the identity Ei. If we associate the value yi with outcome i then we can form the Hermitian operator O= Σyi Ei called the observation's observable. By the spectral theorem a hermitian operator can be uniquely decomposed into the yi and Ei. From the Ei we can get an orthonormal basis |bi>. A representation of a state |u> in terms of the basis |bi> from an observable O is the representation of the state in terms of that observable.

Its a bit hard to dissect this stuff without delving into its technical detail.

Thanks, Bill

Thank you for you indulgence of my groping around. You have given me plenty of material to research and is much appreciated.

 

[write4u]

A little follow up, which may clarify my confusion.,
The original question was prompted by this statement in wiki,

The wave of the wave function, however, is not a wave in physical space; it is a wave in an abstract mathematical "space", and in this respect it differs fundamentally from water waves or waves on a string.[/quote]

http://en.wikipedia.org/wiki/Wave_function

 

[bhobba]

The original question was prompted by this statement in wiki,

That's true.

The wave-particle duality is a myth - as a link I gave explained.

Thanks
Bill

 

[write4u]

That's true.

The wave-particle duality is a myth - as a link I gave explained.
Thanks
Bill

Please forgive my persistence, but in context of our discussion, what does this mean?

First photograph of light as both a particle and wave.

http://phys.org/news/2015-03-particle.html

and this also prompted a question that, if in the double slit experiment we remove the receptors, what happens to the interference patterns (as observable when the receptors are in place)?

 

[bhobba]

what does this mean?

The authors likely want to be sensationalist - its wrong - or at least its full technical detail is likely far less picturesque. There are threads discussing it.

and this also prompted a question that, if in the double slit experiment we remove the receptors, what happens to the interference patterns (as observable when the receptors are in place)?

What do you mean by receptors?

Thanks
Bill

 

[metacristi]

That's a rather subjective type of problem, because there is nothing to say that nature isn't like that - as is often said when explaining relativity or quantum mechanics - "nature doesn't care what we like"*. An objective definition of a problem would be lack of internal coherence or inconsistency or inability to predict known experimental results. Bohmian Mechanics does have an open objective problem: there is no known Bohmian version of chiral fermions interacting with non-Abelian gauge fields.

*unless ultrahardcore Copenhagen is right :)

One objection heard quite often is that Bohm's theory cannot be made compatible with Relativity in a profound sense, I only stressed that it can at limit if we relax the requirement of Lorentz invariance to apply solely to observations (explicit non locality cannot be used for superluminal transmissions of data). So yes I agree with you, it actually fits very well with my fallibilist philosophy presented in my first post here, maybe there is a preffered reference frame in spite of not being able to corroborate this practically at least at the moment. But as far as I see there is also effort to show that Bohm's theory can be made Lorentz invariant in a more fundamental sense (http://arxiv.org/pdf/1307.1714.pdf).

Never heard about the problem you mention at the end of your post as an objection to the Bohmian program (and as far as I know this a problem affecting alternatives as well), actually there is a surprisingly dynamical research along bohmian lines (http://www.bohmian-mechanics.net/research_papers.html#QFT) so I'd say it is too early for 'no-go' theorems which, we all know well, proved so harmful in the past. The Universe can be very well even superdeterministic in reality, why block unnecessarily still legitimate directions of research?

As a side note (i'm sure not very appreciated here) I do not claim that hidden variables programs are the way ahead, they are not even very high currently on a list of alternative scientific approaches, but (unfortunately for those who think that science can only progress, some even think algorithmically, toward truth) there is sufficient reason to be sceptical of the mainstream interpretations of today, we can still be very well on 'the wrong branch', finally even seemingly degenerative scientific programs can become progressive later when the 'background' assumptions (rational ones, nothing linked with politics) are prepared for them. As Popper put it plastically (paraphrased) some very good ideas can even be lost forever if we are constantly told that they are impossible or meaningless.

 

[write4u]

The authors likely want to be sensationalist - its wrong - or at least its full technical detail is likely far less picturesque. There are threads discussing it.

What do you mean by receptors?
Thanks
Bill

I named the plates which show the interference patterns behind the double slits "receptors' for want of a better name. I suppose they are photographic plates,
I wondered what would happen to the interference patterns if these plates were removed. Seems to me these wave patterns would still exist, even if the are not observed (collapsed). Do these patterns eventually dissipate? If so, would there be an effect on the photons also?

From a previous link, I read this, which seems to pose a somewhat similar question.

