## Surreal Trajectories: the main argument against Bohmian ontology

I was extremely busy for the past two weeks and I simply did not have any time to write the weekly post. But without any more delays, as promised, here is the argument against Bohmian interpretation. The argument comes from a famous paper by Englert, Scully, Süssmann, and Walther: Surrealistic Bohm Trajectories.

For clarity, here are the original paper, the rebuttal, and the response.

The argument is simple: in a double slit experiment with a which way detector present before the slit (which incidentally kills the interference pattern), the Bohmian trajectories do not cross the axis of symmetry.

However the wavefunction is:

$$\Psi = \psi_>|detect~up\rangle + \psi_<|detect~down\rangle$$

and $$\psi_>$$ does not vanish in the bottom part and $$\psi_<$$ does not vanish in the top part. As such, the particle can be found in the down section while the particle was detected earlier by the upper which way detector. But this is at odds with Bohmian trajectories which by symmetry considerations do not connect the up with the down.

The conclusion is that Bohmian trajectories do not always have a correspondence in reality. The issue is not whether Bohmian quantum mechanics does or does not make the same prediction as standard quantum mechanics as the rebuttal seems to imply, but the issue is the ontology of Bohmian trajectories. The claimed advantage of Bohmian mechanics is its clarity rooted in realism, but if Bohmian trajectories are at odds with experiments, what is the value of Bohmian interpretation? Remember that in Bohmian interpretation the only thing "real" is the particle trajectory. I could not find a valid answer from the Bohmian community to the surrealistic paper challenge and in my opinion this paper it is a decisive clear cut argument against Bohmian interpretation.

1. Florin,

The reason your conclusion is wrong emerges from the same old mistake of assuming that the only possible classical model is bullets/billiard balls.

You assume that the particles travel like bullets and hit the detector that happens to be in their path.

Once this model is replaced with a classical field model the problem disappears. The particle can exert a force on a detector that is not in the particle's path, but far away, because the particle's field acts at that location.

Just as the Sun acts upon the Earth, without being at the location of the Earth, the particle acts upon the detector without the particle being at the location of that detector.

True, the quantum field associated with the Bohmian particle does not have the same behaviour as the gravitational field (does not decrease with the square of the distance, etc.) but I see no reason to impose such a constraint.

So, the particle is real, the trajectory as well, but the detector does not indicate the particle's position but the place where the field acts the strongest.

Andrei

1. Andrei,

Your argument does not hold water. The electrical or gravitational forces drop like 1/r2. If the particle in below the axis of symmetry then its field is stronger to the detector it is closer. Hence the click is registered below, not above.

Florin

2. On what basis do you assert that any field theory must behave like gravity? Strong force does not behave that way and there is no reason whatsoever to impose such a constraint for all theories.

Andrei

3. I understand the debate here is about Bohmian trajectories not just position but may be the following extracts from Nicolas Gisin paper arxiv.org/abs/1509.00767 can enlighten the debate:

"assumption H: Position measurements merely reveal in which (spatially separated and non-overlapping) mode the Bohmian particle actually is.
...assumption H is wrong. Every introduction to Bohmian mechanics should emphasize this. Indeed, assumption H is very natural and appealing, but wrong and confusing.
...one should ... recognize that Bohmian mechanics is deeply consistent and provides a nice and explicit existence proof of a deterministic nonlocal hidden variables model. Moreover, the ontology of Bohmian mechanics is pretty straightforward: the set of Bohmian positions is the real stuff. This is especially attractive to philosopher. Understandably so. But what about physicists mostly interested in research? What new physics did Bohmian mechanics teach us in the last 60 years? Here, I believe fair to answer: not enough!

As far as I am concerned I think all this boils down to the problem of a missing model (ontology?) for spacetime in our quantum age where (to enlarge the perspective) the geometric/dynamical interpretation of the Brout-Englert-Higgs mechanism that may provide mass to all particles and thus help us make a clear cut between trajectory and position is not settled yet.

4. Hi Cedric,

Interesting perspective. Of course there is no QFT for Bohmian mechanics and as such the Higgs mechanism has no Bohmian explanation.

2. Dear Florin i have a problem with solipsism, honestly all this interpretations, both bohmian, both Copenaghen make my problem more hard.

1. Dear Laura,

What do you mean?