Are Bohmian Velocities Measurable Through Weak Measurements?

[Demystifier]

Recent theoretical results
http://xxx.lanl.gov/abs/0706.2522 [New J. Phys. 9 165 (2007)]
http://xxx.lanl.gov/abs/0808.3324
show that weak measurements of particle velocities necessarily yield Bohmian velocities.
At least, this shows that Bohmian velocities are not such an artificial theoretical construct as the Bohm opponents frequently argue, but do represent some sort of genuine reality.

What do you think?

 

[Maaneli]

Recent theoretical results
http://xxx.lanl.gov/abs/0706.2522 [New J. Phys. 9 165 (2007)]
http://xxx.lanl.gov/abs/0808.3324
show that weak measurements of particle velocities necessarily yield Bohmian velocities.
At least, this shows that Bohmian velocities are not such an artificial theoretical construct as the Bohm opponents frequently argue, but do represent some sort of genuine reality.

What do you think?

I've seen this before. If this is true, then I have trouble understanding why these weak measurements don't allow one to empirically distinguish the deterministic deBB velocity from the otherwise empirically equivalent stochastic variants of the deBB velocity, or vice versa. I know DGZ address this issue, but I have trouble following their reasoning. What do you think?

 

[Demystifier]

The point is that the weak measurement is not the same thing as the usual measurement. The weak measurement can be thought of as a sort of an indirect measurement. In this sense you cannot directly empirically distinguish various variants of pilot-wave theories, but you can do it indirectly (i.e., weakly).

 

[Maaneli]

you cannot directly empirically distinguish various variants of pilot-wave theories, but you can do it indirectly (i.e., weakly).

Not sure I understand what you mean by "indirectly". Also, are you agreeing that weak measurements can actually be used to distinguish a unique deBB velocity? If so, which is it?

 

[Demystifier]

Not sure I understand what you mean by "indirectly". Also, are you agreeing that weak measurements can actually be used to distinguish a unique deBB velocity? If so, which is it?

By indirectly I mean weakly, where "weakly" is defined precisely in the mentioned papers.
I agree with the results of these papers that weak measurements determine unique velocity, which is the standard Bohmian velocity.

 

[Maaneli]

By indirectly I mean weakly, where "weakly" is defined precisely in the mentioned papers.
I agree with the results of these papers that weak measurements determine unique velocity, which is the standard Bohmian velocity.

So in the DGZ paper their claim seems to be that the reason a weak measurement is a true measurement of the particle velocity, and that this doesn't contradict their theorem that the velocity of a Bohmian particle is impossible to measure, is because weak measurements are examples of nonlinear measurements, whereas in their theorem they only consider linear measurements. Nonlinear measurements are of the type where the initial wavefunction apparatus psi_app depends on the state psi of the system. Linear measurements are of the type where psi_app does not depend on the state psi of the system. However, DGZ also claim that one can only apply this weak measurement to the standard Bohmian velocity, and one still cannot empirically distinguish it from the variant Bohmian velocities by just using a weak measurement.

 

[Maaneli]

<< However, DGZ also claim that one can only apply this weak measurement to the standard Bohmian velocity, and one still cannot empirically distinguish it from the variant Bohmian velocities by just using a weak measurement. >>

I still haven't though understood the justification for this claim.

 

[Demystifier]

<< However, DGZ also claim that one can only apply this weak measurement to the standard Bohmian velocity, and one still cannot empirically distinguish it from the variant Bohmian velocities by just using a weak measurement. >>

I still haven't though understood the justification for this claim.

It depends on what one means by "empirically distinguish". If weak measurements count as "empirical", then different variants of Bohmian mechanics can be distinguished. Moreover, in that case it is a prediction of standard QM that the usual Bohmian velocity should be the right one. In other words, standard (non-Bohmian) QM predicts Bohmian velocities.

As they say in the conclusion, measurement is a tricky and complicated business.

 

[Maaneli]

It depends on what one means by "empirically distinguish". If weak measurements count as "empirical", then different variants of Bohmian mechanics can be distinguished.

But DGZ don't reach this conclusion. They still seem to say that the variant deBB velocities are not empirically distinguishable by weak measurements.

Moreover, in that case it is a prediction of standard QM that the usual Bohmian velocity should be the right one. In other words, standard (non-Bohmian) QM predicts Bohmian velocities.

I personally wouldn't phrase it this way, as it would give many nonexperts the false impression that standard QM (which they usually equate with Copenhagen QM) can derive Bohmian QM, and therefore that the latter is somehow less fundamental. Of course, you know as well as I do that the reverse is true.

