I recently learned about an oil drop experiment that showed how a classical object can produce quantum like behavior because its assisted by a pilot wave. How has this not gained more attention? What flaws does Broglie–Bohm pilot wave theory have in explaining particle behavior?

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    $\begingroup$ Related: physics.stackexchange.com/q/100899 $\endgroup$
    – Kyle Kanos
    Jun 12, 2015 at 1:30
  • $\begingroup$ I believe computers are powerful enough to simulate electrons being accelerated through a slit experiment. A program could be created to calculate the effect of synchrotron radiation isotopically emitted from the electrons as they travel through. The reflected and re-reflected radiation (billions of photons) would randomly guide and corral the electrons to points on the detections screen that match the variable frequency of the synchrotron radiation, slit width and separation and distance from slits to detection screen. This could be an example of so called pilot waves. $\endgroup$ Jan 6, 2017 at 7:10

8 Answers 8


It might help to cite your source: I found this one here - is this what you speak of?

Anyhow, actually this kind of idea has had considerable, if not mainstream attention over the years. Many people who have worked with quantum mechanics will have at least heard of the following: it's just that it doesn't make it into many QM courses (being an equivalent way to think about QM).

The de Broglie / Bohm pilot wave theory has a fairly well known hydrodynamic interpretation, as indeed does Schrödinger's equations. The latter was studied extensively by the German physicist Erwin Madelung (see the Wikipedia page Madelung Equations for more information) and he was doing this almost as soon as Schrödinger put pen to paper: beginning 1926.

So fluid dynamical systems do have analogies in quantum mechanics and contrariwise. That doesn't make them the same physical phenomena. Moreover, the big unsolved mystery in quantum mechanics is the measurement problem and this is not described by the Schrödinger equation. It is not emphasised enough that ALL of quantum mechanics aside from measurement is utterly deterministic. So, without an expert opinion, this is highly interesting work, but it is not relevant to the mysteries of quantum mechanics.

Bohmian mechanics, which is the most mature form of the de Broglie pilot wave theory does explain measurement through the mechanism of hidden variables (i.e. by saying that there is state in a quantum system which is hidden from us). However, it is also known that Bohmian mechanics needs to be nonlocal to make the hidden variable explanation work. Roughly this means that it implies faster-than-light signalling, which in turn makes it very hard to make sense of causality: in a universe where faster than light signalling can be done, effects can come before their causes. So my belief is that most physicists would say that Bohmian mechanics is not a good explanation.

  • $\begingroup$ "So fluid dynamical systems do have analogies in quantum mechanics and contrariwise. That doesn't make them the same physical phenomena." The same one can say about fringes from diffraction of light behind edges and Youngs water wave interference. $\endgroup$ Jun 12, 2015 at 4:08
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    $\begingroup$ @HolgerFiedler True, but what quantum phenomena have that fluid dynamics doesn't is the measurement problem. The former is a "bigger system". $\endgroup$ Jun 12, 2015 at 4:56
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    $\begingroup$ The evolution of Schrodingers wave eq'n is deterministic; but it's amplitude expresses probability which isn't the classical notion of determinism. $\endgroup$ Jul 19, 2015 at 13:53
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    $\begingroup$ Sure, I think it's a matter of emphasis; if one can't pick out a value (through measurement); then it's hard to see how one has a probability distribution; I'm assuming this is why the Everettian intrepretation is seen to be realist even though it has many worlds. $\endgroup$ Jul 19, 2015 at 14:26
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    $\begingroup$ 'However, it is also known that Bohmian mechanics needs to be nonlocal to make the hidden variable explanation work. Roughly this means that it implies faster-than-light signalling, which in turn makes it very hard to make sense of causality.' - This is incorrect. In BM, assuming the quantum equilibrium hypothesis is equivalent to Born's rule, then superluminal signalling remains impossible. It can be argued that 'perhaps' the QEH isn't equivalent in certain situations, but this is hardly a foregone conclusion. $\endgroup$ Jun 29, 2017 at 15:04

I've recently answered a very similar question here not realising it was a duplicate of this. Anyway, I'd recommend reading that first as part of this answer and then continuing below.

Responding to WetSavannaAnimal aka Rod Vance, one topic I didn't cover in my previous answer was the quantum equilibrium hypothesis within Bohmian mechanics (which despite the claims of some other answers, is completely synonymous with the term de Broglie-Bohm pilot wave theory). Essentially, in standard quantum mechanics Born's rule,

$$\rho = |\psi|^2,$$

gives the probability of a measurement returning a certain result. In Bohmian mechanics this is no longer a basic law, and instead of assuming it, it treats it as a hypothesis known as the quantum equilibrium hypothesis (QEH). So long as this holds true, then everything is the same as standard quantum mechanics (Copenhagen). If however

$$\rho \neq |\psi|^2$$

then this implies superluminal signalling is possible and causality is violated (think grandfather paradoxes, cats and dogs becoming friends etc). Fortunately it can be shown statistically that typical configurations of the universe obey the QEH, and if at some time the distribution of a system obeys the QEH, then at all future times this relation continues to hold (see Valentini, 1991). Further, the majority of configurations of the universe that don't obey the QEH are shown to quickly tend to it. Since Born's rule is backed up by experiment we can be pretty confident that this is indeed the configuration our universe is in.

