# How does the pilot wave theory explain the double slit experiment?

1. Jan 13, 2014

### Filmmakerdoc

Hi,

I'm not a scientist, but a documentary filmmaker doing research on the nature of reality. An essential disclaimer as my question might seem a bit superficial to most you guys who work in the field.

I would like to know how the pilot wave theory to quantum mechanics explains the double slit experiment. Shouldn't the pilot waves behave the same in the presence or absence of measurement?

Thanks you

Ben

2. Jan 13, 2014

### Simon Bridge

Welcome to PF;

Caveats:
We cannot comment on the nature of reality itself, that would be philosophy rather than physics.
Pilot wave theory is an interpretation of QM - such discussions are tightly moderated due to their highly philosophical nature.

Simplified:
The idea is that the pilot wave traverses both slits, producing the interference pattern while the particle rides along it going through one or the other slit. The pilot wave determines the likelyhood of different possible paths.

The act or determining which slit the particle traversed has to affect the wave too.

The de-Broglie-Bohm (pilot wave) approach uses fancy non-intuitive maths (re: conditional wavefunctions) to describe this. Wikipedia has a summary.
http://en.wikipedia.org/wiki/De_Broglie–Bohm_theory

3. Jan 13, 2014

### atyy

The pilot wave theory has 3 assumptions
1) the pilot wave, which behaves deterministically and in the same way as the wave function of quantum mechanics
2) particles with definite positions, which are deterministically influenced by the pilot wave
3) random distribution of initial positions, even for the same pilot wave

So randomness gets introduced by the third assumption in de Broglie - Bohm theory. The random distribution of initial positions does require explanation, but here the mystery of quantum mechanics is reduced to the mystery of classical statistical mechanics, instead of appearing as a different type of mystery.

http://scienceblogs.com/principles/2011/06/03/watching-photons-interfere-obs/

4. Jan 14, 2014

### haael

I think the OP asked how dBB explains disapperance of the interference pattern when we try to check which slit the particle flied through. Does the measurement disturb the pilot wave?

It would be even more interesting with delayed experiments. We put a measurement apparatus over one of the slits then let the double-slit experiment happen. The apparatus checks if the particle flied through the slit, but we don't look at the outcome. Now the interference pattern should appear or disappear depending whether we decided to look at the indication of the apparatus, even if the particles apparently already hit the screen.

How dBB explains existence and disapperance of the interference pattern in the double-slit experiment dependent of the observer's knowledge of the particle trajectory?

5. Jan 14, 2014

### Staff: Mentor

The pilot-wave and the particle are intertwined.

When we observe the particle the wave 'collapses', so no interference. Its part of the out of Bells Theorem - its non local.

As to exactly how it does this maybe some of the experts on DBB can chime in.

Thanks
Bill

6. Jan 14, 2014

### Demystifier

Yes.

The existence of interference does not depend on the knowledge itself, but on ability to know. It is explained in the same way as in standard theory; by decoherence.

7. Jan 14, 2014

### Demystifier

No, they shouldn't. Measurement assumes the existence of some measuring apparatus, and the apparatus is a real physical object that affects the propagation of the wave.

8. Jan 14, 2014

### Staff: Mentor

That didn't occur to me - but it has to be right. Because the particle is real the mixed state is a proper mixed state by fiat - nice.

Thanks
Bill

9. Jan 15, 2014

Guys, I apologize for bumping in to this thread like this, but the topic did slide into what must be more appropriate for this thread, than the original thread. I'm sorry for this, but hope this is okay for everyone. Quotes and post numbers from the original.

If I understand Feynman correctly, when talking about electrons, he says that the total number of arrivals (N) is not the sum of the single slit 1 & 2:
N12 ≠ N1 + N2

But the absolute squared of the total probability amplitude (a) for slit 1 & 2:
N12 = |a12|2

Hence, the number of electrons that arrive at any position on the screen (when both slits are open) cannot be analyzed as the sum of two pieces (N1 + N2), but only as the absolute squared of the total probability amplitude (|a12|2).

And if I understand you correctly, you say that the Bohmian mechanics wave function (B) is the linear sum of the one slit situation:
B12 = B1 + B2

Question: Why don't we see "one half" interference pattern with one slit open, in Bohmian mechanics?

