The following paper was recently featured in a German science magazine (Spektrum der Wissenschaft): "Experimental nonlocal and surreal Bohmian trajectories" (DOI:10.1126/science.1501466)

The abstract reads

Weak measurement allows one to empirically determine a set of average trajectories for an ensemble of quantum particles. However, when two particles are entangled, the trajectories of the first particle can depend nonlocally on the position of the second particle. Moreover, the theory describing these trajectories, called Bohmian mechanics, predicts trajectories that were at first deemed “surreal” when the second particle is used to probe the position of the first particle. We entangle two photons and determine a set of Bohmian trajectories for one of them using weak measurements and postselection. We show that the trajectories seem surreal only if one ignores their manifest nonlocality.

To what extent does this show Bohmian mechanics is correct in the sense that it explains things normal QM does not explain?

Unfortunately I had to realize I don't know enough about the subject to understand the full paper. I would just like to know if they actually claim to have experimentally shown that an interpretation of QM is distinctly different from standard QM.

I am particularly asking in light of thoughts like this.


I first accepted the answer given by @Timaeus below. There are two reasons I removed the acceptance tick again:

  1. I discussed with a friend who knows a lot more than me about weak measurements. He said they are not really completely understood yet, nevertheless give surprising empirical results. These seem to be hard to reconcile with the standard interpretation of quantum mechanics, though a lot easier to reconcile with things like Bohmian mechanics. It is hard to read from the papers if it actually shows distinguishing features between the interpretations. Now Timaeus argued that they can't because the "interpretations" by definition only predict the same results. Well, apparently they don't so I will repeat my question slightly differently: Does this paper show that Bohmian mechanics is correct and that the standard interpretation is not?
  2. There has been another recent paper by the same group that in fact won the "Breakthrough of the year" award. From the abstract:

A consequence of the quantum mechanical uncertainty principle is that one may not discuss the path or “trajectory” that a quantum particle takes, because any measurement of position irrevocably disturbs the momentum, and vice versa. Using weak measurements, however, it is possible to operationally define a set of trajectories for an ensemble of quantum particles. We sent single photons emitted by a quantum dot through a double-slit interferometer and reconstructed these trajectories by performing a weak measurement of the photon momentum, postselected according to the result of a strong measurement of photon position in a series of planes. The results provide an observationally grounded description of the propagation of subensembles of quantum particles in a two-slit interferometer.

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    $\begingroup$ Related: physics.stackexchange.com/q/213985/2451 and links therein. $\endgroup$
    – Qmechanic
    Commented Mar 3, 2016 at 13:46
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    $\begingroup$ @Numrok: This recent paper does not invalidate the de Broglie-Bohm pilot wave model; this is because the Bell and CSHS tests are designed to separate locally-realistic hidden variable theories from ordinary quantum mechanics. But the pilot wave model is grossly non-local, so it doesn't fit the test. The Bell test "loop holes" that are closed include space-like separation and detection efficiency. But the Bohm model's pilot wave is superluminal, so it cannot be excluded based on these tests. $\endgroup$ Commented Mar 3, 2016 at 16:42
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    $\begingroup$ @CuriousOne apparently they claim to have measured such trajectories though? $\endgroup$ Commented Mar 4, 2016 at 12:49
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    $\begingroup$ @CuriousOne sry I'm just trying to understand what they did in the paper and I don't understand your sarcasm about it. $\endgroup$ Commented Mar 5, 2016 at 11:49
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    $\begingroup$ There are different formulae describing the data in the two systems. C deals with probability waves, Bohmian with non local pilot waves that give the equivalent results . bohmianmechanics.org/background/… . No model has been produced that is Lorenz invariant, so it is just an interesting exercise in mathematical reformulations. This paper does not change this, as its results are also describable by the usual C formalism. $\endgroup$
    – anna v
    Commented Mar 6, 2016 at 6:26

2 Answers 2


Bohmian Quantum Mechanics doesn't make different predictions than any other interpretation.

The trajectories of Bohmian Mechanics are simply a particular choice of probability current. You could measure position at any time and associate a trajectory with that result and look at the path forwards or backwards.

The so called probability current was already there in any interpretation. And Bohmian Mechanics doesn't use the trajectories to make any new different predictions. Just like every other interpretation.

So it isn't about correctness. It's about how some people looked at pictures and said "that's a weird looking picture" as if that mattered. Now you can do experiments where the picture is more closely related to actual experimental results. So it seems less weird when there is data that has similarly shaped results.

But you could get those predictions even without saying the particles move on those trajectories. When you focus on the experimental results, all the different interpretations agree. So the results aren't evidence for any one over the others.

If someone wants to think that results just appear sometimes with certain frequencies and correlations (like Copenhagen does) then no evidence can ever refute that. And similarly you can make a theory where things act a certain way that produces the same results with certain frequencies and that doesn't show the theory is correct about how the things acted other than the fact that you got the results you did with the frequencies you got.

The story can look less weird when the pictures can line up with some experiments. But there will always be a boundary between results and the many many ways the universe could be that are consistent with those results. And nothing will distinguish between them. Which is fine. Use whichever is easier to compute, or teach, or remember, or catch mistakes, or make new discoveries, or modify into new theories. Or use different ones for different situations. Just don't think your evidence is more than it is.

It was never right to object that the trajectories look weird. Now it's a little bit easier to show people that was a wrong objection. But if they couldn't see that before then I'm not sure you've accomplished anything. People shouldn't get too excited about the parts of a theory that aren't used to make a prediction.

Does this paper show that Bohmian mechanics is correct and that the standard interpretation is not?

