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Feynman's perspective on the double slit

  1. Jul 4, 2008 #1
    I am reading The Elegant Universe by Brian Greene. It is really wonderful, however, I am confused by a section about Feynman's view on the double slit expiriment.

    Greene writes:

    "Feynman proclaimed that each electron that makes it through to the phosphorescent screen actually goes through both slits. It sounds crazy, but hang on: Things get in even more wild. Feynman argued that in traveling from the source to a given point on the Phosphorescent screen each individual electron actually traverses every possible trajectory simultaneously... It goes in a nice orderly way through the right slit. It heads toward the left slit, but suddenly changs course and heads through the right. It meanders back and fourth finally passing through through the left slit. It goes on a long journey to the Andromeda galaxy before turning back and passing through the left slit on its way to the screen. And on and on it goes- the electron, according the Feynman, simultaneously "sniffs" our every possible path connecting its starting location with its final destination."

    The problem I have with this is not so much the electron being in two places at one time or any of that. What I don't get is how it could go so far away and back, and not have the measurment take forever. I mean if it can only go the speed of light...than how does measuring the interference pattern not take forever? If it takes every possible path in the universe, assuming its finite, than...wouldn't taking this measurment take like over millions of years? Or is this what they talk about when they say quantum mechanics and relativity are not compatible?

    Thanks, Zach
     
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  3. Jul 5, 2008 #2

    madmike159

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    I never got this my self but I'll have a go at explaining. If we know exactly how fast the electron is going we have no idea where it is, giving it no defined boundaries in accordance with the uncertainty principal.
     
  4. Jul 5, 2008 #3
    See I always thought the uncertainty was within some reason as in "well the electron, is somewhere within so many unit lengths", planck lengths i would suppose, if that even makes sense, i really don't know. But the point is i always thought it was like "Its somewhere within the room, you know? not within the entire cosmos. but thats beside the point.

    Wouldn't it take forever for it to make that path from the source to the andromeda galaxy and back and some how create an interference pattern with itself that went straight from the source to the screen... i mean...they must be going at different speeds...the two electrons that are the same one. I really don't get this at all.

    Was Feynman just wrong? and there is some new theory that makes more sense than his?
     
  5. Jul 5, 2008 #4
    Phase velocity can exceed the speed of light, so it should not be a problem for waves to go so far away and back. The waves in quantum mechanics are not physically real. I mean we can not measure the waves in any physical sence
     
    Last edited: Jul 5, 2008
  6. Jul 5, 2008 #5

    HallsofIvy

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    To essentially echo kahoomann, your mistake is in thinking of the electron as a specific "object" that goes back and forth. At the size level of the electron, such things simply don't exist. I can't speak for exactly how Feynmann himself intended that to be interpreted but it would be perfectly valid to think of an electron with a certain "probability" or amplitude of its wave function to go "through A" or "through B" or "through one and then back to the other" as meaning that "part" of it does each of those. Again, just as I warned against thinking of an electron as being one distinct object, so you should not think of that as meaning the electron "breaks" apart.
     
  7. Jul 5, 2008 #6
    Ok, let me see if I get this. So an electron, is more like a non-existant wave that is everywhere at the same time, in kind of an implicate order that we can't see, and it usually manifests itself in the most probable spot.

    But the electron really doesn't have a path of travel does it? That is just an attempt at explaining properties of the electron that are very strange and hard to explain.

    How could we possibly interact with such a strange thing, I mean how could we possibly get a hold of an electron and shoot it at a double slit if it is so...non physical and bizzare?

    And one more question, are there any guesses at what decides the probabilities for the spot where an electron manifests?

    Thank you for your explaining and for being patient with my inability to understand the insanity of the quantum world.
     
  8. Jul 6, 2008 #7
    maybe you can read "QED - the strange theory of somethingIdon'tremember" by feynman
     
  9. Jul 6, 2008 #8
    The electron really does exist whenever you measure it or look at it, for example, the double-slit experiment.
    But between measurements, it is a wave packet. The measurement will cause the wavefunction to collapse. Einstein reacting to when he said: "I cannot believe that the Moon exists only because a mouse looks at it." ? .
     
  10. Jul 6, 2008 #9
    The book is "QED: the strange theory of light and matter". :smile:
    So far this all sounds identical to the standard interpretation. Looking at wikipedia (path integal formulation) it seems to me that what Feynman did was re-write the rules for drawing up the mathematical description of a superposition of states in such a way that they became more useful.
    Fair summary?
     
  11. Jul 6, 2008 #10
    This is more a question of interpretation of matter waves as described in Feynman path integral formulation of quantum mechanics, as described in, Wikipedia.

    Solving the Schrödinger equation with open boundaries, you don't have to think about it. But you could actually plot some kind of "classical" particle trajectories using the definition of the quantum current density, and then you see that these streamlines could be chaotic for certain energies (circulating back and forward between the slits openings), when a plane wave is injected towards a double slit.
     
  12. Jul 8, 2008 #11

    madmike159

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    Isn't the probability of the electron being some where and something to do with the schroeder equation. They all add up togive the electrond final position.
     
  13. Jul 8, 2008 #12

    Fredrik

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    I would just like to add that the lectures that the book is based on are available here. (Part 2 is the most interesting one).
     
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