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Richard Feynman's sum-over-paths approach to quantum mechanics?

  1. May 12, 2012 #1
    Richard Feynman's "sum-over-paths" approach to quantum mechanics?

    I am in terrible need of some insight or clarification. I have two questions.

    In the double-slit experiment, when a particle is ejected whether it be photons or electrons (I will use electrons in this question), when streams of electrons are shot out towards the double slits an interference pattern occurs on the phosphorescent screen. If the "beam" of fired electrons was thinned so that, say one electron was emitted every 10 seconds, the interference pattern would still occur, provided both slits were still available. But if one slit was covered up, no interference pattern would occur.

    What I don't understand is Feynman's perspective on this. Feynman proclaims that every electron that makes it through to the screen actually simultaneously traverses every possible trajectory in space. Therefore, in traversing every possible trajectory, the electron actually passes through both slits and interferes with itself.

    I know that an electron can be in more than one place at a given time, but I am having a hard time grasping the statement that a single electron can traverse every single possible path simultaneously from its start-point to end-point.

    Question number one: Can someone please give some insight on this to help me understand this phenomenon?

    Question number two: This isn't about Feynman's proclaim, it's about gravity. How does the electron see the other slit? The way I envision it is by creating a 3-dimensional grid around the whole apparatus, depicting space. Everything has some sort of gravitational pull whether it be big or small. Obviously for a massive object like the earth its gravitational pull, which is the warping of space around it is what causes the moon to feel the attraction and orbit the earth. I know for an object like the barrier with the slits is much smaller, but is that how the electron "sees" the other slit? I'm not saying that the electron moves towards the slits because of the gravitational pull, that is just idiotic. I mean, adding a second slit would ever so slightly change the properties of the barrier, and maybe the shape of it warps the space around it differently, and that little tiny warp in space from the second slit is how the electron "sees" that there is another slit there?

    Sorry if my second question is stupid, I am still very new to this field (I'm only entering my second year in the astrophysics program at my university). My mind is all tangled up about this.
     
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  3. May 13, 2012 #2

    atyy

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  4. May 13, 2012 #3
    Re: Richard Feynman's "sum-over-paths" approach to quantum mechanics?

    Your question is far from stupid.

    Wasn't this one of Feynman's postulates - namely that if you had an event which could happen in alternate ways (in this case the electron taking alternate paths to the screen), then you have to add the (complex) amplitudes for those alternatives to get the final answer (which you square if you want the probability) ? So, being a postulate in his formalism, it couldn't be derived from simpler principles. Feynman went on to demonstrate that his formalism was consistent with the alternative picture, namely that provided by the Schrodinger wave equation.

    Of course you are also free to switch viewpoint, and think of the electron, whilst in transit, not in terms of a localized particle, but rather as a wave, then you arrive at the picture in atyy's post.

    The conclusion is that quantum mechanics doesn't say what the electron actually "is" whilst in transit, or where it is, it just gives the rules for predicting the electron's interaction with a detector (in this case the screen). There are different rules depending on which picture you want to take, but they all arrive at the same answer.

    Counterintuitive, but at some point you just have to say that that's the way the world is !
     
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