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Some Bohm questions

  1. Jul 28, 2008 #1

    Hurkyl

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    Or "what are particles good for?"


    Particles (as defined in the Bohm interpretation) exist, have well-defined positions and momentums, and get pushed around by the wave-function. However, they do not actually have any sort of effect on anything at all -- in fact it appears that their role seems more like the hypothetical test particles one commonly uses when analyzing a force field or space-time geometry, rather than corresponding to actual, 'physical' particles. This spawns two questions:

    (1) As a purely analytical question, what sorts of problems are this sort of 'test particle' good at describing?

    (2) If I want to consider Bohm interpretation as being the 'correct' description of reality, how do I reconcile the test-particle nature of Bohm particles with the fact that physical particles really do interact with with stuff? (Or... was I not supposed to make such a correspondence in the first place?)
     
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  3. Jul 28, 2008 #2

    The particles are ultimately all we see in experiments. For example in the single or double slit experiment with one electron or photon at a time being emitted, you see only small scintillation points, which we infer to be particles. And it is from these particles that we eventually infer a wavefunction because the particle positions on the detector screen build up as a wavelike pattern. From this, deBB theory just makes the very simple inference that those point particles exist in the world even before measurements, and sets out to write down the equation of motion for those particles for all times. The particles are also necessary for solving the measurement problem, namely, the preferred basis problem and problem of definite outcomes. For a clear discussion of how deBB solves the measurement problems with the particles, please see section 3.3 "How the deBB theory solves the measurement problem" of this paper by Passon:

    http://arxiv.org/PS_cache/quant-ph/pdf/0611/0611032v1.pdf
    Journal-ref. Physics and Philosophy 3 (2006)

    The particles are also where the mass of the electron is located in nonrelativistic QM, as indicated by the N-particle guiding equation. Also, in the field theoretic extensions of deBB theory, the particle is also where charge is localized. Hope this helps.
     
    Last edited: Jul 28, 2008
  4. Jul 28, 2008 #3
    I would still like to see in details how gluons fit into dBB.
     
  5. Jul 28, 2008 #4
    It's not that hard in principle, as it goes much along the same lines as formulating a Bohmian QED (recall that QED and QCD only differ by a few extra terms in basically the same Lagrangian). In fact, I think it is more easily doable within the context of Light-front QCD. Currently, I am working on a draft for eventual publication on light-front Bohmian QCD. For now, please have a look at the work from an equal-time approach. See sections 5, 7, and 8 of Struyve's paper:

    Field beables for quantum field theory
    Authors: W. Struyve
    to be published in Physics Reports
    http://arxiv.org/PS_cache/arxiv/pdf/0707/0707.3685v1.pdf [Broken]
     
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  6. Jul 28, 2008 #5
    I would certainly not agree with your only, like if it were trivial ! A light quark is not exactly an electron, plus a few extra feature. And a gluon is even worse.

    But thank you for the reference. It is very interesting.
    As I said, I'd like to see that in details. Remember Gribov copies ? I'll wait till they get to the "topological problems".
    This may indeed take a lot of work :
     
    Last edited: Jul 28, 2008
  7. Jul 28, 2008 #6

    Hurkyl

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    This appears to contradict the fact that the particles defined by the Bohm interpretation have absolutely no influence on anything whatsoever, which seemingly makes them completely unobservable.
     
    Last edited: Jul 28, 2008
  8. Jul 28, 2008 #7

    By "only" I just meant that QED and QCD are formally very similar theories (which they are), not that the differences are computationally trivial.

    But I would point out however that light-front QCD considerably simplifies the problems Struyve mentions, so that formulating a Bohmian QCD is much more straightforward, I would claim.
     
    Last edited: Jul 29, 2008
  9. Jul 28, 2008 #8
    The particles just don't act back on their own guiding wavefunctions. Furthermore, it is quite straightforward to see from the guiding equation that the particle is located at the scintillation point (which is where the electron particle of the detector is ejected and radiates). Bohmian QED explains this more precisely.
     