In a 1964 book de Broglie gave a detailed statement of the Einstein’s Boxes thought experiment.10
“Suppose a particle is enclosed in a box B
with impermeable walls. The associated wave
is confined to the box and cannot leave it.

The usual interpretation asserts that the particle
is “potentially” present in the whole of
the box B, with a probability ||2 at each
point. Let us suppose that by some process
or other, for example, by inserting a partition
into the box, the box B is divided into
two separate parts B1 and B2 and that B1
and B2 are then transported to two very distant
places, for example to Paris and Tokyo.

[See Fig. 1.] The particle, which has not yet
appeared, thus remains potentially present in
the assembly of the two boxes and its wave
function consists of two parts, one of which,
gives no information about this.

“We might note here how the usual interpretation
leads to a paradox in the case of experiments
with a negative result. Suppose that
the particle is charged, and that in the box B2
in Tokyo a device has been installed which enables
the whole of the charged particle located
in the box to be drained off and in so doing to
establish an observable localization. Now, if
nothing is observed, this negative result will
signify that the particle is not in box B2 and
it is thus in box B1 in Paris. But this can
reasonably signify only one thing: the particle
was already in Paris in box B1 prior to
the drainage experiment made in Tokyo in
box B2. Every other interpretation is absurd.

How can we imagine that the simple fact of
having observed nothing in Tokyo has been
able to promote the localization of the particle
at a distance of many thousands of miles
away?”11

http://www.bohmian-mechanics.net/research_papers.html#QFT

 

[bhobba]

I wondered what would happen to the interference patterns if these plates were removed. Seems to me these wave patterns would still exist,

You are falling into a VERY common trap. QM is a theory about observations. The primitive of the theory is an observation, like point particle is a primitive a classical mechanics, like event is a primitive of probability theory etc etc. What properties a quantum system has when not observed the theory is silent about. The state is simply a device to help predict the probabilities of observations. It says nothing about if it's real or not. We have interpretations where its real, others where its subjective knowledge, and others where it applies to an ensemble. Again the theory is silent on the issue.

The screen at the back of the slits is an observation. Remove it and the theory says nothing since its about observations. It says nothing about waves dissipating etc etc. You can use the state to figure out what would happen if it was there but that doesn't mean there is anything going on. In fact, since the wave particle duality is wrong that explanation of the double slit experiment is wrong. Here is a correct quantum one:
http://arxiv.org/ftp/quant-ph/papers/0703/0703126.pdf

The explanation of the double slit is each slit 'scatters' the particle at an unpredictable angle because of the uncertainty principle. Note scatter in inverted commas - it doesn't mean it has a real trajectory that's scattered - simply that if you measured its momentum it will be scattered. Just behind the slits the state is the superposition of the state just behind each slit. And when you chug through that math as per the paper above you get an interference pattern on the screen. No screen - no observation - and the theory says nothing.

That quote from Bohm is philosophical waffle - which Bohm rather enjoyed rambling on about - and Feynman for example chided him on that tendency (I recall reading about an interesting exchange along those lines when he explained BM to Feynman - I think it was Surely Your Joking - he said, or at least its my recollection, something like Dave - we have this perfectly valid theory that predicts things perfectly well so what's the point). The theory does not say 'The usual interpretation asserts that the particle is “potentially” present in the whole of the box B, with a probability ||2 at each point.' That's Bohm's interpretation of Copenhagen - his use of the word potentia is his own - Copenhagen doesn't say that. In Copenhagen the state is subjective knowledge.

QM says precisely nothing about when it's not observed. Remove the screen and the theory says nothing. Interpretations may say something - Bohm's picturesque language may suggest things, but the theory says nothing.

Thanks
Bill

 

[write4u]

You are falling into a VERY common trap. QM is a theory about observations. The primitive of the theory is an observation, like point particle is a primitive a classical mechanics, like event is a primitive of probability theory etc etc. What properties a quantum system has when not observed the theory is silent about. The state is simply a device to help predict the probabilities of observations. It says nothing about if it's real or not. We have interpretations where its real, others where its subjective knowledge, and others where it applies to an ensemble. Again the theory is silent on the issue.

The screen at the back of the slits is an observation. Remove it and the theory says nothing since its about observations. It says nothing about waves dissipating etc etc. You can use the state to figure out what would happen if it was there but that doesn't mean there is anything going on. In fact, since the wave particle duality is wrong that explanation of the double slit experiment is wrong. Here is a correct quantum one:
http://arxiv.org/ftp/quant-ph/papers/0703/0703126.pdf

The explanation of the double slit is each slit 'scatters' the particle at an unpredictable angle because of the uncertainty principle. Note scatter in inverted commas - it doesn't mean it has a real trajectory that's scattered - simply that if you measured its momentum it will be scattered. Just behind the slits the state is the superposition of the state just behind each slit. And when you chug through that math as per the paper above you get an interference pattern on the screen. No screen - no observation - and the theory says nothing.

