De Broglie–Bohm theory

interpretation of quantum mechanics

The de Broglie–Bohm theory, also known as the pilot-wave theory, Bohmian mechanics, the Bohm (or Bohm's) interpretation, and the causal interpretation, is an interpretation of quantum theory. In addition to a w:wavefunction on the space of all possible configurations, it also postulates an actual configuration that exists even when unobserved. The evolution over time of the configuration (that is, the positions of all particles or the configuration of all fields) is defined by the wave function by a guiding equation. The evolution of the wave function over time is given by Schrödinger's equation. The theory is named after Louis de Broglie (1892–1987) and David Bohm (1917–1992).


  • But why then had Born not told me of this 'pilot wave'? If only to point out what was wrong with it? Why did von Neumann not consider it? More extraordinarily, why did people go on producing 'impossibility' proofs, after 1952, and as recently as 1978? When even Pauli, Rosenfeld, and Heisenberg, could produce no more devastating criticism of Bohm's version than to brand it as 'metaphysical' and 'ideological'? Why is the pilot wave picture ignored in text books? Should it not be taught, not as the only way, but as an antidote to the prevailing complacency? To show that vagueness, subjectivity, and indeterminism, are not forced on us by experimental facts, but by deliberate theoretical choice?
    • John S. Bell, "On the impossible pilot wave". Foundations of Physics 12 (1982)
  • It is easy to find good reasons for disliking the de Broglie-Bohm picture. Neither de Broglie nor Bohm liked it very much; for both of them it was only a point of departure. Einstein also did not like it very much. He found it 'too cheap,' although, as Born remarked, 'it was quite in line with his own ideas'. But like it or lump it, it is perfectly conclusive as a counter example to the idea that vagueness, subjectivity, or indeterminism, are forced on us by the experimental facts covered by nonrelativistic quantum mechanics.
    • John S. Bell, "On the impossible pilot wave". Foundations of Physics 12 (1982)
  • Why were people so intolerant of de Broglie’s gropings and of Bohm? For twenty-five years people were saying that hidden-variable theories were impossible. After Bohm did it, some of the same people said that now it was trivial. They did a fantastic somersault. First they convinced themselves, in all sorts of ways, that it couldn’t be done. And then it becomes ‘trivial.’ I think Einstein thought that Bohm’s model was too glib—too simple. I think he was looking for a much more profound rediscovery of quantum phenomena. The idea that you could just add a few variables and the whole thing [quantum mechanics] would remain unchanged apart from the interpretation, which was a kind of trivial addition to ordinary quantum mechanics, must have been a disappointment to him. I can understand that—to see that that is all you need to do to make a hidden-variable theory. I am sure that Einstein, and most other people, would have liked to have seen some big principle emerging, like the principle of relativity, or the principle of the conservation of energy. In Bohm’s model one did not see anything like that.
  • What we are proposing here is that this disparity between physical concepts (e.g. particle, wave, position, momentum) and the implications of the mathematical equations arises because the physical concepts are inseparably involved with the Cartesian notion of order, and this violates the essential content of quantum mechanics. What we need is a notion of order for all our concepts, both physical and mathematical, which coheres with this content.
    • David Bohm and Basil Hiley, The undivided universe: an ontological interpretation of quantum theory (1993)
  • Have you noticed that Bohm believes (as de Broglie did, by the way, 25 years ago) that he is able to interpret the quantum theory in deterministic terms? That way seems too cheap to me. But you, of course, can judge this better than I.
  • In the last few years several attempts have been made to complete quantum theory as you have also attempted. But it seems to me that we are still quite remote from a satisfactory solution to the problem. I myself have tried to approach this by generalising the law of gravitation. But I must confess that I was not able to find a way to explain the atomistic character of nature. My opinion is that if an objective description through the field as an elementary concept is not possible, than one has to find a possibility to avoid the continuum (together with space and time) altogether. But I have not the slightest idea what kind of elementary concepts could be used in such a theory.
  • Bohm's Eastern metaphysics, even though it helped shape his interpretation of quantum mechanics, should not be held against the potential fruitfulness of his pilot wave theory. In a similar fashion Isaac Newton's Biblical fundamentalism and his alchemical research cast no shadows over his contributions to physics. Nor did Kepler's belief in astrology throw doubts on his great discoveries.
    • Martin Gardner, "David Bohm and Jiddo Krishnamurti", Skeptical Inquirer, July, 2000