    Last edited: Jul 28, 2008
  10. Jul 29, 2008 #9

    vanesch

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    Eh, that's not true, right ? Although the particles do not influence the dynamics of the wavefunction, they do influence the dynamics of the other particles (and even in an "action-at-a-distance" way). The quantum force on particle 1 depends on the wavefunction and the positions of particles 2, 3, ...
     
  11. Jul 29, 2008 #10
    Yes exactly true. That's the origin of the nonlocality for particle velocities in deBB. It's just that particle 1 is influencing the velocity of particle 2 (and vice versa) indirectly via the wavefunction or quantum potential.
     
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  12. Jul 29, 2008 #11

    Hurkyl

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    Hrm -- I think I see the problem. BM is not about "particles and a wavefunction" as I was led to believe. Instead, it's a theory of "particles and other stuff", where the data representing the particles and the other stuff can be assembled into a wavefunction which is not intended to correspond to a physical entity.
     
  13. Jul 29, 2008 #12
    Why do you say that? The fundamental postulates of nonrelativistic deBB-QM are that the complete state of the world are defined by two things, the wavefunction, psi, and particle position configuration, Q, or, (psi, Q). Then you can write down the Schroedinger equation for the wave, psi, and deduce the guiding equation for the particle configuration, Q. If the theory is take "as is", the wavefunction must then be interpreted as a physical entity ("ontological" in the words of Bohm or "beable" in the words of Bell) like the EM field (of course it propagates through configuration space as opposed to 3-space) otherwise it doesn't make any sense. But this is enough to specify all of nonrelativistic deBB-QM. The quantum potential is a somewhat extraneous object of the theory that comes in from constructing the second order dynamics of the theory and in defining the quantum-classical limit. The particle dynamics however is completely defined by the first-order guiding equation alone.

    If on the other hand you wanted to assume that deBB-QM is an approximation to, say, a stochastic mechanical theory, then, yes, the wavefunction is no longer a physically real field but rather a compact and convenient mathematical expression for the time evolution of the Madelung fluid dynamics with micro-stochastic fluctuations, and the deterministic Bohm particle velocities are macroscopic statistical averages of microphysical stochastic particle trajectories.
     
  14. Jul 29, 2008 #13

    Demystifier

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    Exactly!
    Another point that needs to be stressed is that Bohmian mechanics assumes that only particles are objects that are really observed, while wave function is an object with an auxiliary role. For an analogy in everyday life, see
    https://www.physicsforums.com/blog.php?b=6 [Broken]
     
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  15. Jul 29, 2008 #14

    vanesch

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    This is the delicate point in BM. Although at first sight, BM looks like classical mechanics with "just another force field", the wave function is nevertheless a genuine part of it, and is not some "helper function". If you only have the dynamical state of the particles, you cannot do BM, you need the wavefunction too.

    I guess you can somehow compare (it's just an analogy, which fails at a certain point of course) the wavefunction with the EM field in classical electrodynamics. What "counts" are the charged particles of course, but you cannot obtain the dynamics of just the charged particles if you don't have the electromagnetic field *with its own dynamics*. So even if you don't care about the EM field, you still need it, and it is not a helper function.

    However, this analogy fails in 2 respects:
    - the particles DO have an influence on the EM field.
    - most of the time, the particles even *determine* the EM field, that is, if you really want to, you can eliminate the EM field from the dynamics (we don't keep EM modes that "came from infinity).

    It fails in even a 3rd respect: the EM field lives in spacetime, while the wavefunction doesn't: it lives in Hilbert space.
     
  16. Jul 29, 2008 #15

    Hurkyl

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    The problem with the wavefunction being a physical entity is that it leads to what I was saying in my opening post: particles don't contribute to the evolution of the wavefunction, and the evolution of particles is entirely determined by the wavefunction. In particular, the particles do not have any influence on one another, and cannot be observed. If Bohm particles are meant to be more than mere test particles, then I simply don't see how the wavefunction can be taken as corresponding to a physical entity.