Again, different interpretations make the same predictions. In Bohmian mechanics you handle weak measurements and strong measurements the same way: by writing down the wave function of the combined system of subject and device and writing down the evolution as determined by the Hamiltonian of the joint system (which every interpretation does, so weak measurements aren't mysterious in the slighest) and then adding the one ingredient of Bohmian mechanics. Which is to consider a distribution of initial positions to consider special, and the streamlines of these initial positions evolves to give a distribution on final positions, and which of the separated packets this final position is in tells you which outcome to consider special.

If you post select your results, then you are just sorting the final results to line up with the kinds of trajectories Bohmian mechanics follows. You are still saying that the Schrödinger equation for the actual experimental setup describes the evolution of the actual system. Like any interpretation does.

Sure, interpretations other than Bohmian mechanics sometimes get lazier and don't write down the device part of the system and don't write down the Hamiltonian of the full system of device and subject. Because they want to use a hack to compute the frequency of the final results: a hack designed just for strong measurements. But that just means if you find a situation where their favorite hack doesn't work they will have to do it the full way. Which was never in doubt about being the correct way.

Keep in mind that Copenhagen doesn't make different predictions, many worlds is about as close to what the math says and Copenhagen merely asserts that one branch somehow magically survives when the others somehow somewhen magically disappear, but that's a nonprediction because it is untestable. Bohmian mechanics has the same branching as many worlds (because it also uses the Schrödinger equation and the Schrödinger equation branches for interactions of device and subject) but it asserts that one position in configuration space was always special and so as the branch separates, at most one branch becomes special. But the specialness of a branch changes nothing about the predictions. So like Copenhagen, its additional stuff is also merely a non prediction. Every interpretation is like that.

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    $\begingroup$ @user36790 That's true, although note that different interpretations of the same thing can be really helpful for developing new theory. For example, one can interpret the quantum mechanics of interacting charged particles as either field equations or as exchange of discrete force carrier particles. The latter is really useful in terms of building up perturbation series, etc. $\endgroup$
    – DanielSank
    Commented Mar 6, 2016 at 6:16
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    $\begingroup$ It's simply not true that one can design a system of rules obeying the basic Bohmian assumptions (especially that no random number is produced at the moment of the measurement, and no collapse fundamentally takes place at that moment) that would be equivalent to proper, Copenhagen, quantum mechanics. The inequivalences are absolutely obvious, are lethal defects of Bohmian mechanics, and may be demonstrated in big contexts as well as small ones, see e.g. users.physik.fu-berlin.de/~kleinert/407/407.pdf The whole term "interpretation" in the sense of "some new freedom" is a misconception. $\endgroup$ Commented May 16, 2016 at 14:23
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    $\begingroup$ Dear @Timaeus - you just keep on misunderstanding the basic critical issue here. As I already wrote in the previous comment, it is mathematically impossible to construct a theory of the Bohmian type (just like it is impossible for a theory based on the Bible to predict quantitative properties of fossils) - even if you had quite some freedom to deviate from the existing Bohmian models - that would give the same predictions as quantum mechanics. Even David Bohm knew that very well, especially when it came to physics of bosons and other things. $\endgroup$ Commented May 16, 2016 at 14:51
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    $\begingroup$ The fact that the probabilities may be calculated from the number/density of Bohmian trajectories crossing a particular place on the screen is nothing else than the frequentist definition of probabilities - and Bohmian mechanics itself relies on these elementary things heavily, too. To claim that probabilities can't be measured in the frequentist way is just silly. If the points where particles are detected are extracted from some classical trajectories, and a defining feature of Bohmian mechanics is that they are, there's just absolutely no way to avoid what you want to avoid. $\endgroup$ Commented May 16, 2016 at 14:55
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    $\begingroup$ Its using Schrödinger's equation somewhere doesn't make it equivalent to QM. A theory with the same equation is only equivalent if the theory uses the equation in the equivalent way, with the equivalent interpretation of the objects, and if it has no other objects that affect the observations. Bohmian mechanics clearly violates all these things (for example, it says that particles are seen at some classically real positions - which is totally different from the claim in QM) so all the predictions have to be done from scratch and as Chen-Kleinert or any other example shows, predictions are bad $\endgroup$ Commented May 16, 2016 at 15:00

Here is a related paper that analyses the same data looking for the connection with Bohmian mechanics.

Comment on "Observing the Average Trajectories of Single Photons in a Two-Slit Interferometer" Timothy M. Coffey, Robert E. Wyatt

Kocsis et al. (Science, Reports 3 June 2011, p. 1170) state that the experimentally deduced average photon trajectories are identical to the particle trajectories of Bohm's quantum mechanics. No supporting evidence, however, was provided. The photon trajectories presented in their report do not converge to high probability regions, a familiar and necessary behavior of Bohm trajectories. We reanalyze their data and calculations, conclude that the average photon trajectories do indeed agree with Bohm, and discuss possible interpretations of this result

They say in the conclusions:

Many adherents to Bohm's version of quantum mechanics assert that the trajectories are what particles actually do in nature. From the experimental results above no one would claim that photons actually traversed these trajectories, since the momentum was only measured on average and the pixel size of the CCD is still quite large. Other views of Bohm's trajectories do not go as far as to claim that they are what particles actually do in nature. But instead, the Bohm trajectories can be viewed simply as hydrodynamical trajectories that have equations of motion with an internal force that appears when one changes from a phase space to a position space discription.

Italics mine

So it seems it is a result consistent with the Bohmian interpretation and with the usual interpretation, is how I read their reanalysis.I have not seen this published anywhere so I just take it as an informed opinion. I realize that the paper I quote is a previous version of the experiment and the recent one needs an equal critical analysis.

  • $\begingroup$ Very interesting. I was also wondering by looking at the original paper, that it was weird how the density of trajectories not printed. $\endgroup$ Commented Apr 14, 2016 at 11:51

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