Why Bohmian theory?

This topic contains 27 replies, has 6 voices, and was last updated by  Aurelien Drezet 3 years, 8 months ago.

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  • #2467

    Sheldon Goldstein
    Participant

    Suppose we accept that a fundamental physical theory—while of course having implications about results of measurement and observation—should not involve axioms about measurement or observation. Suppose we thus demand of quantum theory in particular that it be a “quantum theory without observers.” It would seem that the theory would then have to involve local beables, out of whose configurations facts about results of experiments would arise. If that theory were to involve as a fundamental entity also the (Schrodinger-evolving) wave function, as many quantum experiments seem so strongly to suggest it must, then we would seem to be dealing with something very much like a Bohmian theory.

    #2690
    Richard Healey
    Richard Healey
    Participant

    “It would seem that the theory would then have to involve local beables, out of whose configurations facts about results of experiments would arise.”

    Appearances can be deceptive!
    Assume a fundamental physical theory should not involve talk of measurement or observation. (I don’t mention axioms, because I don’t think theories, fundamental or not, need be derived from axioms.)
    Must a fundamental theory posit its own local beables? Must a fundamental theory posit any beables of its own? Of course one could take the attitude that nothing could count as a fundamental theory unless these questions received positive answers. But someone could then adopt a different, more relaxed, attitude toward fundamentality. Observer-free quantum theory is fundamental in two senses: We have been able successfully to use it successfully to predict and explain a host of phenomena that cannot otherwise be predicted or explained (e.g. by classical physical theories) without encountering any empirical problems traceable to its deficiencies; and, in some form, the theory may be applied to all known phenomena with the single exception of those thought (by many) to require a quantum theory of gravity.
    But observer-free quantum theory does not posit its own ontology: it “borrows” an independently available ontology from the rest of physics. The wave function is not a beable at all (many experiments are hard to reconcile with the assumption that it is): “observables” are not beables—corresponding physical magnitudes are beables, but quantum theory should not be understood to introduce them as elements of its own ontology. Bell talks about beables recognized in ordinary quantum mechanics, including settings of switches and knobs, and currents. These are not novel quantum posits and don’t have to be built out of elements of quantum ontology; when we apply quantum mechanics we often help ourselves to them (though nothing prevents us from applying quantum mechanics to these things if we want to understand their behavior better). Any legitimate application of the Born rule in quantum theory concerns values of magnitudes not introduced as novel quantum posits but taken over from the rest of physics, new as well as old. Among these applications are many that successfully account for experimental phenomena.
    The success of quantum theory should teach us that a fundamental theory need not be “self-standing”. It need not present us with a description or representation of reality solely in its own terms. We might experience metaphysical yearnings for a theory that did, but physics–even supremely successful physics–need not conform to our favorite metaphysics. We can understand quantum theory as currently our best fundamental theory in this less narrow-minded sense without talking about observation and measurement, and without becoming instrumentalists or operationalists. It is Bohmian mechanics, not quantum mechanics, that requires defense using philosophical ideas from outside of physics.

    #2709

    Hi Richard, I read your post several times trying to understand your point of view, but I’m still just not sure what you mean to be saying. Can you, for lack of a better phrase, dumb it down for me a bit? It sounds like you’re saying that, according to “observer-free quantum theory”, the ontology (i.e., the stuff that really exists physically according to the theory) includes settings of switches and knobs, and currents, and presumably a lot of other macroscopic things/properties described in classical terms. Whereas wave functions (meaning, presumably, the typically microscopic things like individual electrons or atoms whose states are, in QM, described by a wave function) are not part of the ontology. Am I at least close to right so far?

    What I don’t get is how this kind of picture isn’t just drowning in the sorts of problems Bell identified by noting that ordinary qm is “unprofessionally vague and ambiguous”, i.e., part of what’s usually called the measurement problem. Is there some clean, unambiguous way of saying exactly what, according to the theory, is real? It seems like you mean to say that big, macroscopic, classical things (whose reality nobody (sane) ever doubted) are real. But where, exactly, is the boundary as we move along the continuum from big/macro to little/micro? To me, as long as you can’t specify *sharply* what the theory says is real, I can’t really take it seriously as a candidate fundamental theory. And then this same feeling applies as well to the dynamics, which, it seems to me, inherits and amplifies whatever vagueness/ambiguity there is about ontology: if you only say something like “big/macro things are real, but little/micro things described by wave functions aren’t real”, and there are some equations for how the big/macro stuff behaves, and some other equation for how wave functions behave, and maybe some other equations to describe how big/macro stuff interacts with wave functions, etc., you can’t possibly give sharp unambiguous rules about which equations apply in which situations, until/unless you’ve got some unambiguous way to decide which kind of thing (or non-thing) you’ve *got* — when, say, what you’ve got is something mesoscopic. And then of course there is the general worry about what in the world it could mean to say that big/macro things are real, but the smaller and smaller pieces that they are made of cease to exist at some sufficient level of smallness.

    But really I’m just expressing my concerns with “ordinary QM”. My sense is that, while your view has some kind of overlap with that, you mean for it to be somehow different and immune to these sorts of concerns. Can you help me understand better what your view is and why you think it’s immune to such concerns?