 

[Demystifier]

But DGZ don't reach this conclusion. They still seem to say that the variant deBB velocities are not empirically distinguishable by weak measurements.



I personally wouldn't phrase it this way, as it would give many nonexperts the false impression that standard QM (which they usually equate with Copenhagen QM) can derive Bohmian QM, and therefore that the latter is somehow less fundamental. Of course, you know as well as I do that the reverse is true.

That is true, I have used phrasing somewhat different then DGZ did. It is also true that weak measurements of velocities will allways yield standard Bohmian velocities, even if the actual velocities of particles are given by some alternative pilot-wave theory. But to avoid the paradox, this is exactly why I said that all this depends on what exactly one means by "empirical".

Nevertheless, as I said in the first post, at least there is no doubt that the usual Bohmian velocity is not artificial, but that there IS some sense in which it can be obtained experimentally. As you said, it is fair to emphasize that this does not prove that the whole idea of the Bohmian interpretation is correct. Still, it does make this interpretation more appealing and natural. If the future explanations of Bohmian mechanics will be written with this new additional argument spelled out, probably a larger percent of readers will find this theory appealing.

 

[Demystifier]

Now the experiment has been done:

http://scienceblogs.com/principles/2011/06/watching_photons_interfere_obs.php

http://www.sciencemag.org/content/332/6034/1170.full [Science 3 June 2011: Vol. 332 no. 6034 pp. 1170-1173 DOI: 10.1126/science.1202218]

The weakly measured trajectories coincide with the Bohmian ones.

 

[Demystifier]

The next interesting step would be to weakly measure the trajectories in cases where the Bohmian trajectories are more "counterintuitive", such as a Mach-Zehnder interferometer.

 

[Fyzix]

Yes demystifier I was meaning to ask you about this.

Do you feel like these results are in any shape way or form a confirmation of something like dBB?
Or that it falsifies some interpretations?

 

[Demystifier]

Not really. I would say that this shows that, in a certain sense, Bohmian trajectories are a part of ALL interpretations (Copenhagen, MWI, ensemble, ...).

 

[Fyzix]

Would you agree that de-Broglie Bohm has contributed/predicted more about science than the other interpretations?
Bell inequalities and now these trajectories?

 

[Demystifier]

Would you agree that de-Broglie Bohm has contributed/predicted more about science than the other interpretations?
Bell inequalities and now these trajectories?

I certainly agree that it contributed more than SOME other interpretations. But it would be an exaggeration to claim that it contributed more than ANY other interpretation.

 

[dgwsoft]

When I read about this on the BBC website I thought

1) I've seen this in a textbook: if you measure the average trajectory of a photon, you find it came from somewhere between the two slits and
2) surely you get the same result from the Bohm pilot wave?

My copy of Basic Quantum Mechanics (J L Martin, Oxford Science Publications, 1981) has a nice diagram on p228. He discusses replacing the screen of a two-slit experiment with "a closely-spaced array of detectors, designed to track the ultimate trajectory of the photon - a kind of 'photon cloud chamber' if such a thing were possible. The idea is then to produce the trajectories backwards to determine which slit image they emanate from. But this won't work since it may be shown that the most probable trajectories run along the ridges of maximum amplitude of (phi); these ridges form a system of confocal hyperbolas whose asymptotes pass neatly between the two slit images, leaving the question unresolved once again. The reader is probably now ready to accept that, far enough 'downstream', all information about which slit any photon has come from is entirely lost. He will be quite wrong, however! Replace the original screen by a camera, focussed on the pair of slit images. It is perfectly clear that we can now tell which of S1 or S2 a photon originates by recording whether it is recorded at [the images] S1' or S2'. On the other hand we now have no chance of observing the interference pattern: the camera is in the way!"

Martin does not discuss Bohm. This is all standard quantum mechanics.

 

[Demystifier]

Perhaps the best one can say now is that Bohmian trajectories are no longer "hidden variables". As I argue in my blog
https://www.physicsforums.com/blog.php?b=3077
from the experimental point of view, Bohmian trajectories are neither more nor less real than the wave function.

 

[Demystifier]

... Martin does not discuss Bohm. This is all standard quantum mechanics.

Yes, but Martin does not discuss WEAK measurements. Even though such measurements can be explained by standard QM, they are still not a part of it.

 

[Demystifier]

Today a proposal to weakly measure Bohmian particle trajectories of two entangled particles appeared:
http://lanl.arxiv.org/abs/1207.2794