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Double-Slit Questions

  1. Jul 25, 2005 #1
    1.)I'm wondering to what extent Young's and other double-slit experiments depend on "slit" geometry. Does the same effect show up with two pinholes? I read a brief mention of G.I. Taylor having used a pinpoint somehow, but the description wasn't expanded enough for me to understand the set up.

    2.) Young, obviously, did his experiment in air. Has anyone tried the double-slit with light in a vaccuum?

    3.) With electron double-slit demonstrations the electrons have to be set in motion by electric potentials. I think this means they are accelerating as they go through the slits, unlike light. If so, does this create any signifigant differences from light demonstrations that have to be accounted for?
     
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  3. Jul 25, 2005 #2
    The double slit experiments, similar to Feynman's thought experiments, illustrate the distributions of particles, or waves as they enter the double slit apparatus, so the shape of the slits will not affect the experiment, neither does the fact it is in a vacuum or not.
    If we fire particles at the slit, with one slit closed we get a distribution P, then close the other slit and open the other slit we get another distribution Q. Now leave both open we get a distribution equal to P+Q.
    Now if the experiment is repeated with waves emitted from a source, we get the usual diffraction with distributions X and Y, however the ditribution corresponding to two open slits is not equal to the sum, this due to interference.
    Now suppose we do it with a beam of electrons (acceleration does not affect this), we get distributions A and B, however the distribution corresponding to two open slits is not equal to A+B, this illustrates the essence of quantum mechanical behaviour - we do not know with certainty the electron's position until we measure it, thus "knocking" it into a position eigenstate. Mathematically this comes from the fact that (x+y)^2 is not equal to x^2 + y^2.

    Hope this helps

    Ray
     
  4. Jul 25, 2005 #3

    DrChinese

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    Not meaning to disagree with rayveldkamp's answer, as I think what was said is correct. The interference effects are still present with different shapes.

    However, the slit shapes definitely alter the shape of the resulting interference pattern. For example, a diamond slit shape leads to a slightly different pattern (more like a diamond) than the traditional bar slits do. Ultimately, the interference pattern is a function of all possible paths that the light can take in its journey to the screen. The universe of such paths is therefore affected by the shape, even to some small extent by the texture of the slit edge. Usually, slit geometry is simply ignored because interference occurs anyway and that was the purpose of the experiment.
     
  5. Jul 26, 2005 #4
    In terms of Feynman's "adding arrows" I'm assuming that the dark lines in an interference pattern represent areas where the probability amplitudes of a photon from one slit arriving 180 out of phase with a photon from the other slit are greatest. However, I don't know if that is right since he doesn't specifically talk about double slit interference in the chapters on photons in QED.

    He discusses a single slit, and explains why the smaller the slit the more the light seems to spread out, which is that the narrower slit increases the probability of photons with the same bias (phase) arriving adjacently everywhere. The narrow slit selects out a group of adjacent paths, which, all being similar in time, are similar in bias. Being similar in bias, they don't interfere, don't cancel each other out. The apparent spreading, he seems to be saying, is not actually new behaviour, light is always doing this, it's just that now the impediment to seeing it (canceling by out of phase photons) has been removed. (This is all roughly, on pages 53-56 of the paperback edition of QED)

    Imagine a horizontal slit in a vertical piece of flat metal parallel to a wall. Light comes through the slit and shines on the wall. My thinking about what happens next (Feynman doesn't explicitly say) is that, as all the selected 'in phase" light fans out from the slit, the arrows (that designate where the stopwatch pointer would be pointing when they hit the wall) are pointing in a slighly more advanced position for each bit of distance you go vertically up the wall, or down the wall from a horizontal line on the wall level with the slit in the metal through which the light is coming.
    Each unit distance up or down the wall from the reference line represents a longer path, and the stopwatch will turn a little farther before the photon hits. And what we end up with is a very neat, smooth gradation of phase up and down from the original stopwatch position to the final one. Any given photon will be pretty much exactly in phase with the others on the same horizontal line, and will be only slightly out of phase with the ones that are, say, a thousandth of an inch above or below it. The ones an inch away, above and below are much more out of phase, and so on.

    Adding a second slit, by this reasoning, superimposes a similar fan of photons, precisely graduated by phase, onto the first. The stopwatch pointers of alternate bands of them will naturally fall into "in phase" and "out of phase" categories. The out of phase ones cancel each other out, and the in phase ones reinforce each other. Since all horizontal lines from each individual slit are in phase, the net result is "bands" of light and dark.

    Feynman, however, doesn't explicitly say anything about what happens when you put a second slit next to the first, so I'm not sure if I've reasoned this out correctly.
     
  6. Jul 26, 2005 #5
    What prompted the question was the thought that Nature must be full of double slit situations, like the branches of trees, or tall grass, but you don't see all kinds of interference patterns everywhere.

    I was wondering about the maximum and minimum parameters that have to be in place for this effect to be visible. As near as I can tell very narrow slits are superior to all other configurations for making this effect apparent.
     
