Feynman's sum-over-histories

by idea2000
Tags: feynman, sumoverhistories
 P: 46 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?
 Sci Advisor HW Helper P: 11,915 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).
 P: 46 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?
 Sci Advisor HW Helper P: 11,915 Feynman's sum-over-histories 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.
 P: 46 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?
P: 2,065
 Quote by idea2000 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?
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.

 Quote by dextercioby 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.
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.
 P: 46 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?
 Sci Advisor P: 1,685 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.
P: 1,544
 Quote by idea2000 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?
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:
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.
P: 2,065
 Quote by RandallB Yes it is safe to assume the electron goes through one slit.
 Quote by Haelfix It *either* goes through one slit, or both depending on the setup.
 Quote by jostpuur That means that it did not go through only one slit.
 Quote by dextercioby Definitely the particle chooses a path out of that infinity
P: 1,544
 Quote by jostpuur
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.