What is Bohmian mechanics: Definition and 69 Discussions

The de Broglie–Bohm theory, also known as the pilot wave theory, Bohmian mechanics, Bohm's interpretation, and the causal interpretation, is an interpretation of quantum mechanics. In addition to the wavefunction, it also postulates an actual configuration of particles exists even when unobserved. The evolution over time of the configuration of all particles is defined by a guiding equation. The evolution of the wave function over time is given by the Schrödinger equation. The theory is named after Louis de Broglie (1892–1987) and David Bohm (1917–1992).
The theory is deterministic and explicitly nonlocal: the velocity of any one particle depends on the value of the guiding equation, which depends on the configuration of the system given by its wave function; the latter depends on the boundary conditions of the system, which, in principle, may be the entire universe.
The theory results in a measurement formalism, analogous to thermodynamics for classical mechanics, that yields the standard quantum formalism generally associated with the Copenhagen interpretation. The theory's explicit non-locality resolves the "measurement problem", which is conventionally delegated to the topic of interpretations of quantum mechanics in the Copenhagen interpretation.
The Born rule in Broglie–Bohm theory is not a basic law. Rather, in this theory, the link between the probability density and the wave function has the status of a hypothesis, called the "quantum equilibrium hypothesis", which is additional to the basic principles governing the wave function.
The theory was historically developed in the 1920s by de Broglie, who, in 1927, was persuaded to abandon it in favour of the then-mainstream Copenhagen interpretation. David Bohm, dissatisfied with the prevailing orthodoxy, rediscovered de Broglie's pilot-wave theory in 1952. Bohm's suggestions were not then widely received, partly due to reasons unrelated to their content, such as Bohm's youthful communist affiliations. De Broglie–Bohm theory was widely deemed unacceptable by mainstream theorists, mostly because of its explicit non-locality. Bell's theorem (1964) was inspired by Bell's discovery of Bohm's work; he wondered whether the theory's obvious nonlocality could be eliminated. Since the 1990s, there has been renewed interest in formulating extensions to de Broglie–Bohm theory, attempting to reconcile it with special relativity and quantum field theory, besides other features such as spin or curved spatial geometries.The Stanford Encyclopedia of Philosophy article on quantum decoherence groups "approaches to quantum mechanics" into five groups, of which "pilot-wave theories" are one (the others are the Copenhagen interpretation, objective collapse theories, many-worlds interpretations and modal interpretations).
There are several equivalent mathematical formulations of the theory, and it is known by a number of names. The de Broglie wave has a macroscopic analogy termed Faraday wave.

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  1. gentzen

    I QFT made Bohmian mechanics a non-starter: missed opportunities?

    I once conjectured that Bohmian mechanics arrived at an unfortunate point in time, when interest in QFT overshadowed potential opportunities offered by Bohmian mechanics: One of those opportunities was the analysis of non-locality, later done by Bell, and the reason why I brought up Bohmian...
  2. S

    A How does Bohmian Mechanics actually replicate QM?

    I was recently trying to understand how Bohmian Mechanics could model quantum theory. In an old lecture of Sidney Coleman's called "Quantum Theory with the Gloves off" available here: https://www.damtp.cam.ac.uk/user/ho/Coleman.pdf He shows with a "physicist's proof" that QM predicts truly...
  3. TheHeraclitus

    Particle ontology and quantum fluctuations

    I have been reading about ontologies in quantum physics recently and I came across Bohmian mechanics. If I understood it correctly BM endorses Particle ontology. Particle ontology claims that point-like particles that move continuously in time are the fundamental building blocks. I know some...
  4. gentzen

    A Is Bohmian mechanics a convenient ontological overcommitment?

    Collapse theories (like GRW) only need extremely few collapses to reproduce macroscopic observations, and actually must limit themselves to extremely view collapses to avoid being experimentally distinguishable with current technology from standard QM. Being too generous with world splitting in...
  5. TheHeraclitus

    I Bohmian mechanics and String theory

    Is it easy to combine them or impossible? Is there a tension due to the non-locality found in Bohmian mechanics? Thank you!
  6. Jamister

    A An experiment that claims to doom Bohmian Mechanics

    I read in the article in Quanta magazine about an experiment with oil droplets that dooms Bohmian Mechanics, but I didn't understand why. Does anyone knows this experiment and why it dooms Bohmian Mechanics? The article is in the link...
  7. G

    I How does Bohmian mechanics explain quantum bomb testing?