    I would like to point out that I did not say we need to take only particles as physical entities -- I would presume there is something weaker than the wave function (i.e. "other stuff") one can postulate as real, and have it and the particles all on equal footing. But I don't know what that something actually is.


    Incidentally, the classical EM field doesn't live in space-time: it lives in the sheaf of continuous (or differentiable, or whatever) tangent vector fields on space-time.
     
  17. Jul 29, 2008 #16

    Demystifier

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    Yes they do. First, by classical forces. Second, because not every particle has its own wave function, but one wave function describes a collection of many particles (entanglement), so they influence each other by a quantum force. This is exactly why they can be observed.
     
  18. Jul 29, 2008 #17

    vanesch

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    Sorry but they do. The particles do influence one another (through the wavefunction). You cannot obtain the dynamics of particle 1 by just knowing the wavefunction: you need to know also the positions of the other particles. If you give the other particles other initial positions, then particle 1 will follow a different worldline.

    I don't think you can do with less than the wavefunction, as it usually follows entirely the unitary evolution: the wavefunction part is exactly that of standard quantum mechanics (without projection). I might be wrong, but I'd guess that if you can do with "less than the wavefunction", then this reduction should also apply to standard quantum theory.

    You're a mathematician, right ? :grumpy:

    "living in spacetime" to me is living on spacetime and all its tangent and cotangent backgardens :redface:
     
  19. Jul 29, 2008 #18
    Hello everyone...

    I think it is necessary here to precise that it is wrong to say that there is only one unique bohmian way of understanding quantum mechanics. It is possible to distinguish a large amount of different interpretations of the wave function, with more or less "substance" in the wave function. Talking about bohmian mechanics in general leads to misunderstanding, one asks something about one interpretation and the other answers about another...
    If you are interested in an account of these possibilities, you can read Belousek. He mostly distinguises two axes of interpretation, causal vs. guidance view and monistic vs. dualistic ontologies. The tension between causal and guidance view is also discussed by Baubliz.
    I personally think that a monistic approach is the best one, but it would be too long to argue here (I'm writing my MA dissertation in philo of physics about this right now...).


    PS. The references :
    @article{Belousek:2003,
    Author = {Darrin W. Belousek},
    Journal = {Foundations of Science},
    Pages = {109-172},
    Title = {Formalism, Ontology and Methodology in Bohmian Mechanics},
    Volume = {8},
    Year = {2003}}

    @incollection{Baublitz:1996,
    Author = {Millard Baublitz and Abner Shimony},
    Booktitle = {Bohmian Mechanics and Quantum Theory: An Appraisal},
    Editor = {James T. Cushing and Arthur Fine and Sheldon Goldstein},
    Pages = {251-264},
    Publisher = {Kluwer Academic Publishers},
    Series = {Boston Studies in the Philosophy of Science},
    Title = {Tension in Bohm's Interpretation of Quantum Mechanics},
    Volume = {184},
    Year = {1996}}
     
  20. Jul 29, 2008 #19
    I realize I don't have answered the question just given some references...
    So to be short, you're right to say that the corpuscle is useless in the case of a certain interpretation of the wave function. If the wave function does everything, the corpuscle is just here as a pointer. Note that the other version of the problem is to wonder why the wave function, if understood as a field similar to the EM field has no source...

    But as soon as you give another interpretation to the wave function, things are different. For instance, Bohm and Hiley interpret the wave function as a information field (with a meaning for information which neither the usual meaning nor Shannon meaning). In this case, the special interpretation that they have explains this asymmetry.
    The interpretation Dürr et al. propose is different. They consider the wave function as part of the law (like an Hamiltonian) and, the corpuscle is the only material part of the theory and therefore does all the job (whatever this mean).

    Ok I've tried to be short, I hope I have made myself clear


    PS1. Sorry for the grammar mistakes and the strange sentences composition, but my first language isn't English
    PS2. If someone wants further references about these different theories I can give them...
     