    #2717
    Richard Healey
    Richard Healey
    Participant

    At the end of your first paragraph you ask “Am I at least close to right so far?”
    No. In formulating or understanding quantum theory it is not necessary to appeal to a microscopic/macroscopic distinction. As a fundamental theory, quantum theory may be applied to systems of arbitrary size.
    Quantum mechanics may be applied to systems of particles, so by applying it we are committed to the existence of particles, or at least to treating things as systems of particles (perhaps as a permissible idealization, even though we might not treat them that way if we were instead applying a relativistic quantum field theory to the same things). When we apply quantum mechanics to such systems, we assign them a wave-function (density operator, state vector, whatever). This does not represent a beable. It does not represent the particles’ physical properties or relations: its evolution does not represent their behavior. Its function is not descriptive but prescriptive: it tells the one who applies it what statements assigning values to magnitudes are significant enough to be assigned probabilities, and what those probabilities are. What statements are significant depend on what environment the system is in. The environment may include something we could use as a measurement apparatus, or it may not: either way, it is interactions with the environment that constrain to what statements we can legitimately apply the Born rule. These may be statements about the system, the environment, or both. We can use quantum models of environmental decoherence to help us determine what statements are significant enough to be assigned probabilities. Significance is not a “yes/no” matter, and there is no precise criterion that specifies when, and to what, the Born rule may be legitimately applied. Bell would not like this. But it’s important to stress that this is not a vagueness in the formulation of quantum mechanics, but calls for the same kind of decision that is required in any application of a physical theory, classical or quantum.
    “Is there some clean, unambiguous way of saying exactly what, according to the theory, is real?”
    The quantum state is not a beable: in that sense it is not real. But quantum states are objective: when assigning a quantum state to a system one can make an incorrect assignment. In that sense a quantum state is real. Are particles real? Yes, according to quantum mechanics, since every correct application of quantum mechanics involves claims about systems of particles. Sometimes, according to relativistic quantum field theory: some correct applications of relativistic quantum field theory involve claims about particles (but in other correct applications no such claim would be significant). I expect you and Bell would not like relativistic quantum field theory’s refusal to give a clear, unambiguous answer to the question “Are particles real, or are fields real, in relativistic quantum field theory?” But recent work by philosophers of physics has shown how hard it is to impose either a particle ontology or a field ontology on such a theory! The problem goes away if one rejects the presupposition that a fundamental theory must come equipped with an ontology.
    “To me, as long as you can’t specify *sharply* what the theory says is real, I can’t really take it seriously as a candidate fundamental theory.”
    OK, but here you are expressing what I have come to regard as a metaphysical prejudice analogous to the Cartesian prejudice against Newtonian forces. Both prejudices attempt to constrain the form of any fundamental physical theory. We are lucky that Newton broke free of the first prejudice and that Heisenberg, Schrodinger etc. broke free of the second.
    I hope that helps some. I have published papers containing more details, and I’m presently finishing a book in which I try to lay out my view of quantum theory more carefully and patiently.

    #2724

    That helps a little, but I remain confused. You say that particles (for example) exist, but that the function of the mathematical objects we use to characterize them (wave functions, etc.) “is not descriptive but prescriptive”. OK, sure — but then how *can* one (literally, accurately, and completely) describe these particles (if I should even understand that word, “particles”, literally — and if I shouldn’t I want to know what I should say instead)? If something really exists, shouldn’t it be possible in principle to provide a description of it? And shouldn’t a supposedly fundamental physical theory, about these things, provide such a description??

    It just seems that what you are saying comes down to renouncing the goal of saying what physical reality is actually like on the micro-level, and instead adopting some kind of instrumentalist/operationalist view of the goal of physical theories. Maybe that’s it and our “metaphysical prejudices” (i.e., our ideas about what the goal of a scientific theory should be) are just different.

    #2733
    Richard Healey
    Richard Healey
    Participant

    I started to compose a short reply to your last post, Travis, but decided that your pointed questions required a more extended response. So instead I’ve attached a piece I wrote a few years ago on what quantum theory teaches us about the concept of physical reality.

    In brief, like Einstein I think of the “real” in physics as a a type of program to which we are, however, not forced to cling a priori.
    I approach quantum theory not as an instrumentalist or operationalist, but as a pragmatist. For a pragmatist, quantum theory contributes to the goals of physics (prediction and explanation of natural phenomena) by following a different type of program.

    Like you, I would be happy if physics some day were able to return to Einstein’s realist program in physics. But science doesn’t have to make one happy! Unlike you, I don’t see any sign that pursuing a Bohmian research program will help do this: as Einstein said, that way is too cheap. Meanwhile, I am astonished by the human creativity involved in coming up with a different program for doing excellent physics the quantum way—a way that is neither instrumentalist nor operationalist but pragmatist.

    #2736

    Aurelien Drezet
    Participant

    Dear All, I think that the problem here is not if Bohmian mechanics is the good theory but to know what will happen if you abandon the old Credo of physics concerning realism à la Einstein. For me and many the most interesting aspect of Bohmian theory is that it provides a framework for solving the problems accumulated by Copenhagen followers (Schrodinger cat’s, Wigner friends etc..). These are serious problems which can not be put under the carpet like that. Bohmian theory is a first step not the last one so it is not a waist of time to consider it as important. It is the opposite which could be risky for me since I am afraid that such an attitude could scleroses the future of microphysics.

    #2752
    Dustin Lazarovici
    Dustin Lazarovici
    Participant

    Dear All, If I may, I would like to add some general remarks. They might not do justice to all of your previous points and concerns, but maybe it doesn’t hurt to “dump things down” a bit (to borrow Travis’ phrase).

    1) I believe that “realism” is a very unhelpful notion and that every scientific or meta-scientific discussion benefits from avoiding it altogether. That said, to the degree that “scientific realism” has a clear meaning, it is not presupposed by Bohmian mechanics. Both “realistic” and “anti-realistic” attitudes can be taken towards Bohmian mechanics, by either regarding the particles as ontological or as merely theoretical objects. However, BM can be taken seriously as a description of physical reality, in contrast to standard QM which can’t be taken seriously in this way, even if we wanted to.

    2) What Mister Healey describes as “Einstein’s realist program” is not an invention of Einstein’s, but was the scientific tradition starting from the pre-socratics to Galilei to Newton to Maxwell to Boltzmann and so on. In the early days of quantum mechanics, people thought they had good reasons – even in form of mathematical proof – to abandon this “program”. These reasons – without exception! – turned out to be wrong.

    3) If anything, Bohmian mechanics shows that if we abandon the idea of a precise, unambiguous, objective description of the physical realm, it’s not out of necessity, not as a consequence of the quantum phenomena, but by deliberate choice. Admittedly, when it comes to relativistic quantum theory i.e. quantum field theory, the Bohmian, or, let’s say, the “ontological” alternative is not completely worked out, yet. However, from what I know and understand so far, there’s no doubt in my mind that it can be done.

    Hence, whatever reasons one may have to abandon Einstein’s program – which was simply the scientific program until not so long ago – they also lie “outside of physics”!

    #2783

    Hi Richard — I read through your “open_question…” essay last night. I enjoyed reading it, as it contains a very nice collection of quotes from Einstein, Bohr, etc. But I really just don’t get the pragmatic turn you want to take. As I understand it, your pragmatism does not just mean “sometimes we should maybe try things out and see what works and learn from that without worrying, immediately, about what it implies about what it implies about reality”. That I would be all in favor of, sometimes. But to me, that attitude is 100% compatible with the *ultimate* goal remaining to describe the world as accurately and completely as possible. Instead, it seems like you want to permanently and irrevocably give up on the goal of describing the world as accurately and completely as possible. And I just don’t understand what could motivate this. I agree with what Dustin wrote above: this (“realist”) attitude has been central to the scientific enterprise since its inception, and has, I think, demonstrated itself to be quite practical. It seems like the kind of thing you’d only contemplate giving up if you were backed into some kind of corner where you just had no option but to give it up. And of course people have often claimed that this is exactly the situation that we are backed into by QM. But literally every such claim is wrong, and rather straightforwardly demonstrably wrong (in the sense that Bohmian mechanics is a living breathing inspectable counterexample to all of these claims). So why should I abandon the realist attitude and adopt your pragmatism instead??

