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B Some questions about Bohmian mechanics

  1. May 14, 2017 #1
    stevendaryl, vanhees71, Demystifier, atty and others well verse in Bohmian mechanics and know the ins and outs or the basic. Some questions I'd like to ask.

    1. What would happen if Bohmian Mechanic is not inherently random, for instance.. if the trajectories or initial conditions were controlled by another field that is inherently random.. is it still called Bohmian Mechanics? (if not.. how come?)

    2. What would happen if there was no trajectories but QM particles have substantial (or ontological meaning "really there") existence that can appear and disappear. Would it still be called Bohmian? I am thinking whether substance or ontology is the essence of BM?

    3. What main features of BM make it distinctly BM then and what experimental signatures to look for (trajectories or substance for example)?

    Thank you!
  2. jcsd
  3. May 14, 2017 #2


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    BM is not that strict a term. In each case one should just make clear using plain English what one means. The point of BM is to solve the measurement problem, so it depends on what one means by "inherently random". If the inherent randomness reintroduces the measurement problem or introduces non-realism, then it would be contrary to the spirit of BM.

    It would share with Bohmian mechanics a realistic ontology, but in technical details it is sufficiently different that we call these realistic collapse models such as GRW or CSL.

    At present, I use BM to mean a theory with hidden variables and unitary evolution of the wave function. We still do not have a BM that is consistent with all of the standard model, so I think that is a more important problem to be solved than to look for experimental signatures. However, you can look up the work of Antony Valentini for some excellent efforts.
  4. May 15, 2017 #3
    Do hidden variables automatically equate to trajectories? Are there non-local hidden variables that don't have trajectories?
  5. May 15, 2017 #4
    dBB is a deterministic theory. It recovers quantum predictions only in quantum equilibrium. What creates this quantum equilibrium is irrelevant. It may be simply our failure of knowledge of or inability to prepare the initial conditions. Valentini's subquantum H-theorem follows Bolzmann's H-theorem to explain the appearence of equilibrium.
    DBB theory is not obliged to be about particles, it works for every configuration space ##q(t)\in Q##, all one needs is that the energy is quadratic in the momentum variables ##H= (p,p) + V(q)## with some positive-definite quadratic form ##(.,.)##.
    So, you can have a field theory, which fits nicely, ##H= \int \frac12 \pi^2 + \frac12 (\partial_i \varphi)^2 + V( \varphi) dx^3##. Then, the ontology is defined by the field ##\varphi(x,t)##, and the wave function is some functional. But the quantum excitations, which appear in this theory as quantum effects, have no relation to this ontology.

    This would be the same as if you consider in usual particle BM theory sound waves of an atomic lattice and get phonons. The phonons can be created and destroyed, but are not part of the ontology. The ontology would be defined by the positions of the lattice atoms. so, BM may have no trajectories for the elementary particles we observe, in the same way as BM condensed matter theory may have no trajectories for phonons. But it has a trajectory in some configuration space.
    There are no experimental signatures, because there is an equivalence theorem. Some people try, with sloppy reasoning about "weak measurements", to create some experimental signatures. But as far as I know, this has to fail, because weak measurements are nothing but usual interactions, which can, as well, be described in the standard approach, without anything new, so that the equivalence proof would take over.

    What distinguishes BM from other realistic interpretations is that it is deterministic. Other realistic interpretations see the Bohmian velocity only as an average velocity.
  6. May 15, 2017 #5
    We have. But I doubt that it is allowed to give here the reference.
    Gauge fields are certainly not a problem, the first example was given already in Bohm's original paper. Fermions are a problem, but there is a nice solution for pairs of Dirac fermions, and this is all we need once we consider neutrinos as usual massive Dirac fermions. For such a pair, the sum of spin and isospin defines a representation of so(3), and so you can construct a geometric interpretation for such a pair.
  7. May 15, 2017 #6
    How about the other way around. dBB being a low energy limit of a fully relativistic ontology.. in other words.. particles have trajectories. But that is default mode and when you use the higher ontology. It has no trajectories, non deterministic. dBB being just to manifest them locally. Isn't this possible? Any physicist is working on this?

