Interesting. My guess is that there will be interference.

However, no matter what the outcome, it will not have any implications deciding between the Bohmian or standard interpretations of QM. If a Bohmian description is possible, that is. I would not know how to apply Bohmian mechanics to photons, i.e. particles that are necessarily relativistic. However, if an analogous experiment were done with ultracold atoms, say, then BM is applicable and will give just the same predictions as standard qm.

Thanks K. Kassner for your input. I too think that there will be interference. Concerning the Bohmian description: Lets say this experiment is conducted with nonrelativistic  electrons. As I understand it, there would be a distinct nonlocal quantum potential corresponding to each slit being open, and both slits are never open at the same time, so the question is -- "Why is the electron manifesting trajectories that (at detection) create an interference pattern that results from the quantum potential corresponding to 'both slits open' ?"

Well, that would have to be analyzed in detail. Your narrow-band spectral filter, without which there would be no interference, will also produce a quantum potential via the wave function. It should be that second quantum potential that eventually produces the interference.

My statement about Bohm simply relies on the fact that Bohmian mechanics is bound to make the same predictions as standard QM, if the same initial wave function is taken. These predictions do not come from the particle trajectories. In fact, to have a difference between the predictions of BM and standard QM, the proof that they always make the same predictions would have to be wrong somewhere, and I have no idea how it could. The trajectories of BM are not used anywhere in its applications except for deciding in a formally deterministic way which of the possible outcomes is chosen -- but the probabilities are the same as in standard QM.

DIRAC'S DICTUM: "a photon interferences only with itself".

So, two photons can produce only 2particle interference. And with electrons it won't be better.

A narrow-band filter prolonges the wave-packet. Thus, if you speak of electrons, the wave-packet of an electron is bound to meet the wave-packet of the next electron. The wave-function in this case, as long as the two wave-packets overlap, should be

Ψ(r1, r2, t) ~ eiφ{ψ1(r1, t) ψ2(r2, t) - ψ1(r1, t) ψ2(r2, t).

However, if the expression of ψ1 and ψ2 is the same, you'd never get the two electrons together. Anyway, it would be 2particle interferometry.

Thanks Sofia for your comments. However, we are never dealing with any more than one particle 'per run of the experiment' (photon, electron etc. ...). I clearly state that the source produces "sub-single-photon pulses" (or "sub-single-electron pulses" etc.) which, by definition, contain at most one particle per pulse; these pulses are then split into two time-bins appropriately synchronized with the opening of each slit.

Below is a pic of what happens: for each pulse doublet: the early one passes when top slit is open; the late one when bottom slit is open; there is at most one particle per pulse doublet

So, whenever a detection occurs, it could only have come from one of these two possibilities; before the filter the pulses that have passed the slits do not overlap in time, after the filter they do (temporal quantum erasure)

Aha! Now I understand.

So, if the narrow-band filter lengthens the earlier half-pulse, so as to overlap at least partially with the later coming half-pulse, near the horizontal axis passing mid-way between the slits, the two halfves of the pulse are bound to overlap. Since you say that the filter is narrow-band, I mean, if the frequency is enough well-defined, there will appear fringes of interference.

But, it's ordinary single-particle interference, I see nothing special which could pose new problems to quantum or Bohmian mechanics.

Where and why do do suspect a problem?

Yes, now you have described the scenario as I intended it

. My thought is the following:

Since Bohmian mechanics assigns particle trajectories that are determined by the existing wavefunction (at every moment of time during the propagation of the particle), it seems that, for instance, the location of the filter plane, relative to the plane of the slits and the detection plane, would have significant influence on the form of the particle trajectories, whereas in Copenhagen the filter location [near the slits (but not near-field) or near the detection screen] has no effect. It seems that the trajectories would be radically different if the filter was encountered shortly after the particle traverses the plane of the slits, as opposed to the filter located 'far away' just before the detection plane; in one case the temporal overlap happens early in the trajectory evolution, whereas in the other case the overlap happens much later. Intuition suggests dramatic changes in particle trajectories when comparing these cases.......Will it "all work out in the end" and the same interference pattern persists, regardless of filter location, requires a detailed mathematical description using Bohm's  theory (whether that is worth doing is an open question).