    #2787
    Richard Healey
    Richard Healey
    Participant

    I don’t want to permanently and irrevocably give up on the goal of describing the world as accurately and completely as possible. But I think that goal is at least (probably) humanly unachievable, and possibly even incoherent, since it presupposes that there is some set of concepts rich enough to permit such a complete description. Pragmatism is not incompatible with the realist program: but it is flexible enough to make room for alternative programs. Its central insight is that concepts are intellectual tools for coping with the world, and that we can create concepts and use them in a variety of ways in pursuit of our goals. One way of doing this is to create theories that posit beables: if the theory works, you can hope the beables exist. That, I take it, is the Bohmian program. But the problem with that program is that even if the theory is empirically adequate the existence of the beables remains a hope—it is not supported by the evidence. Quantum theory does not posit beables: instead, it offers advice on what descriptive claims to make about magnitudes and entities supplied by other theories. We have good reason to accept quantum theory because that advice proves to be good, empirically. If your goal is an accurate and complete description of the world, then quantum theory won’t meet it: if your goal is predictive and explanatory success, then quantum theory does meet it. I take science to have the latter goal. I don’t see the Bohmian program making progress toward either goal, since I don’t think the evidence supports Bohmian theories. But (speaking personally) I’d love to see some other theory that is supported by the evidence and that does provide a rich description or representation of the physical world. And I don’t rule out the possibility that further developments in the Bohmian program could lead to such a theory, though I wouldn’t put money on it!

    #2789

    Tell me how the following is unfair:

    “Pragmatism is not incompatible with the realist program: but it is flexible enough to make room for alternative programs. Its central insight is that concepts are intellectual tools for coping with the world, and that we can create concepts and use them in a variety of ways in pursuit of our goals. One way of doing this is to create theories that posit [atoms]: if the theory works, you can hope the [atoms] exist. That, I take it, is the [atomist] program. But the problem with that program is that even if the theory is empirically adequate the existence of the [atoms] remains a hope — it is not supported by the evidence.”

    =)

    #2801
    Richard Healey
    Richard Healey
    Participant

    Everything is fair except the last sentence. The existence of atoms is strongly supported by the evidence. The existence of a Higgs boson is also supported by the evidence, though not nearly as strongly. By contrast, the existence of Bohmian trajectories, a preferred spacetime foliation, etc. is not.

    #2807

    Hmmm. I guess I thought the first few sentences constituted a kind of argument for why “the existence of [whatever] remains a hope — it is not supported by the evidence”. That is, I thought what you were saying was: supposing the Bohmian trajectories (etc.) to exist may allow me to account for what I observe, but this doesn’t imply that those Bohmian trajectories really exist; who can ever know? So, my point was, if that’s what you meant, then it seems (troublingly, to me at least) that the same exact reasoning would have you dismiss the empirical-predictive successes of the atomic theory as not actually constituting evidence that the atoms really exist.

    Now, I’m happy to concede that the situations of the two theories, vis a vis evidence, are not exactly parallel. There are, arguably, several different candidate quantum theories (Bohm, GRW, ???) that can all account for our observations — whereas there was nothing like a distinct competitor to the atomic theory that was able to account for the same very diverse set of observations equally well.

    But still, I don’t really understand, from your point of view, how the two situations are different in principle. There’s a theory that accounts for a bunch of observed facts, and contradicts no observed facts. Isn’t that some (if not “strong” or “conclusive”) evidence that what the theory says is actually true? If not, what other kind of thing do you consider “evidence”?? What kind of thing did the atomic theory do, with respect to the phenomena it made predictions about, that Bohm’s theory fails to do with respect to the phenomena it makes predictions about??

    #2815
    Richard Healey
    Richard Healey
    Participant

    I think we have arrived back at the starting point of my first post on Bohmian mechanics (under a different thread—the one I emailed to you originally). There I compared the Bohmian research program after quantum theory to a Lorentzian research program after special and general relativity.
    Bohm and GRW are not quantum theories but non-quantum rivals (even if a Bohmian theory is empirically equivalent to a quantum theory). Similarly, a Lorentzian theory empirically equivalent to a relativistic theory is not a theory of relativity.
    If we didn’t have the theory(ies) of relativity, we might well use a Lorentzian theory instead of STR while acknowledging its evidentiary infirmities and continue to play “catch up” by working toward Lorentzian theories empirically equivalent to GTR. But we don’t need to since we have relativity—with no such evidential infirmities.
    Similarly, if we didn’t have quantum theory, we might well use Bohmian mechanics
    while acknowledging its evidentiary infirmities and continue to play “catch up” by working toward Bohmian interacting field theories empirically equivalent to the Standard Model. But we don’t need to since we have quantum theory—with no such evidential infirmities.
    You will doubtless reply that the analogy is bad because quantum theory (in all forms) has conceptual infirmities—that it is inherently inexact, vague, supported by terrible philosophy, riddled with talk of observers, etc.
    I maintain that quantum theory may be precisely formulated with no talk of observers or measurements and can be shown to be free of conceptual problems (no measurement problem, no superluminal influences, no tension with relativity, no problematic quantum field-theoretic ontology, no Schrodinger cats or Wigner’s friends, etc.). Perhaps I shouldn’t be too provocative,but I can’t resist quoting Bob Dylan at this point:
    “Don’t criticize what you can’t understand. Your sons and your daughters are beyond your command—the times they are a-changing.”
    I agree that the discoverers of the theory gave many terribly confused accounts of what they had discovered and why one should accept it, relied on bad philosophy, and gave unsound arguments against (e.g. Bohmian) apostates. But creative physicists aren’t noted for the quality of their thinking outside of their specialty (Einstein and Bell being shining exceptions)!

