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I 2-Slit Experiment: a question

  1. Dec 28, 2017 #1
    I realize the 2-slit experiment is discussed at the beginning of countless QM books and YouTube videos. I have read the excellent exposition in the first chapter of Feynman & Hibbs, and appreciate that (using Feynman & Hibbs language):
    A. any determination of which among various alternative paths an electron may take forces these to become exclusive alternatives; while conversely
    B. in the absence of any determination of which among various alternative paths an electron may take, all alternatives are necessarily interfering alternatives.

    My question, easily anticipated, concerns "determination", i.e., measurement. I realize that any conjectured way around the statement above will be flawed inasumuch as there must be some action by the "measuring device" which spoils the interference. But identifying this action is not always easy.

    First example: Suppose you have the usual 2-slit apparatus set-up. Place one clock near each slit and synchronize them. Now allow an electron to pass through one of the two slits and hit a position on a screen. While the electron's mass is very small, nevertheless the clock nearer the slit through which the electron passed will be effected by its gravitational field, and show less elapsed time than the the other clock. Does this destroy the interference pattern?
     
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  3. Dec 28, 2017 #2

    PeterDonis

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    Since you have assumed that comparing the clock readings tells you which slit the electron went through, then yes, because anything that tells you which slit the electron went through destroys the interference.

    (In practice, the electron's mass is much too small for even our most accurate clocks to detect any measurable change in rate.)
     
  4. Dec 28, 2017 #3

    Filip Larsen

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    While I am no expert, I am fairly sure that an important group of experiments that well illustrate what PeterDonis said are quantum erasure experiments that show that is it not necessarily the measurement itself that destroys interference, but how the total entangled state of the system is "processed". And it gets even weirder when you start to consider delayed choice quantum erasure experiments.

    Knowing about these experiments may save you some effort in trying to establish a counter-example for the standard double-slit experiment.
     
  5. Dec 28, 2017 #4

    vanhees71

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    A very good webpage about the for me most elegant realization of the quantum-eraser idea is the following webpage referring to the Walborn experiment:

    http://laser.physics.sunysb.edu/~amarch/eraser/
     
  6. Dec 29, 2017 #5
    Thanks everyone. I was unaware of the erasure idea, and will have to read about this. I was wondering if anyone could identify how the existence of the clocks destroys the interference pattern. After all, even when the 2-slit experiment is run and shows interference, there are people around wearing watches.

    What matters, of course, is the precision with which the clocks can discern which slit the electron passed through. In all "Heisenberg" analyses, when the measurement becomes precise enough to make this determination, that is when the interference is destroyed. Usually it's possible to see the physical connection between the measurement and the destruction of interference. (Feynman-Hibbs give a beautiful example where the screen with the two slits is allowed to move.)

    In the case of the clocks, what is the mechanism by which the interference is destroyed? Obviously the people in the laboratory wearing watches when the 2-slit experiment was performed did not destroy the interference, because their watches were too imprecise to determine which slit the electron passed through. But if you substituted ultra-precise clocks for their watches, what would change? Unlike the usual examples, there are no photons being used, no moving screens, etc. Just a precise clock measuring the way electrons alter spacetime around them.
     
  7. Dec 29, 2017 #6

    PeterDonis

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    The key point is not that the clocks are more precise. The key point is that the clocks are placed so they are affected by the electron's gravitational field. Clocks on the wrist of the experimenters, or mounted to the wall of the lab, won't do that. The clocks have to be placed right at the slits.

    And to do that, the clocks must interact with the electrons. That interaction is what destroys the interference.
     
  8. Dec 29, 2017 #7
    I don't see that. The two clocks can be far away from the slits (as long as each one is the same distance away from its slit, and they are not equidistant from the two slits) if they are precise enough. If one clock is found to be a little bit slower than the other, then the electron passed through the slit closer to that one.

    Right. But how did the clocks intreract with the electrons? That is exactly what I am wondering.

    Here's another thing. Let's say the clocks are far away. Then it takes time for the gravitational effect to be transmitted to them. By the time they could even make the measurement, the interference pattern (destructive or non-destructive) has been established. (This observation wouldn't matter, though, if the clocks were interacting with the electrons all along, but once again .... how are they?)

    Here's the point: in all the usual explanations about how an accurate measurement destroys the interference, the accuracy of the measurement is usually associated with a photon's wavelength or something like that (or see the F&H example) and you can readily see how it destroys the interference. But making a clock more or less accurate doesn't involve the electron that passes through the slit. That's what I'm thinking about.
     
    Last edited: Dec 29, 2017
  9. Dec 29, 2017 #8

    PeterDonis

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    What about all the other gravitational influences in the lab? There are a lot of objects present which are much more massive than electrons. Their effect on the clocks' rates will swamp the electron's effect. And no, you can't just subtract out all these other effects on the hypothesis that they are the same for both clocks, because they aren't. Atoms and molecules in all of these objects are constantly fluctuating, and the fluctuations are random, so their effects on both clocks will also be random and uncorrelated. That means there is a huge amount of noise that will mask any signal from the electron--unless the clocks are close enough to their respective slits.

    Gravitationally. You said so when you described the scenario.

    Won't work. See above.

    Neither does the photon wavelength or all the other stuff you mention. Picking photons of different wavelengths to use to measure an electron is exactly analogous to picking clocks of different accuracy. A clock is a physical mechanism, not magic; its rate is determined by physical parameters. If one of those parameters is the presence or absence of an electron--which you have stipulated that it is for purposes of this thought experiment--then the presence or absence of the electron has to interact somehow with whatever other physical parameters determine the clock's accuracy, in the same way that a photon's wavelength interacts with the presence or absence of an electron. It's just that you haven't bothered to specify the actual physical mechanism of the clock, or how its rate is affected by a gravitational field, you've just waved your hands; whereas for the case of using a photon to measure an electron somebody else already made a detailed model of how that interaction works and you've simply helped yourself to it.
     
  10. Dec 29, 2017 #9
    To be precise, it's not the measurement, there is no need to read out anything!

    "Any increase of partial information about the particle’s path will always mean a corresponding loss in visibility of the interference pattern, and vice versa. Most importantly, it is not relevant whether we read out that information. All that is necessary is for the information to be present somewhere in the universe."

    Caslav Brukner in “Elegance and Enigma - The Quantum Interviews” (ed. by M. Schlosshauer)
     
    Last edited by a moderator: Dec 29, 2017
  11. Dec 29, 2017 #10
    Can I add a reply?
     
  12. Dec 29, 2017 #11

    PeterDonis

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    Yes, you just did. :wink: But if you have a more substantive one, you are welcome to post it. And welcome to PF!
     
  13. Dec 29, 2017 #12

    DrChinese

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    :welcome:

    Should I be drinking some of what you are having? :smile:

    Normally, you should not hijack a thread with your own commentary on a different subject (or in your case, multiple different subjects). This is a moderated forum, and personal speculation is not allowed.
     
  14. Dec 29, 2017 #13

    PeterDonis

    Staff: Mentor

    @Lookcipher I have deleted your post, but left @DrChinese 's reply since it is a good brief explanation of the reason why I deleted your post. Please review the PF rules on personal speculation. When I said you could post a more substantive reply if you had one, I meant within the scope of the PF rules.
     
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