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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.

EDIT

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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Wolpertinger
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    Related: http://physics.stackexchange.com/q/213985/2451 and links therein. – Qmechanic Mar 03 '16 at 13:46
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    @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. – Peter Diehr Mar 03 '16 at 16:42
  • If Bohmian quantum mechanics describes trajectories, then it is unphysical, because there are no measurable trajectories in quantum mechanics. – CuriousOne Mar 03 '16 at 21:06
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    @CuriousOne apparently they claim to have measured such trajectories though? – Wolpertinger Mar 04 '16 at 12:49
  • @Numrok: The last time I checked the technical instructions for my photomultiplier tube they said that photons that were coming out of it were a technical defect. Maybe I need to talk to Hamamatsu about that... it's not a defect, after all... it's just Bohemian Mechanics. ;-) – CuriousOne Mar 04 '16 at 13:13
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    @CuriousOne sry I'm just trying to understand what they did in the paper and I don't understand your sarcasm about it. – Wolpertinger Mar 05 '16 at 11:49
  • What is happening in that paper is that the authors are mistaking "tracks" for "trajectories". Or shall we say they are willfully ignoring the technical terms of your own profession to produce "magic" that doesn't actually exist in the real world... – CuriousOne Mar 05 '16 at 20:05
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    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 . http://www.bohmianmechanics.org/background/current-status-of-bohmian-mechanics.html . 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. – anna v Mar 06 '16 at 06:26
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    Note that the authors themselves say "Single-particle trajectories measured in this fashion reproduce those predicted by the Bohm–de Broglie interpretation of quantum mechanics (8), although the reconstruction is in no way dependent on a choice of interpretation." They are not at all claiming to distinguish between interpretations. – Rococo Apr 13 '16 at 18:39

2 Answers2

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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.