  • Let me illustrate some of the ideas I believe Bohmian mechanics should have triggered. This list is obviously subjective—it is only important that it is not empty. Bohmian mechanics, like quantum theory, is in deep tension with relativity theory. I know of Bohmians who claim that it is obvious that any non-local theory, Bohmian or not, requires a privileged universal reference frame. I also know of Bohmians who claim that it is obvious that Bohmian mechanics can be generalized to a relativistic theory (though, admittedly, I never understood their model). However, I know of no Bohmians who are inspired by their theory and its tension with relativity to try to go beyond Bohmian mechanics, as illustrated in the next two paragraphs.
    • Nicolas Gisin, "Why Bohmian Mechanics? One- and Two-Time Position Measurements, Bell Inequalities, Philosophy, and Physics", Entropy (2018)
  • Generally, position measurements sometimes reveal information about Bohmian positions, but never full information and sometimes none at all. Simple and handy criteria for determining when the Bohmian position measurements of a particle under test highly correlate with the position of the center of mass of some large pointer are still missing. Bohmian mechanics is attractive to philosophers because it provides a clear ontology. However, it is not as attractive to researchers in physics. This is unfortunate because it could inspire brave new ideas that challenge quantum physics.
    • Nicolas Gisin, "Why Bohmian Mechanics? One- and Two-Time Position Measurements, Bell Inequalities, Philosophy, and Physics", Entropy (2018)
  • The first conference, Bohmian Mechanics 2000, was the total fiasco: two leading representatives of Bohmian school, Shelly Goldstein and Basil Hiley, presented two totally different interpretations of Bohmian mechanics. Finally, they accused each other in misunderstanding of Bohm’s views (both had very close connections to David Bohm). My students whom I invited to learn Bohmian mechanics from its creators were really confused. The only useful information which I extracted from Bohmian Mechanics 2000 was that Bohmian mechanics does not give new experimental predictions comparing to conventional QM.
  • In the non-Relativistic version you just postulate some point particles, and a single universal quantum state (represented by a mathematical wavefunction) and two simple dynamical equations: the Schrödinger equation for the wavefunction and the so-called guidance equation for the particle motions. You could have guessed both equations easily, and you get out all of the iconic quantum behavior: two-slit interference effects, violations of Bell’s inequality, decoherence due to observation or more generally due to coupling to the environment in the right way, etc., etc. What’s not to like?
    The only sticking point is the Relativistic version, but there I hold a minority view and would happily violate fundamental Lorentz invariance, explaining observational Lorentz invariance by appeal to what is called quantum equilibrium. There is a lot you just can’t do in complete thermal equilibrium, such as extract useful work from heat and send signals. Something you can’t do in quantum equilibrium is experimentally access a preferred “frame of reference”. C’est la vie.
  • As far as I know the BB scheme reproduces all predictions of quantum mechanics. A decision can therefore be made only on aesthetic grounds. I must confess that the scheme, with both hidden variables and probability rules, seems to me exceedingly ugly, but of course one cannot argue about this.
  • So what is the disagreement in the end? Should it be locality or realism? Should it be quantum mechanics in minimal statistical interpretation, with an operational stance, or Bohmian Mechanics, or maybe something else? I guess Bohmians and I agree that the choice is not between equally viable positions. We only disagree about which one it is. To me one is a sound basis for doing physics, including theoretical and mathematical physics with a foundational interest, and the other has turned out to be fairly sterile. In 60 years the number of interesting new physical or even mathematical problems from the Bohmian and Neo-Bohmian community has been rather modest. The workshop certainly didn’t convince me otherwise, although the hope was what made me come. Bohmian Mechanics feels to me like a theologian explaining the origin of the universe. He could say: “With all your physics, which anyhow does not cover the singularity, you cannot explain Why it happens, but theology can”. I can see that many people would go for that sleeping pill. But it is a really lousy contribution to cosmology nonetheless.
  • You’ve probably seen this picture of the potential that you have to use in the Bohm–de Broglie approach to describe, by hidden variables, the double-slit experiment. You see the electron coming in and doing this crazy thing. You may think that the Himalayas are wonderful, but this potential beats them by far. Yet they never tell you where the ‘screwdriver’ is—where in that morass of valleys and peaks the electron is going to start off. It just transforms the problem that eats them, back to square one. But, in the course of it, it encumbers the landscape with a lot of decoration.
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