Of course, some proponents of this theory just take it as a postulate and ignore all this.

For further reading (as well as, or if you don't have access to the above paper), see Goldstein et al., 1992 (which is open access).

To close with essentially the same point I gave in my previous answer; the reason it hasn't gained more attention is (in my opinion) largely down to social factors. It has some ideas that are perhaps better covered by other interpretations (QEH is commonly considered an example of this), but its issues are no greater as far as I can see to any other interpretation. It has some extra maths Copenhagen doesn't require, so that's one reason many people won't bother with it, but conceptually it's a much better interpretation for gaining an intuitive understanding of quantum mechanics, so I think it'd be great if some introductory textbooks introduced it (viz. spent a chapter on it, not the vague paragraph several currently do). Every year since ~2000 the number of published papers covering it have increased modestly (along with a few other interpretations), to now around 80/year covered by JCR (a few hundred on Google Scholar), so perhaps as the primacy of Copenhagen slowly begins to weaken this will be the case in the future.

If you're interested in why this theory was shunned in its formative years, the book 'Quantum theory at the crossroads: reconsidering the 1927 Solvay conference' (open access) and the article 'Physical Isolation and Marginalization in Physics: David Bohm's Cold War Exile' might be of interest.

  • $\begingroup$ "It has some ideas that are perhaps better covered by other interpretations (QEH is a great example)" Do you mean, "better covered than" ? $\endgroup$ Jul 1, 2017 at 3:04
  • $\begingroup$ No, I mean that to many people it seems requiring the universe to be in a typical configuration is messy. I'm not in that camp and see it as an acceptable solution, but I'm trying to remain neutral (as best I can). This and QFT are two of the most common objections I see for people rejecting BM. On a personal note I do wonder how many people who reject BM do so based on a mistaken understanding of the theory's flaws (maybe that's just my implicit biases through). $\endgroup$ Jul 1, 2017 at 3:22
  • $\begingroup$ I've edited the wording slightly. $\endgroup$ Jul 1, 2017 at 3:39
  • $\begingroup$ Are there theoretical examples which violate QEH? $\endgroup$ Jul 24, 2018 at 19:26

I am not sure if the OP shared the link or not.

I happened to watch this very recently -


This is amazing explanation in terms of real visual.

Between 2:35 and 3:15 the video shows how the pattern is built over a period of time, while the jumps appear to be random at any one time.

Therefore things may not be random, as claimed by some parts/interpretations of QM.

I think the entanglement correlations also build over time, not due to randomness, but due to conservation/balancing. I have scrutinized recent experiment data closely and it gives some indication of such possibility. http://vixra.org/pdf/1609.0237v7.pdf


See the papers by Antony Valentini, about the status of the Born rule in the context of Pilot wave theory: the Born rule means an equilibrium situation between Pilot waves and the particle wave, but particles are not always in equilibrium with Pilot waves. This means that De Broglie's pilot wave is a more general theory than Copenhagen QM, such that Copenhagen QM is correct most of the time, but not always.


The De Broglie-Bohm theory assumes a classical picture, with point particles. QFT does not really do this, as it uses fields all over, and QFT works, in spite of its contradictions, both with itself and reality, to a great extent. That means there is something real in the method of replacing point particles by (nonlocal) fields.

So one could try to be a bit more modern and replace in the De Broglie theory its point particles by solitons, or, more generally nonlinear waves... Nonlinear waves either disperse or singularize, and maybe that's the essence of quantum processes. Still, most of the energy is at the nonlinear core of the wave.

Notice that oil drop experiments do not use objects which are points (zero dimensional), but instead spread out multidimensional submanifolds (the oil drops themselves).