Timaeus
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  • That's what 'interpretation' means. The prediction would always be the same; only the language is different. –  Mar 06 '16 at 04:37
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    @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. – DanielSank Mar 06 '16 at 06:16
  • @DanielSank Use whichever is easier to compute, or teach, or remember, or catch mistakes, or make new discoveries, **or modify into new theories**. – Timaeus Mar 06 '16 at 06:17
  • @Timaeus Yes, I was just giving a specific example and reinforcing this point. – DanielSank Mar 06 '16 at 06:19
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    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. http://users.physik.fu-berlin.de/~kleinert/407/407.pdf The whole term "interpretation" in the sense of "some new freedom" is a misconception. – Luboš Motl May 16 '16 at 14:23
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    @LubošMotl Anyone that studies Bohmian Mechanics can find many papers claiming it disagrees with Copenhagen, and always for the same reason. Misunderstanding and misrepresenting how Bohmian Mechanics works. In the paper you link, it's the well known result that you don't get probabilities by counting the number of Bohmian trajectories crossing the screen. If one accepts that Bohmian Mechanics is designed to make the same predictions as Copenhagen then you can use that to tell when people add wrong stuff to BM. – Timaeus May 16 '16 at 14:36
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    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. – Luboš Motl May 16 '16 at 14:51
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    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. – Luboš Motl May 16 '16 at 14:55
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    @LubošMotl Bohmian Mechanics uses the same Schrödinger equation as any other multiparticle theory of nonrelativistic quantum mechanics. And the particle evolution doesn't affect the wave evolution in the slightest. And the particle isn't actually supposed to affect any probabilities, which aren't supposed to differ from Copenhagen. Impossibility theorems have to carefully state what they are showing is impossible. There are many many papers claiming to show Bohmian Mechanics is wrong, and the good ones merely tell you ways people can misunderstand how you are supposed to do Bohmian Mechanics. – Timaeus May 16 '16 at 14:58
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    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 – Luboš Motl May 16 '16 at 15:00
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    @LubošMotl You claim that Bohmian Mechanics is supposed to use some particular counting argument. Whereas the theory is actually quite clear about the particle not affecting the wave evolution. And the predictions about the wave are enough to give you everything. The trajectories are just things you can visualize, but literally are incapable of causing anything, according to the actual equations. Which is just the Schrödinger equation and the particle evolution equation. – Timaeus May 16 '16 at 15:03
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    Again, your way of argumentation is exactly isomorphic to a claim by a creationist who says that according to an interpretation of a verse in the Bible, God knew about the DNA molecule and used the same insights of biology known to the best evolutionary biologists. However, this creationist still wants to claim that God created the species manually in a few days etc. This assumption has implications and they may be seen to contradict the observations. Exactly the same holds for the incorrect assumption of Bohmian mechanics that positions may objectively exist prior to the measurement. – Luboš Motl May 16 '16 at 15:04
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    @LubošMotl It is designed to be equivalent, which means you are supposed to realize that you are only supposed to use the Schrödinger equation for predictions. It's a deterministic theory, you are supposed to accept that you didn't start out knowing where a particle is exactly. – Timaeus May 16 '16 at 15:06
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    You may try to be deliberately foggy about the nature of the "beables" but it is straightforward to write down a proof that for any choice of beables, one may construct an experimental situation where the predictions of QM (which agree with observations) significantly differ from the Bohmian predictions. There can't be any fixed theory that works. You may try to adapt your theory after every new result in some way, add terms that cancel errors by hand, but that's not called a scientific theory. A scientific theory must be fixed and capable of predicting a class of phenomena. – Luboš Motl May 16 '16 at 15:07
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    It is not mathematically possible to design the numbers 2 and 5 so that 2+2 would be equal to five, or design a book of the Bible that would describe a creation 6000 years ago that would be producing OK predictions for new genetic and fossil experiments, and it is exactly equally impossible to design a theory that would have all the properties you claim to be obeyed by Bohmian mechanics. Is the previous sentence incomprehensible or difficult in any way? Your claim that a theory is "designed" to have some features is a lie. You may want to design but the wish can't be fulfilled – Luboš Motl May 16 '16 at 15:08
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    @LubošMotl I agree that people sometimes misuse Bohmian Mechanics to make wrong predictions. I don't accept that they are doing BM correctly. And indeed BM is deisgned as a theory to make the same predictions, in fact it is helpful to have multiple theories with the same predictions so people can learn to not get excited about the things they disagree about. I don't think you have accepted what BM is, it's just an interpretation. Evolve your wave like normal, make all your predictions as normal. Then, on top, you can imagine a world particle (evolving point in configuration space). – Timaeus May 16 '16 at 15:11
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    @LubošMotl I just told you exactly how to make such a theory. Use the Schrödinger equation to make your predictions. If you don't know how then write down the actual wavefunction of system plus device and the actual Hamiltonian and evolve it. Get the same predictions any interpretation does. Surely this is possible, since every interpretation does it. Then simply evolve a particle on top that doesn't change any of that. It didn't change anything. Since BM was honest from the get go it was merely an interpretation, not a new theory, this is clearly as it was intended to be done. – Timaeus May 16 '16 at 15:15
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    If you don't use the extra Bohmian beables such as the classical particle positions and predict things from the wave function that collapses at the moment of the measurement, then it is the Copenhagen quantum mechanics and not a Bohmian theory. If you do use them, you generally get wrong predictions that disagree with QM and experiments. Something's hard about those things? – Luboš Motl May 16 '16 at 17:16
