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B Quantum Mechanics vs. Pilot-Wave thought experiment

  1. Feb 21, 2016 #1

    I want to share a thought experiment that could tell Quantum Mechanics apart from Pilot-Wave interpretation. It goes like this:

    Quantum Mechanics vs. Pilot-Wave:
    • Quantum Mechanics: Waves collapse to particles. Waves dissapear when particles are detected.
    • Pilot-Wave: Waves are real but undetectable. Waves keep propagating after particles are detected.
    Experimental Setup:
    • We have one emitter launching photons through one slit, but most of those photons impact on the slit walls. We register those impacts becoming spots on the slit walls.
    • We have another emitter next to the slit, firing at the same rate than the first emitter.
    • There's a screen at the same distance for the second emitter and the slit.
    QM prediction:

    Waves collapse to particles, so photons from the first emitter impacting the slit walls collapse to particles.
    Then, only a few uncollapsed waves pass the slit, so the slit acts as photon emitter at a lower rate.
    The second emitter fires photons at the original rate.
    Finally, we have a few waves coming from the slit, and a lot of waves coming from the second emitter.

    So we'll end up with a big particle distribution in front of the second emitter, and a little interference pattern caused by the uncollapsed slit waves that flow to the screen at low rate.​

    Pilot-Wave prediction:

    Waves and particles are real entities. Waves are undetectable but they can affect other particles, so particles from the first emitter impacting the slit walls get stopped.
    Then, few particles but all associated waves pass the slit, so the slit acts as a wave emitter at the original rate.
    The second emitter fires photons at the original rate.
    Finally, we have a lot of waves and few particles coming from the slit, and a lot of waves and particles coming from the second emitter.

    So we'll end up with a big particle distribution in front of the second emitter, but a big interference pattern caused by all the slit waves that flow to the screen at the original rate.​

    Do you think there's something wrong that would not make it work as stated? Can you think of any technical aspect that will not let us make this experiment for real?

  2. jcsd
  3. Feb 21, 2016 #2

    I post a schematic of the experiment, and the different results depending on Quantum Mechanics or Pilot-Wave being right.

  4. Feb 21, 2016 #3


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    That bit about "waves collapse to particles" is something that you'll read in non-serious introductions to quantum mechanics, but it is not what quantum mechanics says. In fact, quantum mechanics does nothing except predict the probability of a particle being detected at each point on the second screen - and those probabilities exactly match the pilot wave theory probability of a particle being guided to that spot by the wave.
    Last edited: Feb 21, 2016
  5. Feb 21, 2016 #4
    Hi Nugatory.

    When you say that the QM probability of detecting a particle is the same that the Pilot-Wave theory, you are right... when you're talking about the particle distribution at the right side of the thought experiment:

    If you had only the emitter and the slit, it would happen as you said:
    • QM: Few uncollapsed waves cross the slit and collapse on the screen, so you have photons creating an impact distribution at a lower rate than the first emitter.
    • PW: All waves will cross the slit, but as only few particles cross the slit, you have only those particles to create the particle distribution, so it appears also at lower rate, although waves are arriving at the original rate.
    However, the thought experiment is mixing the waves and particles from the different sources, in order to spot the difference on the interpretations:
    • QM: The few uncollapsed waves from the slit can collapse as particles on the right side of the experiment, or interfere with the second emitter waves on the central interference area. Either case, they are arriving at low rate in both cases.
    • PW: A few waves and particles from the slit can create the right side particle distribution, but the rest of the waves coming from the slit have all the second emitter waves to create interference, and modify all the second emitter particles paths, so you create the screen distribution with the second emitter particles, but using almost all the waves from the slit to modify their paths and be able to see the slit waves effect.
    Think of waves as being "air blows", and particles as being "paint balls". QM says the "air blows" become "paint balls" when hitting the screen, but if PW is right, in the thought experiment we are trying to use the slit "air blows" to modify the second emitter "paint balls" paths into the screen and see the effects we could not observe otherwise.

    If PW is right, we could mix waves coming from one source with particles of another source to "paint" their effects. This can't be done if QM is right (because waves and particles are the same in different forms, not two different entities, so you can not mix waves from one source with particles from another).
  6. Feb 21, 2016 #5


    Staff: Mentor

    QM does NOT have un-collapsed waves exactly as Nugatory said. QM is silent on what's going on when not observed.

    Its part of the myths about QM:

    Here is what's really going on at slits in QM:

    Its very simple. A slit is a position measurement so via the uncertainty principle the momentum is unknown so when the momentum is observed it can be in any crazy direction.

    That's not what QM says. It says nothing about what's going on when not observed. I suggest you study a proper MODERN textbook such as Ballentine:

    Last edited by a moderator: May 7, 2017
  7. Feb 22, 2016 #6
    Hi Bhobba. You're right I should not use analogies to explain the experiment. I think I'm confusing you more than explaining it.

    The idea is pretty simple:

    In QM there is no localized particle until you measure it. Before that, you use a wave function to describe the probability density of finding the photon at each place. But at any given time, QM says there's just ONE entity describing a photon. Call it whatever you want, but there is only ONE thing at any given time defining what a photon is, no matter how that thing behaves (be it a probability density spreaded on space, or a localized energy spot at specific coordinates).

    On the other hand, PW theory says a quantum object is not one entity changing state, but TWO different entities: you have a particle and an associated wave, but you can only detect the wave effects using particles.

    What I'm trying know with the experimental setup is if a photon is composed of just ONE single entity (QM) or is composed of TWO related entities (PW).