That quote from Bohm is philosophical waffle - which Bohm rather enjoyed rambling on about - and Feynman for example chided him on that tendency (I recall reading about an interesting exchange along those lines when he explained BM to Feynman - I think it was Surely Your Joking - he said, or at least its my recollection, something like Dave - we have this perfectly valid theory that predicts things perfectly well so what's the point). The theory does not say 'The usual interpretation asserts that the particle is “potentially” present in the whole of the box B, with a probability ||2 at each point.' That's Bohm's interpretation of Copenhagen - his use of the word potentia is his own - Copenhagen doesn't say that. In Copenhagen the state is subjective knowledge.

QM says precisely nothing about when it's not observed. Remove the screen and the theory says nothing. Interpretations may say something - Bohm's picturesque language may suggest things, but the theory says nothing.

Thanks
Bill

Thanks for your patience with my uninformed questions. I won't waste any more of your time and do some more studying, before I jump into deep water again..

 

[metacristi]

By the way I was reading a few days ago the comments to this blog post (https://tjoresearchnotes.wordpress.com/2013/05/13/guest-post-on-bohmian-mechanics-by-reinhard-f-werner/), a lot of disagreement there something which could only reinforce in me that perennial question 'Do we really understand Quantum Mechanics' (see also http://arxiv.org/abs/quant-ph/0209123)? I would say that in the current state of affairs openness toward a pluralistic approach is the best way ahead*, in the words of John Bell (talking about how to teach Relativity in 'Speakable and unspeakable in quantum mechanics'):

'There is no intention here to make any reservations whatever about the power and precision of Einstein's approach. But in my opinion there is also something to be said for taking students along the road made by Fitzgerald, Larmor, Lorentz and Poincare. The longer road sometimes gives more familiarity with the country'.

*bolstered by my incursions in the philosophy and history of science which show quite clearly that the demise of the old positivistic and logical positivist perspectives (which informed the operantionalism of Bohr and Heisenberg) was fully justified

 

[bhobba]

*bolstered by my incursions in the philosophy and history of science which show quite clearly that the demise of the old positivistic and logical positivist perspectives (which informed the operantionalism of Bohr and Heisenberg) was fully justified

Personally I think people over think it.

I spend a lot of time explaining something utterly trivial. QM is a theory about observations. Its deceptively simple but very hard to internalise. It took me a long time. I remember going on long walks thinking about things like Schroedinger's Cat - how could it collapse when opened - all the usual stuff, I did it for years. But slowly it sunk in - its about observations.

Once you accept that it fits together once its understood as the simplest probability model that allows continuous transformations between pure states:
http://arxiv.org/pdf/quant-ph/0101012.pdf

Thanks
Bill

 

[ddd123]

You are thinking in terms of the wave-particle duality which isn't actually true - its one of a number of myths about QM:
http://arxiv.org/pdf/quant-ph/0609163v2.pdf

I wasn't really convinced by the (very short) treatment this article gives on the wave-particle duality. It seems to me a straw-man argument. I've always considered the wave-particle duality not to be much about the behavior of a single entity in space that can be either smeared or localized, which is associated to a wave-function, but the fact that we speak of a single entity at all instead of a continuum. We speak of photons, we can count the photons, instead of light as being a continuum, in principle infinitely divisible: this is what is very classically assumed when talking about waves, not just a spatial distribution property which is "wave-like".

 

[bhobba]

It seems to me a straw-man argument.

Consider the wave-function of two entangled particles. It resides in six dimensions. Exactly what is it waves of?

Or to put it in a different light, define, precisely, what a particle is, similarly define, precisely, what a wave is, then from the axioms of QM show a quantum particle behaves like one or the other.

Thanks
Bill

 

[ddd123]

Consider the wave-function of two entangled particles. It resides in six dimensions. Exactly what is it waves of?

The article, if I understood it correctly, says that there's no duality because "electrons and photons always behave as waves, while a particlelike behavior corresponds only to a special case". But maybe I'm decontextualizing the sentence. So I'm tempted to reflect that question back at you, what are they waves of? I don't know. For me, they're waves up to a certain point, with waves you shouldn't have discretized energies for monochromatic light. But maybe I'm fixating on a way of thinking.