  21. Jul 29, 2008 #20
    << I would like to point out that I did not say we need to take only particles as physical entities -- I would presume there is something weaker than the wave function (i.e. "other stuff") one can postulate as real, and have it and the particles all on equal footing. But I don't know what that something actually is. >>

    As I explained earlier, this can indeed be done in the context of stochastic mechanical derivations of the Hamliton-Jacobi-Madelung (the equations of deBB) equations.
     
  22. Jul 29, 2008 #21


    << The interpretation Dürr et al. propose is different. They consider the wave function as part of the law (like an Hamiltonian) and, the corpuscle is the only material part of the theory and therefore does all the job (whatever this mean). >>

    There is a very serious and obvious problem with their interpretation; in claiming that the wavefunction is nomological (a law-like entity like the Hamiltonian as you said), and because they want to claim deBB is a fundamentally complete formulation of QM, they also claim that there are no underlying physical fields/variables/mediums in 3-space that the wavefunction is only a mathematical approximation to (unlike in classical mechanics where that is the case with the Hamiltonian or even statistical mechanics where that is the case with the transition probability solution to the N-particle diffusion equation). For these reasons, they either refuse to answer the question of what physical field/variable/entity is causing the physically real particles in the world to move with a velocity field so accurately prescribed by this strictly mathematical wavefunction, or, when pressed on this issue (I have discussed this issue before with DGZ), they simply deny that this question is meaningful. The only possiblity on their view then is that the particles, being the only physically real things in the world (along with their mass and charge properties of course), just somehow spontaneously move on their own in such a way that this law-like wavefunction perfectly prescribes via the guiding equation. This is totally unconvincing, in addition to being quite a bizarre view of physics, in my opinion, and is counter to all the evidence that the equations and dynamics from deBB theory are suggesting, namely that the wavefunction is either a physically real field on its own or is a mathematical approximation to an underlying and physically real sort of field/variable/medium, such as in a stochastic mechanical type of theory.

    Also, their view of the wavefunction as nomological is also driven by considerations of quantum gravity. They want to say that because the universal wavefunction of the Wheeler-DeWitt equation is unique, then the wavefunction for all subsystems can be regarded as law-like. In addition to relying their argument on a rather dubious approach to quantum gravity (canonical quantization of the Einstein field equation), this ignores the fact that even there the evidence shows that the wavefunction contains lots of contingent physical structure (just as, say, the shape of the earth's continents contains a lot of contingent physical structure).


    << For instance, Bohm and Hiley interpret the wave function as a information field (with a meaning for information which neither the usual meaning nor Shannon meaning). >>

    They just mean that since the quantum potential depends only on the form rather than the amplitude of the wavefunction, the wavefunction acts more like a "radar" or "piloting" field that acquires information (such as position) about distant particles and uses it to determine the motion of other particles, as opposed to the EM field which acts locally on a charged point particle in a way that is independent of the dynamics of other spatially separated particles.
     
  23. Jul 29, 2008 #22
    One other comment about the different names of this theory - de Broglie-Bohm theory, pilot wave theory, Bohmian mechanics, the causal interpretation, the ontological interpretation, or any permutation of such words - there is a reason why some people refer to it by one name rather than another. The names "causal interpretation" and "ontological interpretation" are names given by Bohm and Hiley and is consistent with their own specific interpretation of the equations of the theory. The name de Broglie-Bohm (deBB or dBB) theory is intended to give credit to de Broglie in addition to Bohm, since de Broglie had already fully understood his theory, and in some ways better than Bohm did. Also, the term "pilot wave" was first used by de Broglie at the 1927 Solvay Conference to refer to the theory, and Bohm referred to it similarly, hence the name "pilot wave theory".

    The term "Bohmian mechanics" is a relatively more recent usage started in the early 1990's by Duerr, Goldstein, and Zanghi, (DGZ) to refer to their own specific interpretation and approach to the theory (as well as their own interpretation of what Bohm thought about his own theory, Bohm's own actual interpretation nothwithstanding), which they, naturally, think is the universally correct one. Since then they have done a PR campaign to make sure there is dominant use of the term "Bohmian mechanics" throughout the literature.

