atyy said: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?
bhobba said:There were people like Grete Hermann that spotted the error - but were ignored:
http://arxiv.org/ftp/arxiv/papers/0812/0812.3986.pdf
bhobba said:Its a bit of a sad history really.
TrickyDicky said:So to be clear, both Gleason's and Kochen-Specker theorems only rule out non-contextual hidden variables theories?
von Neumann’s ‘No Hidden Variables’ Proof: A Re-Appraisal...Wikipedia said: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.
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?atyy said: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?
TrickyDicky said: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?
That was basically my point, as I commented in the second part of my post.bohm2 said: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?
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.atyy said:I thought that just meant "deterministic" in the sense that dBB is deterministic with all variability being put in the initial conditions.
TrickyDicky said: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 said: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.Demystifier said: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.)
In Hiley, "Some Remarks on the Evolution of Bohm's. Proposals for an Alternative to Standard Quantum.", 2010.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’.”
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 said: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
TrickyDicky said: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.
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.atyy said: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.
This is quite an unusual definition of realism. Have you seen that definition somewhere else, or is it your own definition?atyy said:What is realism? Realism just means that the theory completely obeys classical probability, as given by Kolmogorov's axioms.
Demystifier said:This is quite an unusual definition of realism. Have you seen that definition somewhere else, or is it your own definition?
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.atyy said: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.
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?bohm2 said: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).
write4u said: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?
atyy said:The usual definition of realism is that things should exist independently of any observer.
I interpret Bohm to be using "mechanical" to mean contiguous local action:write4u said: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?
http://www.encyclopedia.com/doc/1G2-3424300461.htmlThe 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).
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.
Sorry, let me rephrase.bhobba said:Can you perhaps elucidate what you mean by mechanical function?
In BM its a potential.
Thanks
Bill
write4u said: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.
write4u said: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.
write4u said: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?
write4u said:Am I overthinking this?
TrickyDicky said: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.
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.