    Hi. In an Elitzur–Vaidman bomb tester, will the guiding wave be different in a situation with a live bomb compared to one with only a dud? And if yes, how does the bomb interact with the guiding wave? Because usually it is described as a pointlike device that only explodes when hit by the...
  8. Lynch101

    I Understanding Bohmian Mechanics of Instrumentalists

    I recently read @Demystifier's paper entitled, Bohmian Mechanics for Instrumentalists and I found it quite interesting. There is a danger that I am guilty of a certain amount of confirmation bias, as I find that deterministic interpretations are more closely aligned to my own logical reasoning...
  9. K

    I Questions on the Bohmian mechanics interpretation for instrumentalists

    Regarding the paper Bohmian mechanics for instrumentalists I like the ideas put forward in the paper because it provides a basis for an intuitive and logical explanation of quantum mechanics. I have many questions about it, but I will start with 3. Question 1: In this interpretation, what is...
  10. K

    I Bohmian mechanics and special relativity

    [Moderator's note: Thread spun off from previous thread due to topic change.] Thanks! I am working on understanding why non-local effects violate the special theory of relativity. I am not there yet, but maybe when I finally get there I will leave the BM train.
  11. M

    I Did de Broglie contribute later to pilot wave theory?

    If I recall correctly it was in Adam Becker's book "What is Real?" where I read that late in life de Broglie took up again the pilot wave theory that he had introduced at Solvay in 1927 and that Bohm had done so much work on in the interim. Did de Broglie make any contributions to pilot wave...
  12. T

    I Consistency of Bohmian mechanics

    I have a free particle with a Gaussian wave function ##\psi(x,0) = N \exp\left(-\frac{x^2}{2}\right)##. After time evolution with ##H=\frac{p^2}{2}##, the wave function is given by ##\psi(x,t)=N\left(\frac{1}{1+i t}\right)^{3/2} \exp \left(-\frac{x^2}{2 (1+i t)}\right)##. The time evolution of a...
  13. DarMM

    Other David Bohm: Biography of a Revolutionary Physicist

    Title says it all. There's a new biography of David Bohm from Springer: https://www.springer.com/gp/book/9783030227142 I thought some here might be interested in it.
  14. A. Neumaier

    I How to derive Born's rule for arbitrary observables from Bohmian mechanics?

    Where can I find a reference to a derivation of Born's rule for arbitrary observables from Bohmian mechanics?
  15. A. Neumaier

    I Polarization in Bohmian mechanics

    How does Bohmian mechanics explain the working of a polarizer?
  16. microsansfil

    A Bohmian mechanics for instrumentalists and quantum measurement

    Hi, I'm reading Demystifier's article about an interpretation of quantum mechanics. One concept that seems important for this interpretation is that of what is perceptible by us human beings compared to what is not (non-perceptible). Demystifier says: A perception by a naked eye is direct, a...
  17. S

    A Does Bohmian Mechanics yield the existence of a multiverse?

    David Deutsch, a theoretical physicist, talks about David Bohm in his book "the Fabric of Reality": "[w]orking out what Bohm’s invisible wave will do requires the same computations as working out what trillions of shadow photons will do. Some parts of the wave describe us, the observers...
  18. S

    I Confused by nonlocal models and relativity

    Hello everyone! Recently I saw this paper: https://arxiv.org/pdf/1304.4801.pdf ("Any nonlocal model assuming “local parts” conflicts with relativity " by Antoine Suarez). He mentions standard experimental configuration with beam-splitters and detectors. Then he distinguishes possible models...
  19. S

    A Relation between Bohm's Interpretation and Implicate order?

    What relation exists between Bohm's Implicate-Explicate order and De Broglie-Bohm interpretation? If any relation exists at all...
  20. Auto-Didact

    A Experimental evidence of non-local quantum forces

    Becker et al. 2019, Asymmetry and non-dispersivity in the Aharonov-Bohm effect The paper is open access and published in Nature Communications.
  21. A. Neumaier

    I Numerical simulations in Bohmian mechanics

    With respect to the following posts from a now closed thread, https://www.physicsforums.com/threads/copenhagen-restriction-on-knowledge-or-restriction-on-ontology.968982/post-6169047...
  22. A

    A Is there any Bohmian approach to quantum electrodynamics?

    I know that in some Bohmian papers (like https://arxiv.org/pdf/quant-ph/0303156.pdf), electron-positron pair creation and annihilation is modeled by different methods like stochastic jumps in the configuration space. My question is, is there any Bohmian approach to reproduce all of the...
  23. A

    A Does Antony Valentini's "sub-quantum measurement" really work?

