Does recent paper show Bohmian mechanics is correct? 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:


*

*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?

*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.

 A: 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.
A: 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.