    #2827

    Aurelien Drezet
    Participant

    As a kind of comment to that I wrote here a quote By Bell I found in the paper by Daniel Rohrlich:
    ‘ For me, it is so reasonable to assume that the photons in those experiments carry with them programs, which have been correlated in advance, telling them how to behave. This is so rational thatI think that when Einstein saw that, and the others refused to see it, he was the rational man. The other people, although history has justified them, were burying their heads in the sand. I feel that Einstein’s intellectual superiority over Bohr, in this instance, was enormous; a vast gulf between the man who saw clearly what was needed, and the obscurantist. So for me, it is a pity that Einstein’s idea doesn’t work. The reasonable thing just doesn’t work.’
    Well I hope that the destiny of Bohmian mechanics will be better but we are in good company any way.
    best Aurélien

    #2869

    Robert Griffiths
    Participant

    Dear Richard and Travis,

    Due to some health problems I only just got around to reading your exchange, which I found quite interesting; this is the sort of thing which a workshop of this type should facilitate. I hope to add a second comment, but let me start off with the first, addressed, Richard, to you. In your most recent #2815 you say:

    “I maintain that quantum theory may be precisely formulated with no talk of observers or measurements and can be shown to be free of conceptual problems (no measurement problem, no superluminal influences, no tension with relativity, no problematic quantum field-theoretic ontology, no Schrodinger cats or Wigner’s friends, etc.).”

    With which I am in perfect agreement. But you didn’t give us the reference to where we can find this precise formulation. It doesn’t sound quite like the proposal mentioned towards the end of your open_question_on_quantum_physics_and_the_nature_of_reality

    “…a quantum state never describes reality, even incompletely: instead, it has a twofold role in offering authoritative advice to a physically situated agent (which may be either an individual or a community).”

    and which you yourself admit is incomplete.

    Bob Griffiths

    #2875

    Robert Griffiths
    Participant

    A good understanding of quantum theory using a precise formulation free of conceptual problems, such as measurements and observables, no superluminal influences, no tension with relativity, a decent ontology, a Schrodinger cat taught not to bite, etc., should make it possible to provide a detailed critique of Bohmian mechanics: what it gets right, where it goes wrong, and the like. I haven’t written up such a detailed critique, but I have some ideas on how it might go, and would be interested to hear the reaction of others who have been engaged in this conversation.

    Bohmian mechanics (BM) as I understand it makes important use of two concepts found in SQM = standard (i.e., textbook) quantum mechanics: the unitarily developing wavefunction, in principle of the entire universe; I call it the ‘uniwave’, and the probability current in position space, thought of as traced out in a fairly literal sense by a single particle or a collection of particles. Both the uniwave and the probability current have their uses, and I employ both when I teach a course (though I don’t discuss the entire universe).

    A concept in SQM which is not used in BM is the notion that you can employ different representations for the quantum state: the position representation, the momentum representation, the energy eigenstate representation, etc. Different representations are useful for discussing different things, but distinct representations are typically incompatible and cannot be combined, e.g., position and momentum, apart from approximations using coarse grainings (beware of Heisenberg uncertainty!). As an example, harmonic oscillator energy eigenstates are useful when counting photons, but coherent states have the advantage that you can “see” the oscillator oscillating.

    In BM the liberty of choosing different representations is no longer available: you must use the position representation. One advantage is that Hilbert space projectors for position (think of them as indicating the particle is definitely in some small region of space) commute with one another, as in classical mechanics, and so one avoids quantum mysteries associated with the noncommutation of projectors that correspond to incompatible quantum properties.

    The trouble comes when one wants to discuss properties other than positions, e.g., how can we measure momentum? or energy? Here the discussions seem (to me) a bit odd, and one is likely to be told that all measurements are, ultimately, position measurements. Maybe so, but there are cases in which experimentalists claim that their pointer positions enable them to measure other things; are they mistaken? And might it not be the case that too much emphasis on position is behind the difficulty in constructing a clean relativistic version, since Lorentz transformations tend to mix up position and momentum?

    But even if we stick to positions, there is still a serious problem arising from the fact that unitary time development typically transforms the position representation into some other representation, so what were position projectors at an earlier time are mapped into something else. As long as one simply uses the uniwave to calculate the probability that a particle at an earlier time in some region R will later be in some region S, the SQM result (using the Born rule) and BM agree. On the other hand, BM is in trouble when it comes to making sense of position at three (or more) successive times, as pointed out many years ago by critics (see [1] for references) who called the Bohmian trajectories “surrealistic”. In reply, defenders of BM pointed out, with some justification, that SQM is also unable to tell you where the particle was, and therefore there is no reason to doubt the Bohmian claim that a particle can trigger a detector without ever going near it. My response in [1] noted that SQM can be made more precise by a consistent treatment of stochastic time development, and when this is done detectors designed by competent experimentalists do what they are designed to do: they are triggered when particles pass through them, and not otherwise. (I might add that in more recent work [2] I noted a situation in which BM does better than either spontaneous localization (GRW) or many worlds in addressing what I call the second measurement problem, but in general BM seems unreliable.)

    It seems that [1] has been ignored by the Bohmian community, apart from a preprint [3] that appeared many years ago. I was awaiting the published version before writing a response, but subsequent correspondence with Basil Hiley indicated he was no longer interested. Would someone else (Shelly? Travis? Aurelien?) like to take up the cudgels?

    Bob Griffiths

    [1] R. B. Griffiths, “Bohmian mechanics and consistent histories”, Phys. Lett. A 261 (1999) 227. arXiv:quant-ph/9902059

    [2] R. B. Griffiths, “Consistent Quantum Measurements”, arXiv:1501.04813. Accepted in Stud. Hist. Phil. Mod. Phys.

    [3] B. J. Hiley, O. J. E. Maroney, “Consistent histories and the Bohm approach”, arXiv:quant-ph/0009056.

    #2905
    Dustin Lazarovici
    Dustin Lazarovici
    Participant

    Dear Robert (if I may),

    I would very much like to understand better the relationship between BM and the consistent history approach. I think Shelly once made the point that they are actually somewhat similar in spirit, as they aim for a consistent transition from the micro to the macro level. I will certainly take a look at your paper [1]. I’m not sure if I’ll be able to add anything meaningful, but I might try.

    However, I believe the Bohmian position regarding “surrealistic trajectories” has been discussed many times. The Bohmian predictions are not wrong – they are just counter-intuitive. Of course, our classical intuition is based on locality and interactions in Bohmian mechanics are strikingly nonlocal (as they have to be). Once you’re willing to take BM seriously, “surrealistic” trajectories are not really a problem, you just have to accept them as a prediction of the theory that does conform with experiment. However, if you had an alternative theory that was just as clear and successfull as BM but which made more intuitive predictions concerning such which-way experiments, that would be a legitimate argument in favor of that theory.