    The only problem that I can see is if an isolated pilot wave can not affect any other particles that could be out there. If that's the case, QM and PW would give the same results (but then I would want to know why an isolated pilot wave can not affect other particles and waves).
  8. Feb 22, 2016 #7


    Staff: Mentor

    That might be what you are trying to do but your diagram on QM speaks of waves and particle rate which QM does not have. There is no waves or particles - simply observations.

  9. Feb 22, 2016 #8
    Ok, I see where you are having problems with what I said.

    It's precisely on the rate of QM wave/particles and the difference with PW wave rate + particle rate where this experiment could make a difference. Let's use some numbers:

    Imagine you launch 100 photons from emitter 1.
    Then, 50 photons impact the slit walls, so 50 bright spots appear there. Those 50 photons were detected at slit walls, so you don't use any probability density to describe those photons anywhere anymore. Their energy was absorbed at the slit walls.

    But you have another 50 photons that pass the slit undetected, so they still can be described using the wave probability density for the space after the slit walls. They'll end up being absorbed and localized as spots at the screen.

    So you started with 100 photons and 50 were detected on the slit walls, but another 50 will end up making spots on the screen, so the rate of photons reaching the screen is half the rate of photons emitted.​

    You launch also 100 photons (particles + waves) from emitter 1.
    as before, 50 photons impact the slit walls, and 50 bright spots appear there.

    But those 50 spots you see at slit walls are just the particle part of those 50 photons. Their associated 50 waves pass the slit. So all waves pass the slit, no matter if the particles impact the slit walls or pass the slit.

    So you started with 100 particles and 100 waves. 50 particles were detected on the slit walls, but another 50 particles AND all the 100 waves pass the slit. So the particle rate is half the original emitter rate, but the wave rate is the same as the original emitter rate.​

    As said, the only thing I don't know is if there's something preventing all those "orphan" waves having measurable effects on other waves, or particles different than their own particle.
  10. Feb 22, 2016 #9


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    Staff: Mentor

    There's no localized particle after you measure it either. It's hard to see how we can have a sensible discussion about differences between the predictions of the pilot-wave model and standard QM until we have a correct understanding of what QM predicts.

    Have you followed up on the references that Bhobba gave above?
  11. Feb 22, 2016 #10


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    That is wrong. A wave does not affect other particles. In the absence of entanglement (which here seems to be the case), one wave affects only one particle.
  12. Feb 22, 2016 #11


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    As I indicated in the post above, yes there is.
  13. Feb 22, 2016 #12
    Thanks Demystifier.

    I also started to feel we should use entangled photons to do the experiment, because it's hard (if not impossible) to make photons from different sources interfere.

    But imagine we can launch entangled photons from the emitters. Does the "one wave affects one particle" sentence still applies in this case? (I mean, in the PW interpretation, not in QM).
  14. Feb 22, 2016 #13


    Staff: Mentor

    Why do you think entangled particles interfere?

  15. Feb 22, 2016 #14
    I'm just trying to imagine a setting to test it, so I'm thinking out loud here, therefore it might sound stupid(and its almost 3am, I'm likely to talk nonsense) but what if we are splitting a pair of entangled photons(total symmetric) and sending one in counter clock wise the other in clock wise direction in a circular but twisted path, and tilt the propagation axis 90 degrees at one end, their spin states should cancel out each other in the interception area.If one path uses a slowly increasing density medium for one of the entangled photons to travel, it'll slowdown, and carefully adjusting the path length, if we see an interference pattern on the not slowed down photons side detector, before the slowed down photon passes the intercept. In PW this should indicate whether or not trajectories exist prior to measurement. something like this http://imgur.com/nDPMkXr
    Last edited: Feb 22, 2016
  16. Feb 22, 2016 #15
  17. Feb 22, 2016 #16


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    The experimental result is right, but it is wrong to interpret as a test of dBB against QM.
  18. Feb 22, 2016 #17
    Oh I have nothing against dBB, or Bohmian Mechanics, that is why I given the second link. I'm more than ready to go until Gerard t Hooft's or other conspiracy theoris's super-determinism is accepted :D I'm just trying to blend in at 3.30 am in the morning
  19. Feb 22, 2016 #18


    Staff: Mentor

    That's a well known famous paper and caused quite a stir a few years back. I even got caught up in it. The trouble is its wrong with the error being in a misunderstanding of the Dirac Delta function if I remember correctly. Anyway you can look into it and get the detail - there have been a lot of posts about it a few years beck.

  20. Feb 23, 2016 #19


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    For simplicity, suppose that we have two entangled photons. Then the wave function of these two photons affects only those two photons, not any other photons. The generalization to more entangled photons is obvious ...
  21. Feb 24, 2017 #20
    On the OP thought experiment, I think there is no difference in the predicted interference pattern between pilot-wave and the standard model. Pilot-wave uses exact same wave equations, but this time the wave function is for the guiding wave not for the particle.

    In standard model the particle is described as a wave, in pilot-wave the particle is carried by the same wave! so the interference pattern will be the same in both cases.
  22. Feb 24, 2017 #21


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    Your mistake is assuming that the waves are spreading out in 3d space, instead of spreading out in Hilbert space. Hilbert space is much higher dimensional (i.e. exponential in the number of relevant variables). What looks like an overlap in 3d is often not an overlap in Hilbert space. This is the reason that adding detectors to an experiment can change the outcome in counter-intuitive ways.

    Pilot-wave doesn't change that. Sure part of the wave "always goes through the slit", but the "hit slit" case and the "passed through slit" case are totally different directions in Hilbert space. If the pilot goes down one, it's far enough away from the other to not be affected by it anymore. In the diagram the two cases look like they overlap, but in Hilbert space they don't.
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