If you want to understand the nature of the superluminal De Broglie pilot wave, one has to correct the errors in the classical non-relativistic Maxwell-Lorentz electrodynamics. The generalized Lorentz force (in differential form) $$\vec f ~=~ \rho \vec E + \vec J \times \vec B$$ is incorrect, since it violates Newton's third principle of motion, in case of 'open' circuits of stationary current (btw, a closed circuit of stationary current is a most theoretical construct, almost impossible to put to the Newtonian principles tests). Secondly, Maxwell's electric field expression $$\vec E = -\nabla\Phi-\partial_t\vec A$$ implies that dynamic electric currents can induce a non-divergence free electric field: $$\nabla \cdot (\partial_t\vec A) \neq 0$$ however, Faraday's induction experiments do not prove at all a divergent/convergent electric field can be induced by means of dynamic electric currents. So, either one applies Ockham's razor by defining: $$\vec E = -\nabla\Phi-\partial_t\vec A ~~~~and~~~~ \nabla \cdot (\partial_t\vec A) = 0$$ or, one proves by experiment the existence of a scalar form of magnetism: $$B=-\nabla \cdot \vec A,~~~~\partial_t B -\nabla \cdot \nabla \Phi ~=~ \nabla \cdot \vec E$$ $$\vec f ~=~ \rho \vec E + \vec J \times \vec B + \vec J B$$ and this force law agrees with Newton's third principle of motion btw. This theoretical development will eventually lead to the conclusion that the electric potential, $\Phi$, must be superluminal, and that superluminal longitudinal far field waves should exist that are expressed only in terms of $\Phi$, the 'electric' potential. This is the nature of the DeBroglie pilot wave: it is a superluminal and longitudinal 'electric potential' wave, with phase/group/information velocity exceeding velocity 'c' many times. After all, the spread velocity of the Coulomb field has been measured, and found to be much higher than 'c'. Einstein's SR theory is based on Voigt's erroneous "there is no TEM wave medium that can have velocity" assumption. Lorentz added the gamma factor for a more symmetrical result. However, multiple experiments have disproved Voigt's assumption, such as one-way light speed measurements by means of atomic clocks. If SR is wrong, then many well known equations, such as $E = mc^2$ should be reevaluated (the origin of this equation is in non-relativistic electrodynamics). To follow in De Broglie's footsteps, one must be prepared to review more than a century of faulty physics. De Broglie was the best physicist of the 1927 Solvay conference, if you ask me. There was NO flaw in De Broglie's approach to wave mechanics based on the Schrödinger equation (the eigen value problem technique that Schrödinger picked up from fluid dynamics theory), to answer the question shortly. The only mysterious aspect was the nature of the pilot wave.


The de-Broglie-Bohm theory is a modification of quantum theory that adds particle trajectories on top of the wave function.

Many physicists are apparently only interested in being able to make predictions and aren't interested in what is happening in reality. People who take this position are in general hostile to any attempt to improve quantum theory or explain its content.

But let's suppose you are interested in reality. These trajectories make it difficult to construct a relativistic version of the theory. Any theory that reproduces the predictions of quantum theory but features only a single trajectory for each particle is both non-local (Bell inequalities) and non-Lorentz-invariant (Lucien Hardy 'Quantum mechanics, local realistic theories, and Lorentz-invariant realistic theories'). So we would have to discard all of quantum field theory and the special and general theory of relativity and the principles underlying those theories.

In addition, it's not clear what problem the pilot wave theory solves that can't be solved by just consistently working out the implications of quantum theory without collapse: the Everett interpretation. In particular, the Everett interpretation solves the measurement problem by pointing out that the wave function generally has sub-components that don't exchange information with one another each of which looks approximately like the universe described by classical physics:



If the wavefunction doesn't have this property, then the pilot wave theory is in trouble since the particles end up in components of the wavefunction that act like classical universes. Nor does it eliminate those universes since they are still present in the wavefunction with or without the particles. So the theory requires adding trajectories for no explanatory benefit. For criticisms of the pilot wave theory vs. Everett see



The Copenhagen interpretation refutes pilot wave theory because it's stand is that nothing has position until measured..... It has created a long history of discourse among physisist. You have to buy in to the concept and I don't. Einstein once asked a proponent of the Copenhagen interpretation if the moon was in place when you are not looking at it..... The politics of academia has resulted in no serious consideration, since 1952, of the fact that all avenues should be investigated not just the ruling elites view. Copenhagen interpretation is WRONG, PERIOD But you will be admonished just for saying so... Politics is man's Achilles heel. The Copenhagen interpretation was born at the conference pictured below...

enter image description(https://i.sstatic.net/lQOdO.jpg)![enter image description here Copenhagen interpretation claims there are no tragectories, and slams pilot wave theory because the tragectories are surrealistic. Self serving rebuttal. Everything is nowhere untill the observation. Poppycock.

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    $\begingroup$ Down-voted because this response doesn't answer the question. Neither the merits/flaws in pilot-wave theory nor the Copenhagen interpretation are explained here. You said that Copenhagen is "WRONG, PERIOD" but you don't explain why. $\endgroup$
    – zh1
    Jan 1, 2017 at 3:00
  • $\begingroup$ Copenhagen interpretation says no trajectory exists and slams pilot wave theory claiming the trajectories are surrealistic. Self serving criticism which points to its Achilles heel, that nothing is anywhere till it is observed. Poppycock $\endgroup$
    – RaSullivan
    Jan 4, 2017 at 0:42
  • $\begingroup$ The question concerns pilot wave theory, not Bohemian Mechanics. $\endgroup$
    – RaSullivan
    Jan 4, 2017 at 0:53

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