    Concerning your other worry about BM: In BM, the objective, physical state of a subsystem is given by (Q,psi), where Q are the positions of the particles and psi the (effective) wave-function of the system. This state determines the outcome of any measurement of a macroscopic “observable”. In this sense, the experimentalist is right that his pointer position reveals an objective fact about the measured system, although not an intrinsic property that the particles posses outside the context of measurement. Moreover, if you analyze the interactions of different particles/systems, you will find that what we call “energy” or “spin” or “momentum” etc. has pretty much the familiar functional role – although, on an ontological level, everything can be further reduced to the motion of particles.

    (On a side note: the position representation is distinguished in BM, because BM is a theory about stuff in physical space. But of course, on the level of the wave-function, you are free to do all the familiar operations.)

    The Bohmian usually feels that this modest anti-realism regarding quantum observables is exactly what the appearent paradoxes of SQM and the familiar no-go theorems à la Kochen-Specker suggests. However, I understand why someone would like even more realism regarding these quantitites. I the consistent histories approach can achieve this, without twisting the notion of probability too much, it would be a remarkable feat.

    Best regards,

    Dustin

    #2914

    Robert Griffiths
    Participant

    Dear Dustin,

    I appreciate your taking a look at [1] in my previous post, and I hope you will look at some of the work referenced there. Regarding the connection of CH and BM the following additional comments may be helpful.

    In BM the psi of (Q,psi) in your notation is what I call the uniwave: unitarily developing wave function of the universe. One can employ the uniwave in CH in order to generate probabilities at any given time, which is roughly what is done in SQM, of positions or of anything else. So aside from a few niceties about infinite-dimensional Hilbert space, in CH we have psi(t) -> Pr(Q,t). To that extent BM and CH agree. But notice that Pr(Q,t) refers to just ONE time; the correlations between different times are absent.

    In CH if you want to talk about what is happening at two or more times (following the initial time at which psi got started) it is necessary to introduce a family of histories, as in a classical stochastic process, and assign probabilities according to the extended Born rule, provided consistency conditions are satisfied. In BM one instead uses the Q(t) trajectory. And here the answers are sometimes the same, but also sometimes very different. E.g., as pointed out in [2] in my previous post there are cases in which BM supplies a definite answer to what I there call the second measurement problem, and in this respect is to be preferred to GRW or Everett. However there are other cases in which the BM statement contradicts CH and the beliefs of experimental physicists.

    I think you need to take these “wrong answer” cases much more seriously. For if we remove Q(t) from BM what remains does NOT provide temporal correlations valid for 2 or more times (initial setup gives psi, and then two later times), and one is left with something very similar to textbooks. So Q(t) has to be there for BM to be interesting. But if it sometimes gives the right answer and sometimes the wrong answer from the perspective of how experimentalists interpret their experiments, what justifies the claim that BM is an interpretation that agrees with experiments? This, it seems to me, is a key question to be addressed.

    Bob Griffiths

    #2915

    Aurelien Drezet
    Participant

    Dear Robert Griffiths,
    I am sorry I could not find the time to answer to your late remarks during the forum ( the temperature in Grenoble France was then reaching 40 ° Celsius and it was difficult for me to focus on science).
    I would be very pleased however to try something in order ‘ to take up the cudgels” as you propose.
    For me the main issue regarding your consistent history interpretation concerns the meaning of the paths defined using the ‘Wigner formula’ for correlations when there is no observation made (i.e. when discussing about the meaning of a path in an interferometer without path detector). For example, some authors like Y. Aharonov or D. Miller are not afraid to use retrodictively QM between measurements but what about the consistent history interpretation? Are you only considering actual experiments like in Bohr’s approach? If yes what is the difference with copenhagen? Also the consistency condition on the sum on histories (sum on non diagonal term=0) plays a fundamental role in your approach. Why is that since only one history will be actualized any way? If you give some value to all other histories which didn’t happen (but could have) using a consistency condition are you somehow making a new ontological axiom concerning what is allowed to be or not to be?

    Any way I will read again your comments and papers in order to clarify those points.
    On the same footing Basil Hiley in his book with Bohm discussed already the consistency interpretation and Sheldon Goldstein also commented it in his phys today paper. Do you think they missed the points concerning your theory?
    It would be very interesting to have a discussion with you on these topics in order to compare those two interpretations.

    PS: concerning surrealistic paths I wrote few papers on this subject which clarify (at least for my Bohmian eyes) some aspects of the problem

    With best wishes

    #2918

    Bob, can you give a simple concrete example of the kind of thing you have in mind when you say that BM sometimes “gives the wrong answers” and/or fails to make correct predictions for certain (two-time) correlations? I’m pretty sure you are forgetting that what we actually have direct access to, empirically, are “pointer positions” and such things. So for example if there is some particle (in the 2-slit experiment or something) and BM tells us its position x(t), you might think the theory gives “wrong answers” for (e.g.) the correlation between where it is at t_1 (say, when it’s going through one slit or the other) and where it is at t_2 (way, when it’s hitting the detection screen). But if you want to analyze this kind of situation and compare to empirically measured correlations, you must include the measuring equipment and the effects of that measuring equipment on the particle. In particular, for example, the distribution of particle positions at t_2 will be different if you say that, at t_1, a position measurement was made (in which the position of some macroscopic pointer was arranged to become correlated with whether the particle in question went through the top slit or the bottom slit). I’m pretty sure you are just forgetting/ignoring this, if you think that there is something “wrong” with BM’s predictions for 2-time correlations. (Reinhard has also tried to make this same criticism of BM.)

    Anyway, maybe that’s already enough to help you appreciate why actually the theory’s predictions are not at all wrong. If not, if you can give a concrete example of what you have in mind, I think it would be fruitful to talk through in detail.

    #2922

    Robert Griffiths
    Participant

    Dear Aurélien,

    The consistent histories (CH) approach is best thought of as an interpretation of QM in terms of ‘events’, not just measurement outcomes, inside a closed quantum system, without making any reference to things outside this system. Measurement apparatus, if any, is to be included as part of the closed system, and described in fully quantum terms. Measurements are simply examples of physical processes, and the rules for describing them are the same as for all quantum processes. If you want to look into it, the best place to begin is one of the shorter articles I have written, as indicated in the Consistent Histories Essentials of the IJQF workshop.