I'm confused... if we know the exact initial position of each Bohmian particle, then we also know the final position of each particle on the screen, but this doesn't work in experiment, so to solve this we introduce "other particles" without "preselected positions" to get the final interference pattern...?

I have never heard this before, but if I understand you correctly; in Bohmian mechanics, not only the pilot wave influence QM particles, but also "other particles" without "preselected positions"...?

Did I really get this right??

10. Jan 15, 2014

### atyy

Because maybe Feynman was wrong even for ordinary QM. In QM the probability P=|A1+A2|2, which is nonlinear. So with 1 slit you get P=|A1|2 and P=|A2|2. The linear sum would be P=|A1|2 + |A2|2, but instead it is P=|A1+A2|2 =|A1|2 + |A2|2 + |A1.A2|2. This is also true in Bohmian mechanics, in which the wave function is linear, but its effect on particles, and the probability distribution is nonlinear. (I left out complex conjugation throughout, so the formula is not right, but should be notionally ok - but again, Demystifier or someone who knows better, please correct!)

Last edited: Jan 15, 2014
11. Jan 16, 2014

### Demystifier

No. To get the interfernce pattern in an experiment, one particle is not enough. You must have a statistical ensemble of particles, that's why I talk about many particles.

12. Jan 19, 2014

Huuum... this doesn't sound like the tastiest dish on the menu... when I said that Feynman could be wrong, I meant about Bohmian mechanics... something discovered lately, or something, but ordinary QM... Sorry atyy, I don't buy it.

(my bolding)
Maybe it's me... but I just don't get it? Definite positions are "transformed" into random initial positions? Either we know the definite initial positions, or we don't, right??

And how can randomness be an assumption in a deterministic theory? Does (true) randomness even exist in this case, or is it a classical "pseudorandom generator" (that can be 'revealed' with complete information)??

13. Jan 19, 2014

Okay, this I understand, what I don't understand is this:

How can that be? With one slit open we will get the bell curve of normal distribution:

And of course, this is very different from the distribution of interference, so how can you say that we know the final position of each particle?? We don't!

With all due respect, isn't this exactly what Feynman is saying in the video? If we have the ability to know (i.e. a theory telling us which slit), it will destroy interference?

14. Jan 19, 2014

### atyy

Let's take an ensemble of single particles. Each trial is an experiment on one particle. An experiment consists of multiple trials from "apparently identical to the experimenter" initial conditions, because he has prepared each particle in the same way. By his methods, the experimenter can control the initial wave function of each particle, so each particle has the same wave function. However, the experimenter doesn't know how to control the initial position of each particle. Thus although every particle in the ensemble has the same wave function, each particle has a different initial position. Across trials, the initial positions are random, and the trajectories are random; but in any one trial, the particle has a definite initial position and definite trajectory in space. The agreement with quantum mechanics lies in the "magical" specification of initial conditions.

Why does this solve the measurement problem? It solves the measurement problem because the dynamics are complete, and there doesn't have to be a postulate about the "collapse of the wave function upon measurement", nor does there have to be a postulate about "dividing the world into classical and quantum realms". Rather these postulates are derived. The Bohmian interpretation does introduces the "magical" specification of the random distribution of initial positions. This is a problem, but it is exactly the same sort of problem as that of classical statistical mechanics. In other words, the measurement problem is converted into a type of problem that we know how to solve conceptually.

15. Jan 20, 2014

### Demystifier

This can be understood even with classical physics, so it should be easy. The fact that it confuses you suggests that you might have some problems with the relation between classical mechanics (which is deterministic) and classical statistical mechanics (which talks about probabilities).

Instead of giving you an answer, I challenge you to try to answer your own question by yourself, by using only classical physics. In any case, Bohmian mechanics cannot be properly understood without first understanding the relation between classical deterministic mechanics and classical statistical mechanics.

16. Jan 20, 2014

(my bolding)
Thanks a lot atyy, for taking my questions seriously! And also thanks for not using a straw man or any other childish games, to get out of a 'troublesome' situation, to save "The Idea" at all costs. I think this, at its core, is what separate true science from politics/religion... I really appreciate it. Thanks! :thumbs:

I understand your position much better now. We can control the wave function, it is deterministic, and exactly the same condition goes for standard QM, as the evolution of the Schrödinger wavefunction is also deterministic. Nema problema.

