# Feynman paths and double slit experiment

1. Jul 10, 2011

### hammock

I am just inhaling "The Grand Design" and am stuck in the chapter on the "buckyballs" double slit experiment.

The authors say that in case of the experiment, a particle may take any possible way ("perhaps to Jupiter and back"), which then Feynman depicts as adding vectors to a result vector (as I understand).

However, I wonder how this can be real, as the buckyball (or photon) has a definite speed s (or c) on the result vector path. But in case the particle takes the path to "Jupiter and back" the length of the path it has taken cannot fit the speed of the particle on the result vector, resulting in the (presumably false) supposition, that it had a speed greater than s (or c).

2. Jul 10, 2011

### Drakkith

Staff Emeritus
I believe the book I read about QM stated that almost all of these different paths cancel each other out in probabilities so that something like that doesn't happen.

3. Jul 10, 2011

### hammock

So, the particles that travel to Jupiter interfere all together with themselves but they don't travel at a speed greater than s (or c). Right?

 After reflecting that I assume that any path which would result in a speed greater than s (or c) might be eliminated, which then leads to the conclusion that only the direct paths remain [?] But in this case, there wouldn't be an interference, would it?

Last edited: Jul 10, 2011
4. Jul 10, 2011

### Jacques_L

You are self-contradictory, here. Concurrent paths only apply to ONE quanton at the same time. Simply the laws of physical optics continue to apply to fermions, too.

5. Jul 10, 2011

### Drakkith

Staff Emeritus
No I mean that the possible paths interfere with each other similar to the interference pattern on the double slit. Where they destructively interfere the particle(s) have a much less chance to take that path, if they have one at all.

6. Jul 10, 2011

### hammock

Does that mean, that there may be some particles travelling to "Jupiter and back" according to the interference pattern?

7. Jul 10, 2011

### Jacques_L

You are just dreaming with dreams, not more.
The theorist may compute such an aberrant path, but the conclusion will not yield another result than null. So why to exhibit magic sentences when the real result remain null ?

When a photon is emitted by an emitter, its history begins, as seen from our laboratory.
When a photon is absorbed by an absorber, its history ends, as seen from our laboratory.
Meanwhile, it is tight by the laws of physical optics (the Maxwell equations), as long as lasts the synchroneous transfer from emitter to absorber. This leaves not so much room for theoritical and magic fantasies.

More strange is the noise before any transaction succeed, but alas beyond reach of most experimentations.
However the hope is not null : someones claim that some radioactive decays depend on external conditions. Stay tuned for eventual confirm.

Last edited: Jul 10, 2011
8. Jul 10, 2011

### hammock

Hi Jaques,

well, I don't have any problems to wonder how interference may appear by applying the law of optics. From the book I understand that there ist some kind of "model dependend realism" which should let anyone choose the best fitting model in order to explain realism.

BUT in the current chapter basically the different histories of a particle are taken as basic argument in order to explain that the universe has infinite histories (and perhaps infinite futures). And the authors say that understanding that is very important for understanding the chapters afterwards.

Otherwise the book (from Hawking and Mlodinow) would be science fiction?

9. Jul 10, 2011

### ZapperZ

Staff Emeritus
From my quick reading of this thread, this has more to do with trying to understand Feynman's path integral. Unless someone has some extraordinary capability with written communication, trying to illustrate this principle is almost impossible on a public forum such as this.

So maybe a readable source that introduce what a Feynman path integral is might be useful. Try this one:

http://scitation.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=CPHYE2000012000002000190000001&idtype=cvips [Broken]

Zz.

Last edited by a moderator: May 5, 2017
10. Jul 10, 2011

### Jacques_L

This famous work of Feynman was reinventing the wheel, but less practical, with heaps of unuseful mathematical fatigue.
Why ? Just because of american arrogance : what is not published in english is thought not being, for american physicists.
So Feynman simply ignored the periodic character of any quanton that has a mass, its two intrinsic frequencies :
Broglie frequency for all of them : $\frac{m.c^2}{h}$, proved in 1924 (published in french).
Dirac-Schrödinger electromagnetic frequency for fermions, such as the electron : $\frac{2.m.c^2}{h}$, proved in 1930 (published in german).

This fact (the Broglie intrinsic frequency) drastically reduces the alternative paths to mathematically explore, as they very very quickly become unphysical : the interferences become destructive.

EDIT.
Err, there is a frequency in the text cited above, but is not the good one, it is much lesser, not relativistic, not intrinsic :
So with this inappropriate tool, Feynman explores much much broader paths than necessary, much much broader than the physical real paths.

Last edited: Jul 10, 2011
11. Jul 10, 2011

### Drakkith

Staff Emeritus
Sounds like you just have a problem with Feynman and his work, not that it is incorrect or not.

12. Jul 10, 2011

### Jacques_L

In some meaning, yes, it seems pure fiction (I have not seen it yet), as most of the books designed by an editor to the broad public. So there is a terrible temptation to play circus tricks.

For instance I have caught this dismaying book, written by a Nobel laureate (dead since) and a theorist : http://citoyens.deontolog.org/index.php/topic,887.0.html
Alarmingly stupid. And they pretended to have read the Integral of paths, of Feynman...

As long as I trust your description of what you have read, it seems to me fairy tales, without solid physical grounding. We know so little on "Universe", it is so presomptuous to tell so much on its "future" or "futures". But it is so good for the selling figures...

They found their tales on an idea of "particle", terribly flawed. It is usually taught and believed that "particles" are some very tiny, even punctual "corpuscles", but with goblinish and poltergeist behaviour. It yields terrible contradictions, of course...