  7. Jul 26, 2005 #6

    ZapperZ

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    How do "branches of trees" and "tall grass" the same as "interference pattern", which is nothing more than an illustration of superposition principle? The interference pattern is the result of the same phenomenon as the Schrodinger Cat.

    Zz.
     
  8. Jul 26, 2005 #7

    selfAdjoint

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    The slits or pinholes and their spacing have to be on the millimeter scale for light. Diffraction is a form of interference and feathers do produce colors by diffraction.
     
  9. Jul 26, 2005 #8
    Nature of the slits

    I have heard of studies in which the interference pattern is generated by (or can be also explained by) the tunneling effect of the travelling wave-particle through the solid stuff which constitutes the slit borders. look up in Nuovo Cimento - Moyses Nussenzveig.
     
  10. Jul 26, 2005 #9

    ZapperZ

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    Then I'd like to see THAT being used to explained the SQUID interference pattern.

    You need to give a more exact citation than that.

    Zz.
     
  11. Jul 26, 2005 #10
    references

    Sorry for not being so exact.

    But once discussing with Prof. Moyses Nussezveig, researcher with works on quantum optics , microspheres and rainbow theory, he told me that he had once writen a paper i Nuovo Cimento where he attempted to derive interference effect in double slit experiment through the use of tunneling.

    I, as a matter o fact, have not looked up, but naturally I trust him.
     
  12. Jul 26, 2005 #11

    ZapperZ

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    There are two separate issues here that would pop up immediately, especially if you know a bit more about what "tunneling" is.

    1. Is the explanation only SPECIFIC to the standard 2-slit interference effect from light? Or is this a GENERIC 2-slit interference effect, meaning it could be applied to anything with a superposition of 2 separate path? That's why I said I would like to see it being applied to the SQUID case. I'd like to see what exactly is "tunneling" through and where.

    2. "Tunneling" phenomenon produces no "interference". In fact, if you look at it closely enough, a ballistic tunneling phenomenon is nothing more than a "handshaking" between the states on either side of the tunneling barrier, with the tunneling matrix as the "mediator". So if the slit and the slit material act as "barriers", this STILL produces no explanation for any interference effect.

    That is why I asked.

    Zz.

    P.S. Not to mention, Il Nuovo Cimento website SUCKS. There's no way to do an author search. So unless you have an exact citation to the paper, bringing this up is not exactly helpful.
     
    Last edited: Jul 26, 2005
  13. Jul 26, 2005 #12
    That's the kind of parameter I was wondering about.
    In this manifestation, there's a fair amount of it around in Nature, then. Also in oily mud puddles after it rains.
     
  14. Jul 26, 2005 #13
    tunneling and interference

    My guess, regarding the observations you have made, is that the tunneling was used to explain the process of pattern formation on a screen, using the slit wall as a specific and well defined potential, which causes deflections in an electron path, for example. Some Statistics on this ballistic experimente also must have took place. I know that , without the explicit reference to Mr. Nussenzveig, this conversation lose much of its scientifical character.

    I will quit bothering in this specific question. But I would like to aknowledge you so much for the attention.

    Sincerely yous,

    DaTario
     
  15. Jul 26, 2005 #14
    Just commenting: I believe tunneling is also a manifestation of interference.
     
  16. Jul 26, 2005 #15

    ZapperZ

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    You "believe"?

    Derive it. After you think you have shown this, then explain the tunneling density of states obtained from conventional superconductors. Show me where the "manifestation of interference" is.

    Zz.
     
  17. Jul 26, 2005 #16
    Even deriving, I believe faith is still present in my argument. But let me try to better arrange my argument.

    In quantum mechanics of a material particle in one dimension, potential barriers are provided in such a way that, sometimes, the presence of a particle at a given locallity, as classically predicted, is an impossible event. However, with the use of a wave function representation, Schroedinger equation is used to propagate the probability amplitude wave and, after the calculation, as resulting from the action of a wave propagator, non zero amplitudes of position are found in these classically forbiden regions.

    I have no other word to present in order to justify this effect but interference.
     
  18. Jul 26, 2005 #17
    you may remember those results in Fabry-Perot or Mach-Zhender interferometers where multiple beams interferece formalism were used. It is something like this I am referring to.
     
  19. Jul 26, 2005 #18

    ZapperZ

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    You have simply described is the "wavefunction". This isn't interference, and it isn't interference from tunneling. Why don't you actually LOOK at tunneling phenomena in solids, such as from Ed Wolf's text. Then point out to me where is this "interference" phenomena coming from that.

    Zz.
     
  20. Jul 26, 2005 #19

    ZapperZ

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    And where exactly is the TUNNELING phenomenon in these setups? Interferometer has no tunneling barrier.

    This line of discussion is getting to be VERY strange.

    Zz.
     
  21. Jul 27, 2005 #20
    Mentioning the interferometers I was only trying to refer to multi beam interference formalism. But I agree with you on the strangeness of this discussion. My tendency is to look for interference in everything which concerns waves and departs from pure plane wave propagation.

    I would like to acknowledge you for the attention as well as congratulate you for doing this task of replying with attention and kindness.

    Thank you

    DaTario
     
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