It may well be that the Bohmian trajectories will look different from those of an ordinary double-slit experiment. But they don't matter for the question whether interference is observed or not. All that matters is the wave function, giving the probability amplitude for particle detection. And that is calculated precisely the same way and obeys the same equation as in standard qm. To apply Bohmian mechanics to experiment, you never need to calculate a single trajectory. You can do that, if you want a metaphysical picture afterwards, and you could even calculate the probability distribution of particles from the initial distribution and the equation of motion of the particles. But the theory is constructed so that this must give the same result as the calculation via the wave function. So particle trajectory calculations are always redundant in Bohmian mechanics.

It does not matter, by the way, whether we have single-particle interference or many-particle interference. Bohmian mechanics handles both equally well. In configuration space, all that changes is the dimension (from three to six if one goes from one to two particles). All the particles are described by a single point in configuration space.

A falsification of BM (versus standard qm) should not be attempted via experiments, because if successful, it will automatically falsify standard qm, too. All that can be tried is to see whether the compatibility between trajectories and the wave funciton built into the theory fails, i.e., whether it is possible to construct a contradiction between predictions from BM obtained via the wave function and those obtained from the particle picture. If that succeeded, one would have shown that the theory is self-contradictory. It seems a bit hopeless to me, however, as the continuity equation, on which the compatibility is founded, looks  physically sound.

==> "the location of the filter plane, relative to the plane of the slits and the detection plane, would have significant influence on the form of the particle trajectories, whereas in Copenhagen the filter location [near the slits (but not near-field) or near the detection screen] has no effect."

The question is how long is the wave-packet exiting the narrow-band filter (NBF). For getting interference, the following scenario is necessary:

1. At a time t1 the half-packet exiting the upper slit - let's name it ψ+, meets the NBF and from NBF begins to pour a wave-packet of quite well-defined frequency.

2. At a time t2 the half-packet from the lower slit - let's name it ψ-, meets the NBF.

3. If at t2 still pours ψ+ from NBF, then for t>t2 you'll have inteference beyond NBF between ψ+ and ψ- in their form modified by NBF.

So, the interference depends of the length of the wave exiting NBF.

Please see, the two waves exiting NBF don't overlap on all their lengths. From t1 to t2 you have only ψ+ at the exit of NBF. ψ+ alone produces no interference. The first to reach the photographic plate is ψ+, and it may produce a detection on the plate. Both QM and BM would say that. Also, after some time, from NBF would pour only ψ-, which also doesn't produce interference. That is bound to last a time-interval also equal to t2 - t1. Both QM and BM would say that. Only the overlapping part of the two wave-packets produces interference. So, on the photographic plate you will see a clearer interference if the overlapping part is longr than the non-overlapping parts. If the case is opposite, the fringe pattern would appear non-clear.

Where do you see here any relevance of the position of NBF, i.e. closer to the photographic plate or closer to the slits?

Yes, I agree with your description of what happens with respect to the filter and the wavepackets.

All I want to point out is:  It seems like the trajectories would be quite different depending on whether the filter was near the slits (and thus the particle spends most of the time being influenced by a double-slit quantum potential), or if the filter is near the screen (and thus the particle evolves for most of the time according to a single-slit potential and then is subject to the double-slit quantum potential just before detection). Yes, I now do think there will be interference predicted both by Bohm and Bohr, but perhaps this radically different evolution of the particle trajectories, in Bohmian mechanics, may result in "different looking" interference patterns (with respect to, say, fringe width, visibility, etc.) depending on where the filter is.

No doubt that the form of the Bohmian trajectories would be different if the filter is closer to the slits, than if the filter is closer to the screen? A change in geometry entails a change in the form of the trajectories.

About the details of the fringe pattern, please see, the wave-packet exiting the narrow-band filter has a better-defined frequency. The narrower is the frequency range, the longer is the wave-packet in time. As the wave-packet flies toward the screen, it undergoes some dispersion, s.t. it widens. But these details you can get only writing formulas.

As to the fringe-width, it does not depend on where is the filter, it depends on the frequency spectrum. For a monochromatic wave the fringe-width is equal to half wavelength. For a range of frequences the fringe width is not so clear, it is mainly dictated by the most intense from the frequences.

For obtaining the fringe pattern you have to calculate exactly the wave-function at the screen.