    What I personally think is problematic about the use of the term "Bohmian mechanics", and the intentions of DGZ in using the term "Bohmian mechanics", and which is why I have decided to stop using it in public discussions, is that

    1) It ignores the contributions and work done by Louis de Broglie, whose first-order guidance emphasis is actually the same as that of DGZ.

    2) David Bohm himself hated the term "Bohmian mechanics" because it was associating his name with an interpretation of the theory (that of DGZ) that he himself did not even agree with (this is according to Bohm's long-time collaborator and friend, Basil Hiley, as well as Bohm's last PhD student, Chris Dewdney, and Hiley's last PhD student, Owen Maroney). Bohm did not view the theory as a theory of mechanics like classical mechanics, precisely because he recognized the wavefunction and quantum potential not like a classical field or classical potential, but as a "radar" or "piloting" field and potential that represents the "undivided whole" of the "implicate order". Moreover, Bohm's mechanics of 1952 is a second-order theory that is in principle different from the 1st-order guidance theory, as it allows momenta not equal to grad(S).

    3) The usage of this term "Bohmian mechanics" was continued in use against Bohm's wishes, even after he died, which I consider very disrespectful. I mean, wouldn't you feel disrespected if someone used your name to refer to an interpretation that you did not at all agree with, and intended to continue using your name for it even after you died, even if you did not like it?

    Anyway, now that everyone has this information, they can decide for themselves.
     
  24. Jul 30, 2008 #23

    Hurkyl

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    You're right -- I see where I was misreading the equations.



    The only reason I say anything is because I think the differences are being exagerrated; either way it still can be viewed as a member of a structure merely associated with space or spacetime. e.g. the idea of a presheaf of n-ary square-integrable functions on space is not really that different from the idea of a sheaf of differentiable functions on space. (Of course, the technical details required to work with them are different)
     
  25. Jul 30, 2008 #24
    First a disclaimer. I don't agree with all of DGZ arguments, some puzzle me and I think they are wrong on the exact interpretation to give to the wave function. Nevertheless, IMHO, monistic interpretation–interpretation which do not take the wave function as refering to a physical entity–do not have to give a special meaning to the wave function. The main problem of the dualistic interpretations is that they have to introduce a special status for the wave function, sometimes as a new physical entity (the information for instance). Moreover, these interpretation ususally stick to a Newtonian world picture: forces are needed.

    My first question concerns the physical field behind the Hamiltonian. Tell me if my memories of classical physics are wrong, but the Hamiltonian is not the representation of a physical field. In some particular cases–equations of the generalized coordinates time independant–it represents the energy, but only in this condition, what if it is not fullfilled?

    When you ask the question of the physical field/variable are you asking for some kind of force? I perhaps interpret you point of view in the way Belousek object to DGZ, he argues
    that the monistic vision does not give a good explanation because it does not give a precise enough description of what is really going on in the motion of the particle. This requirement is asking for a causal explanation (and his solution involve forces as a material entity being represented by the wave function).
    But I wonder if this requirement is necessary. You say that it is 'physically weird' to work with the guidance equation as equation of motion. In a way I agree, said like this there is no direct link between the apparatus (the external potential) and the motion of the particle, the wave function does all the job. On the other hand, the principle of least action works in a similar way. The action S is the source of the movement, you can derive it from the potential, but it needs some mathematical manipulation.


    Typically, the problem I have with this kind of explanation is that it is not really physical. How can the particle be a boat guided by the radar of the wave function. Is this kind of explanation satisfactory? To be a bit provocative, it sounds to me like little omniscient faeries whispering to the hear of the corpuscle...


    Finally, I am aware of the problem bohmian/deBB caracterization. I personally talk about 'corpuscle interpretation of quantum mechanics', which is neutral. I don't want to take part in the dispute....
     
  26. Jul 31, 2008 #25





    Vanknee,


    My first question concerns the physical field behind the Hamiltonian. Tell me if my memories of classical physics are wrong, but the Hamiltonian is not the representation of a physical field. In some particular cases–equations of the generalized coordinates time independant–it represents the energy, but only in this condition, what if it is not fullfilled?