So Feynmans and followers carry their ficticious particles up to Jupiter and back, without any physical grounding. This is absurdly streched out of an already absurd confusion : Feynman made no distinction between to distinct steps :
1. The quest for handshakes,
2. The transfer of a photon, an electron, a particle.

The path of the real transfer is necessarily narrow - for human distances - in comparison to its length. Of course it depends of the wavelength. The shorter the wavelength, the narrower the path. Though on astronomical distances, the mid-journey width of a photon becomes astronomical too.

But before the successful hanshake, both the demand from the potential absorbers and the offer from the potential emitters are broad. It is a broad palpation of the surroundings, both orthochrone (emitters mainly) and retrochrone (absorbers mainly).

The fairy tales of your book mix the two steps. This mixing may be fascinating for the lay men, but remains completely un-physical. As it has no real meaning, it is a good trick for hypnosis...

Last edited by a moderator: Apr 26, 2017
13. Jul 10, 2011

### nnnm4

Feynman set out to formulate quantum theory in terms of the particles and not the fields. (Read his Nobel Lecture for a wonderful personal history). He was at a party and another physicist asked him what he was working on. He responded by asking if the physicists who had asked had ever seen a method of incorporating the lagrangian into a quantum theory and he suggested he look up the paper of Dirac where it is suggested. Feynmann path integrals are useful for calculating paths of quantum systems through configuration space -- not necessarily for the motion of a single particle. With a single particle there are much more efficient methods, but for many-body systems or fields path integrals are often more useful. Also, substituting formally time in the integral for imaginary time gives powerful methods of calculating partition functions in statistical mechanics.

It's funny that you come up with American arrogance in relation to the path integral. Feynmann recalls a European being hung up with the fact that "Americans always ask how something is useful."

14. Jul 10, 2011

### Drakkith

Staff Emeritus
Jacques, your posts do nothing but show your ignorance and misunderstandings on what Feynman was doing and why. And about QM itself. And remember that you have 40+ years of history that Feynman didn't have when he was coming up with theories and such.

15. Jul 11, 2011

### Born2bwire

Ok... going back to the OP...

Feynman's path integrals are not stating that the particle is physically taking the path out to Jupiter and back. It is probably best to think of these paths as an abstraction from the mathematics. However, you can glean physical insights into the paths by how they behave over a "bandwidth" of paths. It would help if you took a quick look at steepest descent and stationary phase. Basically the path integral is an exponential integral. Each "path" has the same magnitude but what differs is the phase. If the phase is highly oscillatory between adjacent paths, then what happens is that the oscillations cancel each other out when you sum them together over the integral.

Take for example the integral of a sineusoidal function:

$$\int_0^\phi \cos \theta d\theta$$

What happens when we take \phi to be any multiple of 2\pi? The result is zero due to the cancellation regardless of how many periods we take. This is what happens in these unlikely "paths." But how does this relate in any physical sense? Mainly by the fact that the classical trajectory is the limit of the steepest descent path. That is, the trajectory or trajectories where the phase varies the slowest (or not at all). That is because where the oscillations are very slow are the ones that contribute the most to the overall result. And as we take the limit of the path integrals to the classical limit, the oscillations become faster and faster until the only paths that contribute are the steepest descent paths.

Still, keep in mind what the path integral is saying. It is only stating the wave amplitude for a particle going from position A and time t_a to position B at time t_b. It isn't stating how it from A to B, just the probability that it will do so. But it does fall out that if we take the limit of the path integral to the classical limit that the integrating paths take on a more physical picture. But this is to be expected of course, you can say the same thing about taking the limit of the Schroedinger equation to the classical limit. On the one hand, path integrals will replicate the Lagrangian picture while Schroedinger will replicate the Hamiltonian picture.

EDIT: Take a look at the link given by ZapperZ. You may also find Feynamn and Hibb's text to be insightful as well (and it recently got a long overdue reprinting, in cheap softcover too!). Regarding the talk about how oscillations and stuff cancel, take a look at steepest descent, stationary phase, Laplace's method stuff.

Last edited: Jul 11, 2011
16. Jul 11, 2011

### Jacques_L

Maybe you should have to consider that "science" and "obedience" are not exactly synonyms, and that "ignorant" and "not believer" (or "skeptical") are not exactly synonyms, too.

17. Jul 11, 2011

### Jacques_L

Nevertheless, you still have to deal with, and to explain why during all his life, Richard Feynman remained ignorant of the periodic characters of any quanton that have a mass.
Though they were published in 1924 and 1930 respectively.
The periodic character of the photon is not discussed, but alas its frequency is not intrinsic but depends on the frame.

18. Jul 11, 2011

### Drakkith

Staff Emeritus
It is CLEAR that everything you have posted in this thread has an enormous bias against Feynman and apparently Americans. I don't even need to know QM to see that. I ask you to please construct your posts with a little more thought before posting again.

19. Jul 11, 2011

### phinds

Hammock, my perhaps overly simplistic view is that yes, theoretically, there IS a path to Jupiter and back, but there is ALSO theoretically an equal path in the opposite direction and the two cancel in the total sum of possible paths.

Where this view DOES leave me with a problem is that if it's true then why don't ALL paths cancel and there is always NO resulting motion, which is just silly.

20. Jul 11, 2011

### ZapperZ

Staff Emeritus
I'm not sure how this thread has degenerated into Feynman/American bashing, but if it doesn't stop immediately, this thread will be locked and several of you will go down with it.

Zz.