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About surrealistic trajectories in dBB theory
#1
This is interesting: new paper that disputes 1992's "ESSW", Englert et al, http://www.degruyter.com/view/j/zna.1992...2-1201.xml.

The paper from Mahler et al (Aephraim Steinberg is the only author I've heard of), "Experimental nonlocal and surreal Bohmian trajectories", http://advances.sciencemag.org/content/2/2/e1501466 came out in February but I noticed it in a popular write-up from 5 days ago at https://www.quantamagazine.org/20160517-...l-support/.

Of course it tells us nothing we didn't already know but it's worth checking out. Good to see dBB treated fairly in popular press.
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#2
Thanks very much for the links, this is really helpful, I would have to find the links myself to comment yet another attack by Lubos Motl, in this case not directly against dBB theory but against the article in the Quanta Magazine. The article is quite fine, the only inaccuracy I have identified is
Quote:... their velocities at any moment fully determined by the pilot wave, which in turn depends on the wave function.
where the "pilot wave" is the same as the wave function, in fact, it is simply the original name of the wave function, the one used by de Broglie. But even this use can be defended, given that the pilot wave is the wave function on configuration space, but "wave function" is defined also on momentum space, thus, is a more general concept.

What is Motl's objection? The article is about a paper Mahler et al., Experimental nonlocal and surreal Bohmian trajectories, Sci. Adv. 2016; 2 : e1501466 19 February 2016. Motl quotes the abstract of this paper, which says
Quote:We have verified the effect pointed out by ESSW that for a WWM with a delayed readout, Bohmian trajectories originating at the lower slit may be accompanied by WWM results associated with either the upper or the lower slit. However, this surreal behavior is merely the flip side of the nonlocality we also demonstrated.
and comments this with
Quote:So an experiment by ESSW was done and the predictions were confirmed.
and, given that the ESSW paper can be considered as being somehow against dBB theory, it follows that the result is a refutation of dBB theory.

But in the Mahler et al. paper itself we read the following:
Quote:Englert, Scully, Süssmann, and Walther (ESSW) (12) asserted that in the presence of such a Welcher Weg measurement (WWM) device, the particle’s Bohmian trajectories can display seemingly contradictory behavior: There are instances when the particle’s Bohmian trajectory goes through one slit, and yet the WWM result indicates that it had gone through the other slit. ESSW concluded that these trajectories predicted by Bohmian mechanics could not correspond
to reality and they dubbed them “surreal trajectories.” This serious assertion was discussed at length in the literature (13–17), after which a resolution of this seeming inconsistency was proposed by Hiley et al. (18). Here, we present an experimental validation of this resolution, in which the nonlocality of Bohmian mechanics comes to the fore.

Here, (18) refers to B. J. Hiley, R. Callaghan, O. Maroney, Quantum trajectories, real, surreal or an approximation to a deeper process? ArXiv:quant-ph/0010020 (2000). Which is, as one can easily see (if Hiley as one of the authors is not sufficient for this) proposes a resolution which supports dBB theory. And it is this pro-dBB resolution which is supported by the observation. So, the Bohmians, who, I suppose, tend to read important papers and not only the abstracts (as string theorists, with their thousands of papers, are essentially forced to do), will know that it is their beloved theory which is supported. Whatever, Lubos Motl explicitly asks for help:
Quote:So how can anyone ever say that this experiment brings "new support" for Bohmian theory (there has never been any old support, let alone new support)? It's probably meant to be justified by the sentence (and related comments):
Quote:However, this surreal behavior is merely the flip side of the nonlocality we also demonstrated.
What? ;-) The ESSW paper and the serious observations in it don't depend on any "nonlocality" whatsoever. The word doesn't appear in the ESSW paper at all (the highly problematic term "weak measurement" doesn't appear there, either). Two trajectories either agree or disagree. And yes, they disagree. That's the problem ESSW found and Mahler et al. confirmed. What does it have to do with nonlocality?
Hm, this looks similar to the problem that one should be able to explain things also to the own grandmother, as a criterion that one has understood the problem oneself. Is one able to explain the problem to Lubos Motl, without going into too many details of the Hiley et al. paper (32 pages) and the Mahler et al. paper (8 pages)?

That's difficult, of course, but, whatever, let's try. There is the simple symmetry rule of the simple double slit experiment, everything is symmetric for \(z \to -z\), the Bohmian velocity too, thus, \(v^z(z=0)=0\) and no particle can switch sides. But we do not have here this simple situation. We have a device which measures the "which path" information. So, let's describe the result of this "which path" measurement by \(\psi^{which}(x)\). Then we have to consider the full wave function, which is
\[ \psi = \psi_{up}(z) \psi^{which}_{up}(x) + \psi_{down}(z) \psi^{which}_{down}(x).\]
And if we now try a symmetry \(z \to -z\), we also have to change the measured which path information correspondingly, \(\psi^{which}_{down}\leftrightarrow\psi^{which}_{up}\). Moreover, we have different Bohmian velocities at \(z=0\), namely all values of \(v^z(x,0)\). That they have to sum up to 0 does in no way mean that they have to be zero themselves. So, the "Bohmian prediction" that up remain up holds only in the simple case, where no "which path" information is measured. If the hole is measured, thus, if \(\psi^{which}_{up}(x) \) and \(\psi^{which}_{down}(x) \) do not overlap, then the symmetry gives us nothing, and the Bohmian particle follows the same wave function which we have to use if only one hole would have been open. Which easily allows him to cross the z=0 border.

But what if \(\psi^{which}_{up}(x) \) and \(\psi^{which}_{down}(x) \) do overlap? What if they are, say, \(\delta(x-x_1)\pm\delta(x-x_2)\), so that their support is even identical? Then, from the Bohmian point of view, we have to distinguish the two cases \(x(t)=x_1\) and \(x(t)=x_2\). In above cases, we have a an effective superposition, simply with a different amplitude \(\pm1\). And in above cases we obtain a symmetry, and the "up remains up" rule remains valid.

But what if we delay the "which path" measurement? That means, we make a measurement immediately, so that we obtain a state
\[ \psi = \psi_{up}(z) \psi^{which}_{up}(x) + \psi_{down}(z) \psi^{which}_{down}(x),\]
but we do not complete the measurement immediately, so that it becomes a macroscopic, irreversible one, but leave it some time in the \(\delta(x-x_1)\pm\delta(x-x_2)\) state, and only some time later decide that we measure the "which path"? In this case, we may have to apply one part of the considerations before and the other one after the measurement. Which requires some non-locality. The usual weak non-locality, which cannot be used to transfer any information, because it is hidden in the correlations, and one needs the complete information from above parts to see that it is necessary to explain the observations.

So, I hope this helps to understand how non-locality becomes relevant for understanding ESSW.

How all this brings "new support"? In the same way as every experiment which does not falsify a given theory is, sloppily, named "new support" to a theory in popular literature. Nothing serious, given that we have an equivalence theorem.

Or, maybe, more? At the actual moment, I think, yes, even much more. I have had an idea, today, which, if it really works, would give really much more. I have to write it down, and, given the quite exceptional nature, the probability is yet high enough that it is simply wrong. I have had a lot of such ideas, and rejected them later because they did not work, so this would be nothing new. But at least today it looks so consistent to me that I even risk to announce it in this way. So, what I announce here is the following: Or I will present in some time a paper with a really interesting and unexpected claim, or (more probable) I will find the error in this construction - and, then, promise to explain it, as an illustration of the everyday work of scientists, which, quite often, have nice ideas but, later, find they don't work.
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