To me, this show that your third assumption of "random distribution of initial positions" is a most crucial 'ingredient' in Bohmian mechanics, to make it all work, to be in agreement with quantum mechanics. This also shows that Demystifier's statement in #23 "So let us suppose that we know the exact initial position of each Bohmian particle. Then we also know the final position of each particle on the screen" is a 'Gedankenexperiment' that is doomed to fail in any future theory/experiment, because it will violate current experiments and QM. It just doesn't work, period.

The best proof of last conclusion is that: IF it was (hypothetically) possible to have full classical determined knowledge of the exact initial position of each Bohmian particle in the ensemble, and thus be able to fully predict the future in which slit and final position, for each particle – the first thing Bohmian mechanics would do is to proclaim that the "magical" random distribution of initial positions is history, finito – the war is over!

Again, I really appreciate that you admit there actually is a problem, and explain why maybe it isn't completely crucial. As I understand Bohmian mechanics; the stance is to 'acknowledge' the randomness in classical statistical mechanics as emergent from the lack of complete knowledge, but absolutely not fundamental at the core of nature (of course).

Whereas standard QM and Feynman claims this randomness to be fundamental, and forever unreachable, to be explained by any theory.

Correct?

Confession (for what it's worth): If the laws of nature were up to me, I would choose Bohmian mechanics or any other theory that could get rid of the "flabby randomness". I like Einstein much more than Bohr/Heisenberg... if you know what I mean...

17. Jan 20, 2014

Well, that shouldn't be hard, even for an ignorant avocado – a devastating majority of physicists unconditional agrees on that the double-slit experiment can't be explained using only classical physics. :tongue:

18. Jan 20, 2014

### atyy

Yes. But actually the war is already over, since the achievement of Bohmian mechanics is conceptual - to show that such models are possible. In fact, there are many different possible models, of which the original Bohmian dynamics is only one. An earlier workable dynamics was in fact proposed by de Brogle, which is why one often says "de Broglie-Bohm theory". What Bohm added was how the dynamics of additional variables and a "magical" random distribution of initial conditions could solve the measurement problem - the problem of why textbook quantum mechanics postulates a cut between a classical measurement apparatus and a quantum system. Thus Bohmian mechanics should only be considered one of a class of solutions.

Overall there are two classes of solutions to the measurement problem

1) Quantum mechanics is complete (eg. many-worlds, if it works)

2) Quantum mechanics is incomplete (eg. Bohmian mechanics, GRW theory)

If solutions of type 1 are correct, deviations from quantum mechanics will never be found. If solutions of type 2 are correct, it is possible that one day deviations from quantum mechanics will be found. Obviously, not in the double slit experiment in the lab, but perhaps in cosmology or some regime of physics not yet explored.

Yes. However, the main achievement is not the removal of fundamental randomness, but the removal of the need to postulate a cut between classical and quantum realms in every application of quantum mechanics.

Here is one explanation of the "measurement problem" by Bell http://www.tau.ac.il/~quantum/Vaidman/IQM/BellAM.pdf. He devotes one section to the exposition of quantum mechanics by Landau and Lifshitz in which the split between classical apparatus and quantum system is postulated. I consider Landau and Lifshitz a very good example of "shut up and calculate", because they acknowledge explicitly that there is a split and implicitly that is a problem in principle, but that in practice we have no problems recognizing a classical apparatus, so that the naive textbook or orthodox or Copenhagen interpretation has not yet been falsified. Another book, which I disagree with a little, but like very much is that of Peres's - he too acknowledges there is a split between macroscopic and microscopic realms which is fuzzy.

Bohmian mechanics does not get rid of the fuzzy split - but it gets rid of it as a fundamental postulate. Instead the fuzzy split emerges from more natural postulates, in the same way that we are not troubled that our concept of a neuron is fuzzy (where "exactly" is the edge of a neuron?), since a neuron is not a fundamental concept, but one that emerges from more fundamental physics.

The beauty of Bohmian mechanics and similar ideas is that you can have your cake and eat it, since in Bohmian mechanics the Copenhagen interpretation is emergent.