    Recall the classical Hamiltonian is a function on phase space and is composed of the sum of the kinetic energies for each particle in an N-particle system, plus the external potential energy (could be gravitational PE or electrostatic PE). Yes, the Hamiltonian is not itself a real field 'out there' in the world, as it lives in the R^6N dimensional phase space, as opposed to physical 3-space where all particles and physically (meaning experimentally) measurable fields live in. What the Hamiltonian, and more precisely, the gradient of the Hamiltonian or

    grad H(x,p,t) = grad ( Sum[N; p^2/2m_i] + V_ext ),

    says is that at the location of the ith particle, there is a force (F = m*d^2/dx^2) on the particle caused by a gradient in the rhat direction of the ith particle's own kinetic energy (in any Galilean frame), plus a gradient in the rhat direction of the ith particle's potential energy (remember potential energy, whether gravitational or electric, is a relational property in every reference frame). The Hamiltonian is an abstract, nonlocal, mathematical encoding of these N-particle properties. So the physically real things are the local gradients in the potential energy (remember that potential energy itself is not physically real because its magnitude is entirely conventional) of the ith particle, plus the kinetic energy of the ith particle. So the physically real things that exert forces on the ith particle at a point in space are the gradient of the intrinsic kinetic energy of the ith particle, plus the gradient of the relational potential energy of the ith particle.

    Now imagine if the Hamiltonian was just given by the potential energy so that H = V(x). Well, if the potential energy was, let's say, electric potential energy given by

    V(x) = Sum[N; k*qi*qj/|ri - rj|],

    Then it is obvious why the Hamiltonian is not a physically real field in the world, because the electric potential energy is a conventional object, and only the gradient of the electric potential energy, which gives the local electric field at a point in space, is what is physically real and what is really exerting a force on the particle, and is what actually exists in 3-space, and independently of the particle. Indeed we could add an arbitrarily large constant to V(x), and the gradient would give the same value for the electric field.

    Now imagine if the Hamiltonian was just given by H = 0. This means the particle in some Galilean frame is at rest and has zero kinetic or potential energy. OK, now suppose at a later time t, the Hamiltonian now is given by H = p^2/2m. This means that some external force was exerted on the particle (either by collision with another particle with nonzero velocity, or by an external gravitational or electric (if the particle has charge) field). This also means that the particle has been given an additional physical property that it originally did not always have (unlike its rest mass which is a constant and intrinsic property of the particle).

    In all these cases, we know that although the Hamiltonian is not physically real on its own, and rather is an abstract, nonlocal, mathematical encoding of the sum of kinetic and potential energies of N particles, we can clearly identify what physically real objects it is describing, in addition to and independently of the particles. This is not the case in the nomological interpretation of the wavefunction given by DGZ. They deny that there are additional fields/variables that actually induce a velocity or force on the Bohmian particle, even though they want to say the wavefunction is nomological in the same sense as is the classical Hamiltonian. So my point is that if one wants to claim the wavefunction is comparable to the Hamiltonian, then the wavefunction miust be encoding physical information about other physically real variables in addition to the particles. Otherwise the comparison totally fails to be valid.



    When you ask the question of the physical field/variable are you asking for some kind of force? I perhaps interpret you point of view in the way Belousek object to DGZ, he argues
    that the monistic vision does not give a good explanation because it does not give a precise enough description of what is really going on in the motion of the particle. This requirement is asking for a causal explanation (and his solution involve forces as a material entity being represented by the wave function).