    In https://arxiv.org/pdf/quant-ph/0203049.pdf, which is in the realm of Bohmian mechanics, Antony Valentini claims that by having a "non-equilibrium" particle with arbitrarily accurate "known" position, we can measure another particle's position with arbitrary precision, violating Heisenberg's...
  24. A

    I De Broglie-Bohm theory and Bohm-like models - how is vacuum treated?

    Hi all, I've been looking at de Broglie-Bohm theory and more recent attempts at Bohm-like models that are relativistic and attempt to reproduce QFT. What I'm not clear on (non-expert) is how the vacuum is modeled in these cases? If we have a set of infinite quantum harmonic oscillators...
  25. A

    A Why is this Pilot-wave model on a discrete spacetime stochastic?

    Look at the paper in the link below: https://link.springer.com/content/pdf/10.1007%2Fs10701-016-0026-7.pdf It introduces a pilot-wave model on a discrete spacetime lattice. However, the pilot-wave model is not deterministic; the motion of quantum particles is described by a |Ψ|^2-distributed...
  26. A

    A What are Bohmian trajectories for a free electron?

    A free electron, or any other quantum particle, has an uncertain position/momentum, according to Heisenberg uncertainty principle. The squared amplitude of the wavefunction determines the probability of finding the electron at any point of the space. Accordingly, atomic orbitals are attributed...
  27. A. Neumaier

    A Initial-value problem for Bohmian mechanics

    Does Bohmian mechanics have a mathematically well-defined initial-value problem with unique solution for given initial data? The right hand side of the guiding equation has singularities at all configuration space positions where ##\psi## vanishes. Thus the particle dynamics breaks down. Thus...
  28. I

    I A question about velocities in Bohmian mechanics

    Hi all, In 'Bohmian mechanics,' (BM) velocities are given by the 'guiding equation' as explained, for instance, in this article of the Stanford Encyclopedia of Philosophy https://plato.stanford.edu/entries/qm-bohm/#DefiEquaBohmMech These velocities can, in principle, be greater than c. This...
  29. ErikZorkin

    I Counterpart of Feynman integral in de Broglie-Bohm theory

    I am looking for good references / clarifications on the subject. First of all, my question is concerned only with mathematical formulation of something that sort of plays the role of the Feynman path integral of the "standard" QFT. It is not concerned with the physical or philosophical...
  30. B

    I Quantum eraser in Bohmian Mechanics and many worlds theory

    All the literature on the quantum eraser that I've seen is grounded in the Copenhagen interpretation of quantum mechanics. It's very easy to understand the experiment in those terms. Do you know how quantum eraser experiments are interpreted by the de Broglie–Bohm theory? What is erased in this...
  31. J

    A Is Bohmian Mechanics incompatible with String Theory

    Bohmian mechanics requires a preferred reference frame. But String theory doesn't have any preferred frames, so isn't BM incompatible with ST?? Maybe it would be compatible with other theories of quantum gravity that permit a preferred frame (LQG, CDT)...
  32. J

    A Would this experiment disprove Bohmian mechanics?

    Bohmian mechanics claims that although it is deterministic, randomness emerges from the fact that we cannot know the initial conditions of the particle due to Heisenberg's uncertainty principle. However this experiment can put that to the test and determine whether randomness in quantum...
  33. Deepblu

    I Why Bohmian Mechanics needs non-locality?

    I always think about entanglement as pure conservation of energy and conservation of angular momentum. In fact I see that only conservation of energy is non-local, and that quantum objects have nothing to do with non-locality, for example you can entangle 2 atoms that have never interacted with...
  34. S

    I Did Paul Dirac say anything about Bohmian mechanics?

    Could you, please, give me reference to any paper or talk by Paul Dirac where he expresses his views about or give comments to the de Broglie-Bohm theory (Bohmian mechanics)?
  35. B

    Some questions about Bohmian mechanics

    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...
  36. Sophrosyne

    I New experiments supporting Bohmian mechanics?

    I recently read this article about recent experiments which seems to be resurrecting the idea of a Bohm-deBroglie interpretation of quantum mechanics over the Copenhagen one. Is this legit, or pseudo-science hype? https://www.wired.com/2014/06/the-new-quantum-reality/
  37. Maxwell's Demon

    A What’s the physical nature of the pilot wave?