    Now to your specific questions. The CH approach allows retrodiction from measurement outcomes to previous properties; e.g., in the EPR-Bohm situation, if Alice measures S_x and gets the value -1/2, she is justified in concluding that the particle had this value of spin just before it entered her apparatus. This is worked out in some detail in [1]. (This topic also came up in the IJQF workshop in the Time-symmetric theories section where I started a thread Retrocausation vs Retrodiction.) However, the discussion of events, microscopic or macroscopic, is not limited to situations where there are measurements, so there is not a limitation to actual measurements, as in Bohr’s approach. We consistent historians regard our approach as ‘Copenhagen done right’: we show that the results which emerge from the usual calculations based on textbook presentations are (usually) correct, but the arm waving that accompanies them is often misleading or unnecessary.

    The consistency conditions are employed to single out families of histories to which probabilities can be assigned using the extended Born rule, probabilities which are not limited to measurement outcomes. Whereas in a given consistent family only one history will be actualized, CH is a probabilistic interpretation of QM, and standard (Kolmogorov) probability theory requires a sample space of mutually exclusive possibilities. I am not sure these remarks are addressing your concerns, and it might help to take up a specific example if you have one in mind. (E.g., various history families are discussed in [1].)

    Regarding Bohm and Hiley. It is twenty years since I looked a their treatment, so I had to pull out my old notes. Their discussion is based entirely on the earliest Gell-Mann and Hartle publication in 1990; there is no reference to my work or that of Omnès. At that time (1990) the CH approach was still undergoing substantial development; my own ideas were not entirely clear until the mid 1990s. So a lot of the Bohm and Hiley discussion is out of date. You will find a list of later criticisms of CH, though not from the BM perspective, in [2].

    As for Shelly’s 1998 presentation in Physics Today, it is full of mistakes; unfortunately he did not take the trouble of sending me a copy in advance, so I had to write a lengthy letter published in a later Physics Today; it you want I can try and dig up the reference.

    Your attachments were already in my files, but I took another look at your 2006 PLA to refresh my mind. It is too bad you were not aware of my work on Bohmian trajectories, as I think you would have found it much harder to refute.

    I hope these comments are of some help, and that things have cooled down a bit in Grenoble. Otherwise you should plan to take your laptop up into the mountains, which I understand are very impressive.

    Best wishes! Bob Griffiths

    [1] EPR, Bell, and quantum locality. Am. J. Phys., 79:954–965, 2011. arXiv:1007.4281.

    [2] R. B. Griffiths, “A Consistent Quantum Ontology”, Stud. Hist. Phil. Mod. Phys. 44 (2013) 93; arXiv:1105.3932

    #2924

    Robert Griffiths
    Participant

    Dear Travis,

    The standard simple example is found in Bell’s SPEAKABLE … on p. 111 (I think the same in both editions) and given in a figure on the bottom of that page. Bell seems to ascribe it to Wheeler, and maybe that is where it originated, but Bell’s version is very clearly worded. The basic issue is that two wave packets cross in empty space and the Bohmian particle ‘hops’ from one to the other, or you can say it “bounces”. You will see an example of this phenomenon in Lev Vaidman’s contribution to this workshop (In “Bohm’s Theory). Bell acknowledges that this behavior is counterintuitive: “It is vital here to put away the classical prejudice that a particle moves on a straight path in ‘field-free’ space …”

    What Englert et al pointed out was that if you insert a ‘which way’ detector ahead of the location at which the “bounce” takes place there can be occasions when the detector is triggered despite the fact that the Bohmian particle takes the other path and never comes close to the detector, and this was their basis for declaring the Bohmian trajectory to be ‘surrealistic’. As I noted in my earlier post, the Bohmian defence was that SQM doesn’t tell one where the particle happens to be except if it is measured, and therefore their story was as good as any. My reply was (and is) that consistent histories (CH), which is a fully consistent extension of SQM minus various obscurities, can very well say something about where the particle is when it is not being measured, and in the situation under consideration it says there is no bounce where Bohmian mechanics calls for one. And I remark that the experimental program at CERN, or at least the interpretation of the experiments, would be put in serious doubt if physicists did not have the “classical prejudice” (justified by CH) that contradicts BM.

    I agree that what we have access to at the macroscopic level is “pointer positions” and “preparation procedures”. But quantum mechanics was developed in order to have a physical description of the microscopic world, and when we say that it has been confirmed by experiments we mean that it provides a microscopic story that allows us to understand experiments which probe (or so most physicists believe) the microscopic world, even though their inputs and outputs are necessarily understood in macroscopic terms. I add that CH takes full account of experimental apparatus to the extent that it can be modeled at all in quantum terms; two chapters, 17 and 18, of my book along with a large number of toy models are devoted to that task.

    So I think your criticisms miss the mark. On the other hand I don’t claim to be infallible, and if you, or Aurélien, can find some mistake in my analysis of the situation discussed above–see [1]–or of my general proof of quantum locality–see [2]–you will certainly be doing me and the community a favor.

    Bob Griffiths

    [1] R. B. Griffiths, “Bohmian mechanics and consistent histories”, Phys. Lett. A 261 (1999) 227. arXiv:quant-ph/9902059.

    [2] R. B. Griffiths, “Quantum Locality,” Found. Phys. 41 (2011) 705;
    arXiv:0908.2914.