Canonically, the photon wave function in position coordinates doesn't exist. However, recently the Bialynski-Birula couple published a relevant construction (PRL,108, 140401 (2012); arXiv 105.0516v2 [quant.-ph]). For massive particles, a two slit experiment in metricless notions might be found in: http://www.gallup.unm.edu/~smarandache/PiP-2016-02.pdf

You think trajectories and corpuscles and "which way" ? No hope.

Your narrow-band filter acts as a bell or a diapason : one brief impulse, and they sound long. Then another impulse, and yet another... But the direction of propagation from the slits is lost.

I wonder how could be built your narrow-band filter, and how it works.

I wonder what could be your causal chain, in your minds of corpuscularists.

Interference is always due to two different sources or to two different slits that work at the same time. The single slit can produce only a process of diffraction.

Anyway the experiment of the double slit proves no way the dualism wave-corpuscle of elementary particles. On the contrary it proves in irrefutable way the massive particles (electrons, protons, etcc...) are corpuscles without wave nature and energy particles (photons, energy quanta, etcc...) are nanowaves without real mass. In fact it is known that the single photon can produce diffraction, but the single massive particle (for instance electron) cannot produce diffraction.

 Surely Daniele Sasso has never practiced radiocrystallography. Sure, X-ray diffractograms are crisper, but the electronic diffractograms work too, at least for identifying which lattice. We have used it on the big Siemens electronic microscope, for identifying some inclusions were carbide, with a Laue diffraction image.

Single electrons, and single helium atoms too have proved each one diffract.

Dear Jacques,

I didn't understand well your comment. Anyway I wrote single photons produce diffraction while single electrons don't produce diffraction. I didn't write the electronic diffraction doesn't exist. 

if you write single electron generates diffraction, do you can send me proofs of this effect? Thanks.

Just ask "single electron diffraction" and you have a lot. Even in video.

It has been proved with ultracold helium atoms too.

Collective laws flow from the laws of physics at the individual level. Not the reverse.

A single electron has a phase. A beam of electrons never has.

Article Fifteen surreptitious, copenhaguist and corpuscularist postu...

Reading your paper it seems to me that:

1. you don't accept the dualism wave-corpuscle that claims every particle is wheter wave or corpuscle.

- I agree with your viewpoint.

2. you affirm corpuscles don't exist and all particles are wave.

- I disagree with your viewpoint. I think your concept of corpuscle isn't appropriate. Corpuscle is any physical object that is characterized by small sizes with respect to atom sizes.

In the Non-Standard Model, my model of reference, there are two types of particles: massive particles and energy particles. Both are corpuscles because they have small sizes with respect to atom sizes, but massive particles have mass and only in virtual way it is possible to associate an equivalent nanowave with them (lambda=h/mv) while energy particles are nanowaves and only in virtual way it is possible to associate an equivalent mass with them (m=hf/c^2). Consequently in my model a few particles are massive corpuscles (electron, proton, etc..) while other particles are energy corpuscles (photon, X quantum, etc..). Therefore the single photon is an electromagnetic nanowave that produces diffraction, the single electron is a massive particle that doesn't produces diffraction. Beams of massive particles instead produce diffraction.

Article On the Physical Structure of Radiant Energy: Waves and Corpuscles

What is you profit in denying the experimental results ?

What is you profit in denying the theoritical work made by Dirac and Schrödinger ? Both Nobel in 1933.

Dear Mr. Lavau,

I am an independent researcher. I accept what is convincing and I refuse what isn't convincing. In postmodern physics there are many things that aren't convincing. I don't think future of physics has to be decided by committees of prizes and by editorial staffs. On the other hand it seems to me that you too don't accept all of postmodern physics. My research is based on a critical work toward the mainstream physics because physics is a science in progress. My profit is in the fulfilment of giving a satisfactory answer to problems of contemporary physics. To that end in order to explain my critical work towards Dirac, Schrodinger and Heisenberg, I submit you the following paper

Article Basic Principles of Deterministic Quantum Physics

@Daniele Sasso. With your maintained corpuscular hypotheses, you are ninety years too late.

Dirac wrote the wave equation for the electron. And it has been extensively proved.

@Jacques Lavau,

I don't think physics ends with Dirac. Like this you prove you are ninety years too late.