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    Note the hidden assumption of quantum equilibrium here. So, there are actually testable differences between ordinary QM and Bohm theory, the Born rule is not necessary going to be valid. – Count Iblis May 16 '16 at 17:39
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    @LubošMotl Bohmian mechanics is a no collapse theory. As such, like all no collapse theories, the theory requires you to model the device. I spelled all this out in my answer including my concession that Copenhagen's magical collpase is as unverifiable as Bohm's magical special configuration. The extra magic has to be added in a way that doesn't contradict the Schrödinger evolution. The correct predictions, as always, come from the wavefunction of the actual system including the device. I'm beginning to wonder whether you even read my answer. – Timaeus May 16 '16 at 23:09
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    @CountIblis If the Bohmian Interpretation of non relativistic quantum mechanics inspires a Bohmian type new theory, you have to give it a different name. You always have to give new theories new names. The OP is quiet clearly asking about the interpretation, which is just Schrödinger for the wave with an additional evolution for something that doesn't affect the wave. And it requires you specify the device as part of the system. Which means there isn't room for anything else (such as the particle) to affect the predictions because you've fully specified the system. A different theory isn't dBB – Timaeus May 16 '16 at 23:14
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    @Timaeus - its being a no-collapse theory is a lethal problem because the collapse may be experimentally verified. For example, when a photon is emitted by an atom and detected at a given place after the prism, the atom has to collapse to the appropriate (final, lower-energy) energy eigenstate. This is needed to preserve the energy conservation law. Bohmian mechanics doesn't allow this collapse, so it violates the energy conservation law, in disagreement with experiments. ... Your comments about the apparatus are off-topic - the apparatus has a well-defined position etc. in Bohmian mechanics. – Luboš Motl May 17 '16 at 04:23
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    @LubošMotl The apparatus is not off topic. The special position is irrelevant to any predictions. And the sure, Bohmian Mechanics has problems with photons, but that is because it is a nonrelativistic theory. But no collapse theories aren't wrong, they are detailed. No collapse theories perfectly explain how part of an entangled system changes when a different part of the entangled system interacts with a device. Mischaracterizing a theory doesn't advance science. – Timaeus May 17 '16 at 13:13
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    @LubošMotl Bohm (1952) proved the equivalence between dBB and QM. Any claim that dBB has been falsified would also instantly falsify QM. Also note that in part II, Bohm extends dBB to the EM field and demonstrates photoelectric and Compton effects. So, your claims about QFT in dBB are wrong as well as we already knew they had to be by the equivalence theorem. http://fma.if.usp.br/~amsilva/Artigos/p166_1.pdf and http://www.physics.drexel.edu/~bob/Entanglement/Bohm_hiddenvar2.pdf – user7348 May 27 '16 at 22:11
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    There's no valid proof of any such equivalence of the whole theories. The theories are self-evidently inequivalent. The agreement of QM with reality is overwhelming. The apparatus changes nothing about any statements about BM because its particles exist independently of the particles. And so on, and so on. Not a single sentence any Bohmist has written here has the slightest resemblance to the truth. Can we please stop this unproductive exchange? [Comment was modified by a moderator to conform with the SE 'be nice' policy.] – Luboš Motl May 28 '16 at 04:34
  • @LubošMotl Show me where Bohm's proof fails in his paper. You can't do it. Publish it in a journal as Schmelzer has asked you to do. It's a rigorous mathematical theorem that the two theories are equivalent. Show me a calculation where you get, say 5J in BM and 6J in QM or something like that. – user7348 May 28 '16 at 04:43
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    I have given about 15 proofs of that already. I won't try to send anything like that to journals because there would be a high probability that a Bohmist crank would be chosen as a referee and the exchange would be identical to one we are having here. I won't reply to your further "comments" because it is an absolute and total waste of time. [Comment was modified by a moderator to conform with the SE 'be nice' policy.] – Luboš Motl May 28 '16 at 05:02
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    @LubošMotl The wavefunction of the system in dBB includes the configuration (and spin) of the apparatus AND the subject. The particle position affects nothing, but the apparatus does matter. In fact, the apparatus is essential to getting the correct predictions. Excluding the apparatus creates a straw man of a theory. Which is exactly the thing that disagrees with QM. Everyone agrees that if you do dBB incorrectly, to try to make a different physical theory rather than an interpretation that you then get bad predictions. – Timaeus May 28 '16 at 05:15
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    @Timaeus There's no point in arguing with Motl. He refuses to accept proven results if they disagree with his pre-determined opinion on the subject. I doubt he's even read Bohm (1952) that I linked to him. I highly doubt he would appreciate what a remarkable tour de force it is if he did read it. Instead he criticizes the theory based a horrible misunderstanding of what the theory even means. He's ignorant beyond anything I've ever come across, and to add to it, he's extremely mean and rude. It's unprofessional, and ironic that he's the one who's clueless. – user7348 May 28 '16 at 05:29
  • @user7348 Did you read the paper he linked? It attacks a different theory that it calls dBB. This is just a semantics argument. And it's my fault, I really did write my original answer in a manner that allowed people to think a popular misunderstanding of dBB was actually dBB (the misunderstanding was inconsistent with everything else I wrote, but it's unfortunately a popular misunderstanding so I shouldn't have allowed the smallest opening to that view). As long as there are people that claim that dBB-inspired (but different) theories are actually dBB, this argument will persist. – Timaeus May 28 '16 at 05:47
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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.

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anna v
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  • Very interesting. I was also wondering by looking at the original paper, that it was weird how the density of trajectories not printed. – Mikael Kuisma Apr 14 '16 at 11:51