    #2931

    Aurelien Drezet
    Participant

    Dear Bob, I found your paper ‘Bohmiann mechanics and consistent histories’ fascinating. Before reading this paper I always missed the point(s) concerning your interpretation (even though I apparently downloaded your preprint 10 years ago…). Now it seems that things a getting more clear for me.
    If I follow the reasoning of your paper CH (consistent history) paths have only an approximate meaning since projectors should not be too precise if we dont want to disturb the wave packets too much. For Bohmian mechanics of course the precision is instead infinite since the theory defines a dynamical trajectory for a point like object. In your CH model you can not preserve interference and path(s) at the same time since your precision is limited by the law of measurements (for example in the region J of the figure 1 we have fringes). Bohmian mechanics can explain both path and interference in one model and in the region J the particle must bounce in order to explain fringes and nodes. There is no contradiction between both models if we compare them ONLY with observables i.e. detectors outputs limited by the Heisenberg principle and the law of entanglement. Now, for me the question is the following : Are you ready to accept an approximate precision in the definition of an ontology? This is clearly not the case for Bohmian but it seems to be clearly the case in your CH interpretation.
    Of course, I agree with you that Bohmian mechanics will contain a metaphysical part leading to surrealistic behavior but this will never contradict facts and even explain them (this is the aim of an ontological model after all). This is the price you have to pay in the Bohmian universe and I agree with you: it is fundamental to accept that limitation. Your model instead, is the best that we can keep by sticking to the strict laws of observables (with the Wigner correlation formula P(1–>2)=tr(P2P1rhoP1P2) etc..). The price you have to pay is that you definition is coarse grained and that the more precise you could define a path the more invasive you will be. Still my question ‘are you ready to accept such an imprecise ontology?’ remains. For me there is no contradictions as far as you accept to consider these paths as detector paths like in a bubble chamber or in the experiments used by Serge Haroche with Rydberg atoms. If instead you want to define path with an infinite precision and go back to an ontology without approximation a la Newton or Einstein I am afraid that you should use instead something like the de Broglie Bohm dynamics. Of course, I want to point out, that I have a very deep respect for both ways of looking at the problem and since I am mainly an experimentalist working with photon detectors and correlators I am very sensitive to your approach which is pragmatic and still keep a track of ontology (unlike the too positivist Bohrian do). Still I am convinced that the aim of physics is to describe the universe as it is not only as we see it (with imprecise eyes). By doing that I am necessarily weakening the correspondance between facts and theory which was admitted to be one to one in the Newton time (at least in theory of course: Newton or Laplace were not idiots and understood very well the diffference between dreams and real experiments with unperfect data and apparata). This is a philosophical aspect I found fascinating something like the end of Popper.
    I would be very interested to know your point of view on my short analysis.
    I will go through the phys Today debate and to the comments by Basil during this day if I can find the time.

    With best regards

    PS: I added a paper I wrote where my view was balanced between Bohr and Bohm (actually I prefer de Broglie 🙂 )

    #2936

    Robert Griffiths
    Participant

    Dear Arélien,

    You raise a couple of points. For convenience in replying let me number them, as I find this helps me keep track of things.

    1. Approximate paths. In the CH there is nothing except Hilbert space and Hilbert subspaces at the fundamental level, and in Hilbert space there are no mathematically precise positions and thus no mathematically precise paths. However, as noted in every textbook it is in many circumstances possible to have paths which are pretty-well defined if one keeps the usual uncertainty relations in mind, and that is the approach that I took in my paper. For the example of interest, in which one can think of the distances traversed by the particle as macroscopic, the sort of approximation I made are the usual sort of thing employed in theoretical physics, so I confess I don’t see why you are making an issue of it. The failure of Bohmian mechanics to give a physically plausible answer is a matter of centimeters, not nanometers. Would you agree?

    2. Approximate ontology. My answer to your question, ‘Are you ready to accept an approximate precision in the definition of an ontology?’, is that the CH ontology [1] is based on Hilbert subspaces, and if for treating certain situations it is useful to use approximations to these subspaces I see no harm in doing so. While it is very useful to employ precise mathematical models in physics in order to keep our thinking straight, it is also a good idea to keep in mind that no theory in physics is exact. We do not know the exact form of the general relatistic corrections to the spectrum of a hydrogen atom, nor even how to do an exact (non-perturbative) treatment in QED.

    3. Your Afshar attachment. I was not aware of your article and have added it to my long list of references on that topic. It may interest you to know that early on when he was trying to convince people that there was really something very exciting, he flew to Pittsburgh in order to get my opinion. I am afraid I disappointed him; I told him how to analyze it using histories, but he was not very interested.

    Best wishes, and I hope the weather is a bit more comfortable. Bob Griffiths

    [1] R. B. Griffiths, “A Consistent Quantum Ontology”, Stud. Hist. Phil. Mod. Phys. 44 (2013) 93; arXiv:1105.3932

    #2945

    Aurelien Drezet
    Participant

    Dear Bob,
    Thank you for the different answers. My point concerning the precision of the path concerns the ontology used in the CH model. If your aim is to define counterfactuals associated with paths not observed but supposed to exist then it seems that your CH model is less precise than BM since you don’t have determinism, i.e no precise position x(t) and no trajectory. If you accept that of course this is OK otherwise the theory is incomplete.

    Any way, by reading some of your previous papers and re-reading the book by Roland Omnes and one by Bernard Despagnat I realized that the usual Mach Zehnder interferometer experiment is analyzed in a very ‘orthodox’ way in your CH model. This leads to curious properties no so intuitive for a realist.
    Indeed, consider a state ‘psi_0’ sent on a beam splitter 1 (BS1) and splits into two paths ‘left’ and ‘right’. These path are subsequently sent on a second beam splitter BS2 and all the state finishes its journey in the exit door 3 with probability P(3)=1; the exit door 4 being always empty. I convinced my self this morning in front of a good coffee (before the heat of the day start :)) that the set of histories ‘Psi0–>Left–> 3’, ‘Psi0–>Left–> 4’, ‘ Psi0–>right–> 3’, ‘Psi0–>right –> 4’, is not a consistent set in your interpretation (as you indeed wrote many times) because the different wave functions involved are not orthogonal (sorry if I repeat some obvious things for you but this theory is quite new for me). Now, the probability to observe 3, i.e. P(3)=1, is the sum of
    P(3,Left)+P(3,right)+2Real[ <Psi0–>Left–> 3|Psi0–>right–> 3>]=1/4+1/4+2*1/4=1 and the probability to find ,the particle in the gate 4 P(4)=0 is similarly P(4,Left)+P(4,right)+2Real[ <Psi0–>Left–> 4|Psi0–>right–> 4>]=1/4+1/4-2*1/4=0. The non always positive diagonal terms induce interference and allow to obtain the good probability P(3)=1 and P(4)=0 from histories which have all a weight 1/4>0. I understand that you consistency condition prohibits such an history set by definition and that the question ‘which path was followed by a particle in an interferometer’ is a wrong question in the CH interpretation. But then what is good history set and what does it implies concerning realism?. A good set of histories in the CH interpretation is obviously associated with ‘Psi0–>sigma+–> 3′,’Psi0–>sigma+–> 4’, ‘Psi0–>sigma- –> 3′ ,’Psi0–>sigma- –> 4’ where the state sigma+= (right +i*Left)/sqrt2 and sigma-=(right -i*Left)/sqrt2 which are associated with cat states have been introduced.
    Now, we have P(3)=P(3,sigma+)=1 and P(4)=P(4,sigma+)=0 since all other terms, including the non diagonal elements, vanish. What I find most striking here is that by allowing a second beam splitter BS2 you find, in full agreement with orthodox ‘copenhagenists’, that between the preparation and the final actual measurement at gate 3 or 4 the good histories can not include paths ‘left’ and ‘right’ while it can do it of course if only the first BS1 is present. How can that be in an ontological theory? Your reality is thus changing as a function of the context? This is what we indeed learn in text books but in the context of Bohr approach which refuse to speak about the nature of the system between measurements (counterfactuals have no meaning for Bohr). I was convinced that you tried to save realism while your theory seems better to destroy it unless you admit some non contextual features that your theory can not explain. This implies the paradoxical fact that the presence of the second BS2 which can be introduced after the wave packet crossed BS1 can change the nature of the object even retrodictively by acting into the past (see the Wheeler delayed choice experiment). So your theory is not so intuitive as I expected. BM do not need backward causation and the nonlocality is induced thanks to a preferred frame. I dont say that this is better but both approach are ‘surrealistic’ contrarily to your claim. Clearly it means for me that CH is not better than BM for explaining QM in an ‘intuitive’ way (this is not so surprising finally).

