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Electrons and the Double Slit experiment questions

  1. Feb 23, 2015 #1
    First of all, I want to apologize ahead for three things:
    1) Opening another tread about this experiment, with probably the same title than other 800 threads: I took a little time to read the other threads with similar titles and didn’t found this doubt in none of them, and also didn’t seem right to post this questions in any of those threads.
    2) Giving the electron the property of “wave-particle duality”: I will not explicitly write down this term in the lines below because one of the things that I learned in many of the other threads is that this term causes misunderstanding since electrons are not particles nor waves, they are just “electrons”. However I think it could be implicitly understood in my expressions, especially because in most of the literature I have read the term subatomic PARTICLE is applied to all of them, photons, electrons, neutrinos, quarks, etc.. So I have great difficulty in accepting that an electron is not a “particle”, especially for my first question where the electron’s mass is involved into the problem.
    3) Giving the electron a human characteristic by using the terms “it knows”: I am afraid this could be a terrible mistake but I find no other way to phrase my questions without it.
    Second, the introduction:
    As I understand, the experiment consist of 3 elements: (a) a source which shoots electrons. I hope it’s safe to say that it is capable of shooting one electron at the time when we push a button, so we know exactly when each one of them leave the source; (b) a wall with two small slits on it, and on top of each slit there is a detector that is capable to indicate whether a single electron or not passed through the slit; (c) a screen that will mark the position where the electron arrived.
    Finally, the questions:
    1) Electrons, which for the moment I will accept that are not particles nor waves, have mass. If that is the case, they cannot travel at the speed of light. In the case that we have the detectors ON over the slits, in order to determine which way the electron went, one should be able to calculate how much time did it take for the electron to go from the source to the screen. Knowing the distance between them we can then calculate the speed of the electron which should be slower than the speed of light. The question is: What happens when the detectors are OFF, so we do not know which way the electron went and the screen reveals that it behaves like a wave. In other words, what is the speed of the electron when it behaves like a wave?
    2) Supposing that we manage to create a layout of the experiment where the slit is in the middle distance between the source and the screen, why does measuring the position of the electron at half way would determine the position at the end? Does the result changes if we move the slit closer to the source or to the screen? For all the electron “knows”, it was detected at a certain point, but it could be crossing many other slits after the one with the detector, thus start behaving like a wave, but it doesn’t. I seems like once it is detected, the rest of the experiment is already fully determined. So what if we put another barrier with two slits in front of the first one? Will the electron at that point begin to behave like a wave if no detectors determine which one of the second slits in went through? How does it even “knows” that it was crossing a second slit? Why would that behavior not happen if there were not this second barrier with slits?
    3) (This question was actually in one of the other threads that I read but I didn’t catch a direct answer) If the detectors are OFF, does each single electron still leave only one mark in the screen? If that is the case, then many electrons need to be fired before the wave behavior can be appreciated on the screen, which can also be interpreted as each individual electron takes a different path after the slit. I don’t know if you understand where I’m going with this but thinking about it takes me back to the second question.
    Thanks for reading and best regards,
     
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  3. Feb 23, 2015 #2

    jfizzix

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    1.) The uncertainty principle applies here in two ways. First, any measurement capable of telling which slit the electron went through (even using just timing) will destroy the subsequent interference pattern. Second, it isn't possible (as far as we know) to prepare an electron to be in a state with well defined timing and frequency (due to the energy time uncertainty principle). Because of this, if you prepared electrons in such a way that you could launch them at very precise times, and detect them on the screen, the uncertainty in frequency will be large enough that the electrons will be naturally incoherent with one another, and you won't be able to see interference anyway.

    2.) The double slit experiment is something best taken as a big picture. The electron doesn't "know" it's been measured at one time and not another. The experiment is configured so that a given set of possible results is seen. Change the experiment, and change the results.

    3.) Quantum mechanics is only really prepared to describe what you are likely to see if you measure something. If the detectors are off (assuming you mean also the screen), then you are not measuring anything. If you're asking what you see when the screen is "on", but there is no information that can tell you which path the electrons are going through, you should see a pattern of detector clicks, one at a time, until an interference pattern becomes visible.
     
  4. Feb 23, 2015 #3

    DrClaude

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    You've hit upon an interesting point: if the electron doesn't "know" whether there will be other slits, how does it "know" whether to behave as a "wave" or not? It doesn't. Travelling through free space can be seen as passing a screen with an infinite number of infinitely small slits, and the resulting interference looks like a straight trajectory. This is the basic idea behind Feynman's path integral formulation of quantum mechanics.

    Yes, each electron is always detected at a single point, and the interference pattern is built up from many electrons. This is one of the reason why wave-particle duality has been dropped. The electron is alwyas detect as a particle. It may seem that it goes through both slits at the same time, but if you try to detect it, you find that it either went through one slit or the other.
     
  5. Feb 23, 2015 #4
    But if you don't try to detect it, maybe you register its position as a particle as a single point, but it does not follow the feymann's path... Is like observation is affecting the path, making it straight instead of random...? But there is still the problem of the electron knowing or not if it is being observed, and at which point it can still change its mind and go in a different path...
     
  6. Feb 23, 2015 #5
    Hi. Rather than answer your questions directly it would be better to clear up some basic misunderstandings first.

    1 The propagation of an electron is ALWAYS governed by a wavefunction. When you detect it, it ALWAYS displays particle properties. There is no question of it deciding to act like a wave or act like a particle as it travels.

    2 It is true that the wave function can be derived as an integral of all possible paths but that's nothing to do with acting like a particle.