    Now this is not related to my questions or concepts above.
    In the orthodox interpretation. The particles values only appear during measurement.. but in BM.. the values don't disappear even after measurement.. therefore can't you use this concept to make a system as memory device of a computer in BM?
  8. May 15, 2017 #7
    Then it is not a question about dBB, but about that other unknown theory. If something is possible in some unknown theory is nothing I can tell you.
    Not in quantum equilibrium, because in this case it is equivalent to quantum theory. Which is a theorem.
    Outside quantum equilibrium a lot of other things would be possible, in particular FTL signaling. And a dBB computer working outside quantum equilibrium could be, indeed, more powerful than a quantum computer.
  9. May 15, 2017 #8
    Going back to this. Is Demystifier BM about particles or fields as the ontology? How about the orthodox BM.. are particles always the ontology here? What do you call BM where the ontology is the field or particles.. there must be different labels to distinguish them.

    So for those that use fields as the ontology.. so the Bohmian field is deterministic and not relativistic.. and only the particles (akin to phonons) are relativistic.. right? How many percentage of Bohmians are aligned to this concept?

  10. May 15, 2017 #9
    Ask Demystifier. The usual way dBB theory is presented is for non-relativistic particles. I think this is a big pedagogical error, and one would be better to present Bohmian field theory from the start as one of the examples of a dBB theory.

    You can, of course, name this usual way to present BM "orthodox". But what is "orthodox" if not what is presented in the first paper? Which includes already a Bohmian variant of the EM field.
    If the field equation is a relativistic one, why would you name the theory non-relativistic? Because it has a preferred frame, similar to the Lorentz ether? Strange, given that the theory gives the same predictions, and those who object claim that all what matters are predictions. If all what matters are predictions, then metaphysical objections against a preferred frame should not matter.

    What is relativistic is the classical wave equation ##\partial_t^2 - \partial_i^2 \varphi(x,t) = 0##, the Lagrangian, the Hamilton formalism, all the observable predictions as for the classical, as for the quantum case. That should be enough relativistic symmetry for anybody who does not care about metaphysics.
    I don't know. There are certainly Bohmians who dream about a relativistic version without an explicit preferred frame. I don't understand them. This was the point of Bell's theorem: Don't try to make dBB theory Lorentz-covariant, this necessarily fails, any causal realistic interpretation needs some FTL causal influences.
  11. May 15, 2017 #10
    But you mentioned in earlier message above that:

    "This would be the same as if you consider in usual particle BM theory sound waves of an atomic lattice and get phonons. The phonons can be created and destroyed, but are not part of the ontology. The ontology would be defined by the positions of the lattice atoms. so, BM may have no trajectories for the elementary particles we observe, in the same way as BM condensed matter theory may have no trajectories for phonons. But it has a trajectory in some configuration space."

    In using the lattice atoms analogy.. the phonons can be created or destroyed so relativistic.. while the lattice atoms can't be created or destroyed hence I assume they are not relativistic. But then.. relativistic QFT is about particles that can be created or destroyed.. so if they can't be destroyed.. they are not relativistic. You make analogy of the lattice atoms as the field which you mentioned has trajectories.. I thought all that has trajectories are not relativistic.. no?

    I read this message by atyy where you recently discussed with him. He said "If the theory breaks down at high energies, then we can consider the possibilty that the low energy relativistic theory - including the Lamb shift - emerges from a non-relativistic high energy theory." I thought you were referring to his high energy field theory as non-relativistic. I guess it's different concept? Can you please rephrase what he was saying and what you are describing now to distinguish the different concepts? Ty.

  12. May 15, 2017 #11


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    What do you mean by "Demystifier BM"? Do you mean the idea outlined in https://arxiv.org/abs/1703.08341 Sec. 4.3?
    If you do, then fundamental ontology are non-relativistic particles, from which relativistic fields emerge as effective description, from which relativistic particles (which are really quasiparticles) emerge as excitations of those fields.
  13. May 15, 2017 #12
    Thanks for pointing out the source of the BM phonon analogy. It is very clear now. But it is really very inelegant. I'll explain.