    I hope that my explanation was not too detailed with best regards Aurelien.

    PS: I agree with you that the disagreement with a ‘plausible answer’ in BM is in cm not in nanometer. I could even add in meters or kilometers since beam splitters and optical fibers are used on large scale nowadays. Bujt the same is now also true for the CH interpretation is wou can act retrodictively over kilometers it seems that the notion of past becomes anbiguous in your approach.

    #2950

    Robert Griffiths
    Participant

    Dear Aurélien,

    Let me reply to your opening paragraph by saying that the ontology of CH and of BM are very different; in fact, there is little if anything in common. In CH the ontology begins with Hilbert subspaces, whereas in BM the central idea is a collection of classical particle positions. Certainly one can find Hilbert subspaces which approximate particle positions, but the whole mathematical structure is very different. So if you wish to criticize CH for not having particle positions, my reply will be: do you criticize the cosmologists for refusing to tell you the location of the center of the universe? After all, that was well defined and located at the center of the earth during the Middle Ages. The other point of overlap between CH and BM has to do with the unitarily evolving “wavefunction of the universe”, what I call the “uniwave”. In BM this is a very important part of the theory; whether part of the ontology seems to depend on whom you talk to. In CH the uniwave is generally not necessary, but if it is used at all it is considered a pre-probability, a generator of probabilities, and therefore NOT part of the ontology.

    Next, on to your discussion of beam splitters. Mach-Zehnder interferometers and Wheeler’s delayed choice. These matters are discussed extensively from the CH perspective in my book [1], chapters of which are available online if you don’t have the paper version. See in particular Chs. 12, 13, 18 (for successive measurements after a beamsplitter), and 20 (delayed choice). I think you should be able to follow the ideas, and if you work out some of the examples yourself, you will get some feeling for the CH approach to these things. There are also figures, which could aid discussion given that email is not too good for communicating figures.

    One issue that you mention is retrodiction, which is easily confused with retrocausation. With reference to this you may want to take a look at the thread ‘Retrocausation vs Retrodiction’ in this workshop, under the heading of ‘Time-symmetric theories’, which I began and which contains a discussion with Wharton and Stuckey. CH is often criticized, and I think this is part of your concerns, for letting the the future ‘influence’ the past in the following way. If you are constructing a family of histories by choosing an initial state, a projective decomposition of the identity (PDI) at a later time, and another at a still later time, etc., you may find that as you add later PDIs the earlier family you constructed no longer satisfies the consistency conditions, and so the “future is influencing the past”. This overlooks the fact that families of histories are constructed by theoretical physicists in order to provide a consistent quantum description of events in a closed system (which is where consistency conditions apply), and the choices of theoretical physicists have no influence on reality. What we do is somewhat similar to historians writing historical accounts, and given the proximity of Bastille Day I refer you to a little analogy you will find towards the end of the last section of Ch. 14 of my book.

    Bob Griffiths

    [1] Consistent Quantum Theory (Cambridge 2002)
    http://quantum.phys.cmu.edu/CQT/

    #2957

    Aurelien Drezet
    Participant

    Dear Bob, I Think we should may be continue this discussion by email since the page of the forum is sometimes blocked for unknown reasons.

    First, concerning the ontology: BM uses also the Hilbert space for defining the guiding waves otherwise the theory will not work. The ontology is double : particles and waves. Both are necessary and are on an equal footing.
    Now, in your CH interpretation the key ingredient is the counterfactual interpretation of the many-time correlation formula also known as ‘Wigner’ formula (for example trace [P2P1rhoP1P2]] where P2 and P1 are projectors associated with measurements at different times ). You want to use this formula to speak about things which were not observed but could have happened. Since you didn’t observe them I am pretty sure that a Bohrian like Zeilinger would class your theory in the ‘hidden variable’ drawer together with BM. They are some differences since the ontology are different but I am affraid that they are both metaphysical in the sense of Heisenberg. I am convinced that, in the present state of our knowledge, in order to solve the problem of which ontology is ‘better’ one would need ‘god eyes’. In other words, if we dont find new data in the future the game is over for making any progress. I can not believe in that of course but this can not be excluded. May be we have already reached the end of ontological science. If quantum mechanics is rigorously true for ever there is no hope to solve the dilemma.

    Second, I have your fantastic book in front of my eyes and I went through the chapters you mentioned specially the chapter 14 and 20. What I do not understand is that if you think about an history you can update for sure your information and select was is necessary like for an historian analyzing the Bastille attack. However, the historian can not change the past : facts are facts and he can only put filters to select the good information from the full mess (which was already written in a block world picture to which I subscribe). Now, the choice of the projector families used to define your ontology is forced by your consistency condition, which is by the way not exactly the same as the one used by Gellmann and Hartle, and not all the sets of correlators are consistent if you want to find the usual classical sum rules for probabilities. However, by doing that you introduce some very strong constraints which can lead to contradiction like in the Wheeler delayed-choice experiment involving retrocausality (a point which is absent in BM at least in the preferred frame: each theory has is own surrealism). Your stochastic theory analyzes the interferometer with the two BSs using consistent histories which are not the same as the ones used without the second BS. This is a contradiction for me if you don’t involve retrocausality. Did I missed something? In the same vain I have also the feeling that even worst contradictions could come from Hardy’s experiment watched in different Lorentz frames since what is allowed for an observer in a reference frame is not necessarily possible for an observer in a different frame when the causal order of events is changed.

    with best regards Aurélien Drezet
    PS: I like very much this discussion and may be we will find a way to disagree or agree in a short text for this forum or the IJQF journal at the end.

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