Feynman's sum-over-histories

  1. Hi,

    I'm a new user here just trying to learn a bit more about quantum. I just
    read a website about feynman's sum-over-histories method that claims that experiments
    have proven that Feynman was correct.

    I know enough about science to understand that everything is pretty much just
    a theory. And the reason we think theories are true is because we haven't seen any evidence to believe otherwise. Because of this, I know that Feynman's sum-over-histories cannot possibly be PROVEN to be correct, but I am curious about how much evidence is out there that Feynman was right. Is it pretty much accepted in the physics community that the particle does in fact travel in every possible path? And if so, are the effects of its electric field in fact all over the universe at the same time?
     
  2. jcsd
  3. dextercioby

    dextercioby 12,303
    Science Advisor
    Homework Helper

    No, the particle COULD travel in every possible path. Every possible path has a number attached to it, namely the probability that the particle should take that path from A to B. It is found that in QM the path with the biggest probability is the classical path, namely the one a classical particle follows from A to B (see the variational principle and the sizzling chapter in Feynman general physics book).
     
  4. Hi,

    Pardon my confusion...

    Of the infinite number of paths that the particle could take, does the particle still only choose one path to take at a time?
     
  5. dextercioby

    dextercioby 12,303
    Science Advisor
    Homework Helper

    Definitely the particle chooses a path out of that infinity, it's just that we don't know which. All we can compute are the probabilities for each path.
     
  6. Ok, I got it...but one more thing...

    Why do we see the interference pattern of the one electron/photon interfering with itself, when each electron/photon only takes one path at a time? Do we only see the interference pattern after enough electrons/photons have gone thru the slits?
     
  7. When one electron goes through slits, it has non-zero amplitude for having gone through both of the slits. That means that it did not go through only one slit.

    Wait a minute... this is something that should happen if we could measure the path that a particle had gone through (like in bubble chamber), but if we only measure the final position (like in the double slit experiment), then the particle does not choose (or measurement device doesn't choose, whatever...) any particular path. Right?

    I mean, isn't there amplitudes for different paths that the particle could have gone, in similar way as there is amplitudes for a particle to be in different positions. Saying that particle actually took some path sounds like some Bohmian stuff.
     
    Last edited: Aug 25, 2007
  8. Ok, I'm really confused now...lol

    One electron could go an infinite number of paths, but it chooses one path and it goes thru one slit. Another electron picks another path and goes thru the other slit. But each electron does go thru one slit at at time. It is only after a long period of time that we see an intereference pattern. Is this correct? Or does one electron go thru both slits at the same time?
     
  9. Haelfix

    Haelfix 1,728
    Science Advisor

    Read the first chapter of the Feynmann lectures on physics volume 3. Its hard to understand whats going on with a few lines on a message board, b/c its wonderfully counterintuitive and a shock to the senses.

    The answer to you're question (does it go through one slit, or both) is it depends on what experiment you are performing. It *either* goes through one slit, or both depending on the setup.

    The great mystery is that depending on the observation and setup thats made and utilized, it seems to change the fundamental properties of the prior history of the particle (eg was it really a particle, or was it really a wave). You can arrange it so that the same *entity* morphs into one or the other throughout a long multiple measurement experiment.
     
  10. You’ve already been given some good references. So thing of this as oversimplification - -
    Yes it is safe to assume the electron goes through one slit. And if there was only that one slit I’m sure you would be comfortable with a large group of paths (or Feynmann histories) that could be taken by that electron describing create a wide spot of impact possibilities heaviest in the center correct.

    However just because you consider an electron that does go though that one slit the ability to calculate the total probabilities that it might have instead gone though the other slit provided it is open still exists. That group of probabilities also defining a wide spot of impact possibilities heaviest in the center correct - almost identical maybe just offset by a minor amount.

    Now what Feynmann is saying is still must SUM OVER all those possible histories including those for the other slit (even for electron you assume used the first slit) in order to correctly predict the probable landing spots for that one electron. That sum will predict a pattern. Unless of course you have some way of knowing for sure the slit used by the electron (which way); then you do not get to use the histories through the other slit.