    3 Electrons (all objects actually) NEVER travel ballistically.

    4 The idea that the behaviour of the wave depends on information is a derived result which requires a thorough understanding of quantum information in order to formulate a statement correctly. Otherwise just stick with interactions.

    5 In a similar way, it all depends what you mean by ON and OFF. If OFF still interacts with the electrons it still destroys the interference - even if the information is not recorded. If OFF actually ceases to interact, then the interference pattern returns.

    6 There is no particular reason why you shouldn't time an electron as it goes past. However you can't detect the wave itself, you can only take a positional measurement, which is a particle property. The wavefunction tells us the probability distribution of those measurements.

    -DP
     
  7. Feb 23, 2015 #6

    bhobba

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    This wave-particle duality stuff is one of those myths of QM that unfortuneately is hard to dispel:
    http://arxiv.org/pdf/quant-ph/0609163.pdf

    It a hangover of the semi-historical approach most texts tend to follow and De-Broglies hypothesis which it used as a justification for Schodinger's equation. It was consigned to the dustbin of history when Dirac came up with his transformation theory at the end of 1926:
    http://www.lajpe.org/may08/09_Carlos_Madrid.pdf

    Here is the double slit experiments explanation without using that myth:
    http://arxiv.org/ftp/quant-ph/papers/0703/0703126.pdf

    Whats going on is this. Each slit is a position measurement. After the slit it has a definite position so by the Heisenberg uncertainly relation it momentum is unknown. It's kinetic energy is still the same so the magnitude of its velocity doesn't change - its scattered in an unpredictable direction.

    When you have two slits the wavefunction is a superposition of the the wavefunction at each slit and when you work through the math as detailed in the above link you get interference.

    Thanks
    Bill
     
  8. Feb 24, 2015 #7
    Just to clarify something:

    If instead of two slits the experiment had only one, what would be the expected pattern on the screen? What I understand is that if the detector at the slit is ON then the expected pattern should be a line along the projection of the only slit. In the other hand, if the detector is OFF (no interaction with the electron) then the patter in the screen would be a cloud, something like points everywhere, without any interefence.

    Is this correct?
     
  9. Feb 24, 2015 #8

    bhobba

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    The pattern for one slit is explained in the link I gave.

    What detector are you talking about - a detector in the slits or at the screen?

    Thanks
    Bill
     
    Last edited: Feb 24, 2015
  10. Feb 24, 2015 #9
    No it's not. Not even slightly :wink:

    As I said, electrons NEVER travel ballistically.

    The slit "prepares the wavefunction to a position state" i.e. limits it to a very narrow peak at the slit. After the slit, the wavefunction spreads out into a hemicylinder and thus the pattern is of more-or-less even illumination over the entire screen.

    A detector can make no difference - the single slit already constrains the position fully so detecting it again cannot change anything.

    edit - BTW, there seems to be a redface smilie attached to this message. I don't want it but I can't get rid of it.
     

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  11. Feb 24, 2015 #10
    Then I find it very difficult to understand why with two slits and detectors you get the electrons stricking the area of the to lines of projection of the slits. More I think about this the less I understand it :H
     
  12. Feb 24, 2015 #11
    Is there any substantial difference in doing this experiment with electrons or with photons?
     
  13. Feb 24, 2015 #12
    (
    The reason you do not understand it is because it is not true! As I said, electrons NEVER travel ballistically.

    Actually, what you describe is a very common misconception and is found all over poor-quality websites and videos so I'm not surprised you've picked it up. However, it is simply false. Electrons are always diffracted by the slits so that they cover the whole screen. You never get bar patterns like you suggest (unless, of course, the slits are so wide that diffraction is negligible and then interference is not visible anyway).

    Yes, the whole thing can be done, in principle, with any particles using an appropriate set up. In fact I often forget whether we are talking about electrons or photons. I wouldn't recomment trying it with quarks or Higgs bosons though. :cool:
     
  14. Feb 24, 2015 #13

    bhobba

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    Did you read the following I posted before:
    http://arxiv.org/ftp/quant-ph/papers/0703/0703126.pdf

    Thanks
    Bill
     
  15. Feb 24, 2015 #14

    bhobba

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    Yes there is.

    For photons position is not an observable.

    Conceptually to start with, best to stick with electrons.

    Thanks
    Bill
     
  16. Feb 24, 2015 #15
    Yes I did. I read all the three you sent. There was one about QM Myths and fact that for the moment I just read the slit experiment part but I’ll check it out fully later. Thanks for that

    If particles are always diffracted, what's the use of this experiment?
     
  17. Feb 24, 2015 #16

    Nugatory

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    You can still get interference or not, and that's the interesting part of the experiment. Diffraction is what makes the single-slit-open pattern illuminate the entire screen, not just a single bright spot with sharp edges behind the slit.
     
  18. Feb 24, 2015 #17

    bhobba

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    Its often used as a motivation for the QM formalism as an introduction to the wave-particle duality idea. Its a false idea but its often used.

    In reality its explanation is a combination of two key ideas - that slits 'scatter' because they are a position measurement and we have the uncertainty relations plus when you have two of them its a superposition so you get interference.

    Trouble is once the full quantum formalism is introduced they don't go back and show how it explains the experiment that motivated it.

    Thanks
    Bill
     
  19. Feb 24, 2015 #18
    Why not?
     
    Last edited by a moderator: Feb 24, 2015
  20. Feb 24, 2015 #19
    Because in order to detect a photon you need to absorve it, i think..
     
  21. Feb 24, 2015 #20

    Nugatory

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    What would the position eigenstates of a photon be?
     
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