    Within the context of the de Broglie-Bohm pilot-wave theory, can anyone explain what the pilot wave is in physical terms? I’m having a hard time understanding how, for example, the pilot wave influences the trajectory of a photon in the double-slit experiment. Are we dealing with...
  38. J

    I Is Bohmian Mechanics the Wrong Interpretation of Quantum Mechanics?

    http://motls.blogspot.com/2014/05/measure-for-measure-debaters-love-to.html?m=1 According to lubos, bohmian mechanics is certainly wrong because "its basic classical object – the guiding wave – is in principle unobservable because a change of it should in principle impact things at a distance...
  39. O

    I Doesn't wave duality for massive objects favor pilot-wave?

    It is well known that wave particle duality was also observed with large particles up to 10000 amu: Abstract of Paper : https://arxiv.org/abs/1310.8343 Doesn't that make pilot wave theory a more logical interpretation? For example it is easier than the whole material becoming a wave...
  40. N

    I Physical properties of a particle in Bohmian mechanics

    Are the physical properties of a particle spread out through the wave function in bohmian mechanics? This is from wikipedia "Also, unlike in classical mechanics, physical properties (e.g., mass, charge) are spread out over the wavefunction in de Broglie–Bohm theory, not localized at the position...
  41. nomadreid

    I Exploring Bohmian Mechanics: Questions for Non-Physicists

    One of the favourite themes for threads which create long discussions here is on Bohmian mechanics. Unfortunately, most of them operated under the assumption that the reader is familiar with the intricacies of this ... interpretation? theory? I do not wish to rehash all that has been written on...
  42. N

    I How does Bohmian Mechanics deal with the destruction of....

    How does BH deal with the destruction of interference in the double slit experiment when a detector is placed at the slits? If the wave function never collapses, then shouldn't the particle still follow the path? Does the measuring device change the shape of the wave function so that it doesn't...
  43. A. Neumaier

    I A skeptic's view on Bohmian Mechanics

    Reading this paper, I found their reference to a blog article by Reinhard Werner, one of the leaders in quantum information theory, on Bohmian mechanics, with sharp comments and questions such as the following: At the end he poses http://www.itp.uni-hannover.de/~werner/Bohm.html , for which...
  44. F

    A An argument against Bohmian mechanics?

    There is a paper by Arnold Neumaier, where it is argued that Bohmian mechanics, is simply wrong, because it doesn't predict all the results that we observe from experiment. See here. Neumaier wrote down his argument for a particle in the ground state of a harmonic oscillator, but there's...
  45. entropy1

    I Discovery shakes up QM (or not....)

    A yet unverified experiment may mean a paradigm shift in QM: http://advances.sciencemag.org/content/2/2/e1501466.full http://futurism.com/new-evidence-could-break-the-standard-view-of-quantum-mechanics/ What do you make of this?
  46. B

    Quantized electron orbits in Bohmian mechanics

    I entered in physicsforums archive search the wildcards "bohmian why electrons don't lose energy atom" but only got one hit that isn't related to it. In Bohmian mechanics, electron is localized and has trajectory.. why can't it lose energy as it rotates around the nucleus? What wildcard words...
  47. A. Neumaier

    I What is the correct generalization for spinning particles in Bohmian mechanics?

    Equation (8) defines the conditional wave function of a microscopic physical system in terms of the wave function of the universe and the true positions of the particles in the environment (= the universe except the microscopic system). Such a definition is essential for the interpretation of...
  48. Z

    Problem of superluminal communication in Non-local HVTs

    Hi there. I have been studying on Bell Inequalities and hidden variables problem for quite some time now however my general knowledge on the problem of superluminal communication is superficial at best. I know that non of the standing interpretations (Everett, Copenhagen, Bohmian, QBist etc.)...
  49. bohm2

    Bohmian Mechanics and The Quantum Sweeper Effect

    The Quantum Sweeper Effect http://arxiv.org/pdf/1502.04034.pdf Extreme beam attenuation in double-slit experiments: Quantum and subquantum scenarios http://arxiv.org/pdf/1406.1346v1.pdf
  50. N

    Bohmian Mechanics meets Neo-Lorentzian Ether Theory?

    Yes, the title of this thread has sounded the crackpot alarm! Anyway, I'm curious for your thoughts and suggested readings... As background, I've learned that Neo-Lorentzian Ether Theory is a valid alternate for Einstein's Special Relativity. This ether is undetectable, but does in imply a...