    Just another way of building a workable analogy to QM, not to say that one is necessary better than another.

    PS:
    Also from your OP
    It is not that “everything is pretty much just a theory.” at least not in science.

    Science expects to use good theories based on rational ideas that others can evaluate based on using the Scientific Method.
     
    Last edited: Aug 28, 2007
  11. :confused:
     
  12. You are not making clear your confusion
    If you are expecting to understand how a theory like Sum of Histories explains things you need to be clear which theory you are trying to understand.

    However, I suspect you are expecting someone to tell you definitely, what is correct --does an electron or “parts of it” go through both slits.

    Think about it – there are several theories for a reason.
    Those that say yes “something” goes though the other slit – cannot define what that “something” is.

    You get a prize IF YOU can show to everyone’s satisfaction which theory is real & correct.
     
  13. JesseM

    JesseM 8,491
    Science Advisor

    But we compute amplitudes and phases for paths, not probabilities (we only assign probabilities to measured outcomes which are consistent with many different possible paths). If each path could be assigned a classical real-valued probability such that the sum of the probabilities for each path was 1, and the probability of a given final outcome was just the sum of the probabilities of the paths which end in that outcome, then it would make sense to say that the particle definitely took one path or another and we just don't know which one, but since we can't do it this way and get the correct probabilities for measured outcomes, I don't see how you can say "definitely the particle chooses a path out of that infinity, it's just that we don't know which."
     
    Last edited: Aug 29, 2007
  14. I'm not sure if this helps but here is another vauge analogy that perhaps may assist in grasping the actual meaning of going through several paths.

    Consider a poker game. Each poker player is attempting to predict the behaviour of the other players. They do so by finding the probability for each possible "move" conditional on the given information (seen cards etc).

    (Read here: consider a system of interacting parts)

    Now, in this classical scenario it's clear that each player really only does have some particular cards at hand, but their behaviour does not depend on the actual (unkonwn) cards of the other players - it depends on the players *expectation* on what cards the other players has + of course the players own cards + given prior info about card history. Ultimately this means that the behaviour of each player and thus the players interactions, does depend on all the possibilities of their respective expectations of each other.

    This sort of means that it is almost more fundamental what cards all other players _think_ they have, because this is what will determine their next move.

    This is a classical analogy, but still it gives a hint of the logic how the parties expectations is the important thing.

    My actions, and I can't believe otherwise than it applies even to electrons, are entirely dependent of my expectations of the environment, what the ACTUAL case is, will probably be clear to me as interactions continue and then I will correct my expectations accordingly, just as a pokert player revises his strategy upong each observation of cards on the table, but the fact is still that my decisions/actions are based on *expectations*, not some not yet seen but "hypothetised truth" (how that now would supposed to even be properly defined).

    What cards the other players REALLY have is really not the most important question, and often it can't even be known. The expectations is all we've got, wether we like it or not.

    If this didn't help, just ignore it. Game/learning theory analogies is just my personal favorite.

    edit: cleaned up some misplaced words, andd added some, that was distorting the readability.

    /Fredrik
     
    Last edited: Aug 29, 2007
  15. Feynman says..

    According to Brian Greene's The Elegant Universe, "Feynman proclaimed that each electron that makes it through to the phosphorescent screen actually goes through both slits. It sounds crazy, but hang on...." I also remember Roger Penrose saying that interfering atoms go through both slits in The Emperor's New Mind - that was my first exposure to the concept, and it took me a while to get to the next page after that!

    There's more supportive evidence for this in the Mach-Zehnder interferometer. It is hard to see how every single photon can end up at the same detector unless the photons actually take both paths.

    Also, I just found out about the Ashfar experiment, which makes it look like the photon goes through both slits and also goes through one slit(!)
     
  16. Actually it's spelled Afshar
     
  17. Just came on to this, very much later. My understanding of the two-slit experiment is that we are dealing with the likelihood of the electron's passing through either slit. Since the possibility for each is the same, passage through both is what we see. It refers not to particles, but to possibilities.
     
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