    It could be a force or an impulse. I agree with Belousek's objection. Think of it this way: If are only particles in the physical world like DGZ claim, then if we ask how a single Bohm particle will move through spacetime when it collides with another Bohmian particle, it will still be the case that the Bohmian particle will move according to a nonlocal, nonclassical law of motion prescribed by the wavefunction. If we then ask the question of how the Bohmian point particle differs from the classical mechanics point particle, mathematically there is no difference. They are both point masses and nothing more. On the other hand, if we ask what in the physical world makes the Bohmian point particle moves differently after collision with another Bohmian particle, than when a classical mechanics point particle collides with another classical mechanics point particle, we can say in the latter case because some external but locally propagating field initially gave the two point particles some momentum, and they took the path of least action towards their collision point (where they actually “touch” each other) and afterwards; and before they collided, their trajectories were totally uncorrelated. Of course, even here in classical mechanics, there is still a mystery about why the two point mass particles can scatter off each other, as opposed to stick together (i.e. why there are elastic and inelastic collisions). Because in classical mechanics these are only postulates, if we want an explanation of these postulates, we are obliged to then add more properties to the point particles, than just masses – we have to add electric charge. Then we have a less ad-hoc explanation of how the particles undergo either elastic or inelastic collisions. But according to DGZ, because the Bohmian point mass particles are the only physically real things in the world comprising matter, both of the spatially separated Bohmian point particles must somehow have nonlocal knowledge of each other's motions so as to conspire to move in a nonlocally correlated way that is totally nonclassical, and without any additional mediating field; but there is no way to understand how these Bohmian particles could have this knowledge if they are just point masses, as the mathematics of the guiding equation under their interpretation implies. To make this even more explicit, consider the scattering of two Bohmian point particles. If the DGZ interpretation of the wavefunction is correct, then two Bohmian point particles moving towards each other will eventually scatter at a certain time when, mathematically, their two wavefunctions with opposite energy and momentum sufficiently overlap in configuration space, even if the Bohmian particles in physical 3-space never actually directly contact each other. If there are ONLY Bohmian point mass particles, how do they know to scatter away from each other at a particular time, even when they are spatially separated?



    But I wonder if this requirement is necessary. You say that it is 'physically weird' to work with the guidance equation as equation of motion. In a way I agree, said like this there is no direct link between the apparatus (the external potential) and the motion of the particle, the wave function does all the job. On the other hand, the principle of least action works in a similar way. The action S is the source of the movement, you can derive it from the potential, but it needs some mathematical manipulation.


    Well consider another example of the weirdness of the DGZ wavefunction interpretation. In the hydrogen ground state, the Bohmian particle has zero velocity because the action S is a constant and grad S = 0. So the Bohmian particle is stationary at a point in space. Now, when you perform a measurement interaction with some pointer apparatus that is spatially very far away from the stationary Bohmian particle in the hydrogen atom, the latter begins to move exactly when its purely nomological wavefunction entangles with the purely nomological wavefunction of the pointer apparatus, so that the action of the Bohmian particle in the hydrogen atom is not constant in spacetime. But in the physically real world, since, according to DGZ, the wavefunction is not a real field and isn’t an approximation to any underlying physically real fields, the Bohmian particle in the hydrogen atom ground state somehow knew at a certain time that a pointer apparatus was coming in close proximity to it, and suddenly decided to have a nonzero action and to start moving towards the pointer apparatus! So the implication of the DGZ interpretation is that the particle in the real world somehow sensed the pointer apparatus (in an "action at a distance" sort of way), and started moving on its own accord, even though there was no actual physical field or medium between the Bohmian point mass particle and the pointer apparatus to allow them to indirectly interact with each other. Seems like far too much of a coincidence don't you think?



    Typically, the problem I have with this kind of explanation is that it is not really physical. How can the particle be a boat guided by the radar of the wave function. Is this kind of explanation satisfactory? To be a bit provocative, it sounds to me like little omniscient faeries whispering to the hear of the corpuscle...


    I think you’re taking the analogy either too literally or misunderstanding it. They just mean that the quantum potential force on a particle depends instantaneously on the positions of all the other particles in the world (the source of the nonlocality in the theory), and is independent of the magnitude of the wavefunction, instead only depending on the form of the wavefunction. More precisely, if R = |psi| and Q = -(hbar^2/2m)*Laplacian[R]/R, then C*R = C*|psi| leave Q unchanged. So all that matters is the form of |psi|, not its magnitude.


    OK on keeping out of the deBB/Bohmian mechanics terminology controversy.
     
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