Last edited: Jan 20, 2014
19. Jan 21, 2014

### Demystifier

Let me remind you that, at this particular part of the discussion, we were talking about SINGLE-slit experiment. Majority of physicists agrees that this CAN be explained by using classical physics.

20. Jan 21, 2014

### Demystifier

WTF? :surprised
Are you a Croat? Or something close?

21. Jan 21, 2014

### bohm2

An pretty good macroscopic QM analogue of the pilot wave model and the double-slit experiment can be found in Couder's experiments with walking droplets. Check out slides 66-77:

A macroscopic-scale wave-particle duality
http://www.physics.utoronto.ca/~colloq/Talk2011_Couder/Couder.pdf

You might find this short summary useful:
Realism and instrumentalism about the wave function. How should we choose?
http://arxiv.org/ftp/arxiv/papers/1401/1401.4861.pdf

Last edited: Jan 21, 2014
22. Jan 22, 2014

What!? :surprised

Aha, okay... I think most would consider the peace agreement between Chamberlain & Hitler as also 'conceptual', kinda...

Thank you very much for this link! Bell is, as always, brilliant. I was about to ask you to explain how Bohmian mechanics gets rid of the "measurement problem", and specifically how to fix this 'little' problem:

(my bolding)
But the answer was in Bell's article:

Voilà! Everything is fixed – all we need is a "little experiment" that also prove this!

(Thinking more about it... does "Weinberg's dilemma" on determinism vs probability really go away... uh, that's what you just said it won't... umm...? :uhh:)

Questions on Bohmian mechanics:
• Only positions? Is this really determinism? Or is it "pseudo-determinism"?

• Or do we get momentum from calculating "from position to position / time"? If this is correct, that would mean we can't get complete knowledge at any instant, right? And HUP will still hold, right?

• If everything in Bohmian mechanics is real and definite, is time also real? (to my knowledge Lee Smolin is the only one believing this for the moment)

• If the real pilot wave can influence the real particle, why can't the opposite happen?

• How are you guys going to solve the conflicts with empirically verified Special Relativity?

• Isn't it a problem to have real and definite positions, for every particle, but still you are 'forbidden' to reveal this information, because that would destroy the double-slit experiment?

• Or maybe the question above is wrong, and the pilot wave does fix the interference pattern, even if particle positions are determined? If so: Where is the importance of Bohmian definite positions?
If you can give me convincing answers on all questions, I might be ready to leave my "itching agnosticism" and enter the "Holy Church" of Bohmian mechanics!

P.S: I love infinite cake! So count on me, getting ready on my knees for the ceremony...

Last edited by a moderator: May 6, 2017
23. Jan 22, 2014

You are the one trying to steer the discussion into an extensive exposition about the single-slit experiment, not me.

Of course, a majority of avocados also agree on this basic fact. Most would also agree on that beside the grand canonical ensemble, we could have Little Green Men shooting tiny avocados through the single-slit, or Captain Hook firing his massive cannon; and still the classical result, with both slits open, would be pretty much the same, i.e. "The Twin Peaks of WYSIWYG".

I have no idea why you want to explore the classical single-slit, since the interesting part is the double-slit interference we get in QM.

I don't have anything more to say about the single-slit, than has already been said by Nobel laureate Richard Feynman, in this very clear and educational video:

Everything You Always Wanted to Know About the Single-Slit* (*But Were Afraid to Ask)

Last edited by a moderator: Apr 28, 2017
24. Jan 22, 2014

No no, grumpy and nagging avocados don't grow in the fertile soil of Croatia; we need the Arctic Circle to get real bad!

But of course Pljeskavica is still yummy!

25. Jan 22, 2014

This is a very nice demonstration, and the single-slit it seems to work.

But in the double-slit it isn't quite so easy, is it? There's a "mutual interaction" between the fluid and droplet, isn't it? The droplet follows the wave and "feeds it" at the same time, doesn't it? Which means that in a double-slit experiment the wave will be stronger in the actual slit where the droplet goes through, and weaker waves in the other = impossible to get a 'balanced' interference after the slits.

This is the result of a "hobbyist researcher", naturally a pro would do better, but to me it still looks like a dead end...