    Our universe is very elegant. But our theories are not. For example. UPS send parcels manually by airplane or ocean. But 1 trillion years from now.. would this remain so and for a universe that came from Big Bang and so fantastic. Would we be limited by this. In an elegant universe, UPS should be able to send parcels by teleporting them from one part of the earth to another. Bohmian mechanics won't give this capability. It is so Newtonian and mechanistic. The orthodox interpretation where realism doesn't exist is really more elegant because it gives nature more flexibility like future machines that can teleport parcels. In a very elegant universe, this should happen. Very illogical if it doesn't.. think about it. Anyway. I think all interpretations are wrong... there may be hidden variables but it is not Bohmian.. therefore you must explore this in your future papers...
  14. May 15, 2017 #13


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    But how is there a Bohmian theory that can deal with chiral fermions and non-Abelian gauge fields?

    I know about https://arxiv.org/abs/0908.0591 and https://arxiv.org/abs/1305.1045, which would help the construction of a Bohmian standard model, but I haven't read them carefully enough myself to know if they are right, and I don't believe any consensus has developed about them.
  15. May 15, 2017 #14
    Chiral fermions simply as particles are not a problem, given that without gauge interaction they are simply (with massive neutrinos) Dirac particles. And for a pair of Dirac particles the construction of https://arxiv.org/abs/0908.0591 seems fine. That it needs, additionally, a massive scalar field for each pair, so what, nice DM candidates.

    So, what is problematic is gauge fields. Non-abelian is also not the point, with Wilson lattice gauge fields. Chiral gauge fields are only a problem if one insists on exact gauge symmetry. But why would one have to care about this, once one needs only an effective field theory (so that even non-renormalizable gravity is fine), and, moreover, the observed chiral gauge fields are massive?
  16. May 15, 2017 #15


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    Please review the PF rules on personal speculation. You are at that point with your latest post.
  17. May 15, 2017 #16


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    Quite possibly, but I don't think the lattice community has reached a consensus yet, so I state it as an open problem.
  18. May 15, 2017 #17
    Reading wiki about Hidden variable theory https://en.wikipedia.org/wiki/Hidden_variable_theory Note even Einstein mentioned it (before Bohmians) so hidden variables are not the stuff of Bohmian.. so I wonder why you stated that you use BM to mean a theory of hidden variables and unitary evolution. Also its stated in wiki:

    "Although determinism was initially a major motivation for physicists looking for hidden variable theories, non-deterministic theories trying to explain what the supposed reality underlying the quantum mechanics formalism looks like are also considered hidden variable theories; for example Edward Nelson's stochastic mechanics."

    So it is indeed legal or correct to state that it is possible orthodox interpretation or Copenhagen has hidden variables but it doesn't automatically make it a Bohmian, right? Please emphasize if this is right before I share this in a discussion with others.

    About unitary evolution. Many worlds have unitary evolution.. but how come unitary evolution is already attributed to BM??
  19. May 15, 2017 #18
    There may be many hidden variable theories, dBB theory is simple one such theory.
    First, the Copenhagen interpretation explicitly rejects any hidden variables.
    Second, not every hidden variable theory is dBB theory. But dBB theory is an example of a hidden variable theory.
    The Schrödinger equation of QM defines an unitary evolution of the wave function. So, if there is a place to attribute unitarity, it is simply QM. Some interpretations introduce, additionally, some non-unitary evolution - the collapse of the wave function - to handle Schrödinger's cat.
  20. May 15, 2017 #19
    Why, in the wiki, it was written: "Historically, in physics, hidden variable theories were espoused by some physicists who argued that the state of a physical system, as formulated by quantum mechanics, does not give a complete description for the system; i.e., that quantum mechanics is ultimately incomplete, and that a complete theory would provide descriptive categories to account for all observable behavior and thus avoid any indeterminism."

    What if Copenhagen is still incomplete and the indeterminism is just lower limit of another theory altogether?

    So in BM, the wave function doesn't collapse but what does BM do unitarily wise that differentiate it from Many Worlds which make them still both Unitary? In Many worlds, it is naturally unitarily because the wave function just goes and on.. but in BM.. it doesn't go on and on.. why is BM considered unitary?
  21. May 15, 2017 #20
    I don't understand the point of this question. In the Wiki it was written because it is a more or less accurate description. Which happens sometimes, in particular in scientific questions. If QM is still incomplete, then the Copenhagen interpretation is wrong about QM being complete.
    BM also contains a trajectory of the configuration, which is also what we see around. It is not obliged to differ from Many Worlds in everything. It is only obliged to make sense in itself. If other interpretations are wrong, or fail to make sense, this is not a problem of BM, but of these other interpretations.
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