B Feynman QED Questions

[photonographer]

TL;DR Summary

Why does Richard Feyman's explanation for reflection of light say that only some minor differences can be ignored and he sums all the paths between the two points?

Figure 22 - Why does Feynman say that the different lengths A to M are so minor that he is going to ignore them but the time difference differ by the same amount and they are not ignored. Was it just the same for the drawing representation of the arrows?

Figure 24c - Why are different paths A to M vectors added to each other when each path are done independently/in parallel and not sequentially/in series?

What exactly does the sum of all the A to M vectors represent? What does "This also happens when the total time is the least." mean? Vector G is not parallel to the resultant vector sum of A to M so it does _not_ contribute the most to the magnitude in its direction.

 

[Nugatory]

Which Feynman book/paper/lecture are you working from? Until you tell us that, we won’t know what’s in the figures that you’re asking about.

 

[DaveE]

What exactly does the sum of all the A to M vectors represent?

I have no idea. I don't know what A is. I don't know what M is.

[Moderator's note: Some off topic content deleted.]

 

[weirdoguy]

The title of the book is in the title of the thread.

 

[berkeman]

Maybe @photonographer didn't come up wit the idea to post a picture of the relevant pages - I, for example, for quite a long time thought that this is not legal.

At least in the US, under Fair Use Copyright Law[1] you can quote/copy/paste limited amounts of information from copyrighted works (with proper attribution) for the purposes of asking questions or making comments about that work. That would have helped a lot in this case, and hopefully the OP can add that information in a subsequent reply.

[1] https://fairuse.stanford.edu/overview/fair-use/four-factors/

 

[photonographer]

As mentioned by @weirdoguy, the book name is QED by Richard Feynman. This is the 2006 printing but I don't believe it matters because the Feynman text is likely the same.

[Moderator's note: Some off topic content deleted.]

 

[berkeman]

Is there a way to block people on this forum?

There is a feature called "Ignore", but that can be awkward when you ignore replies that may be helpful for you, and others reading a thread don't understand why you are still asking a question that has been answered (by someone on your Ignore list).

And since this is only your 2nd post/reply so far on the forum, let's try resetting. Can you please upload the figure you are asking about (use the "Attach files" link under the Edit window)? I also no longer have my copy of Feynman's QED, so I would find it difficult to help unless you show us the figure. Thanks.

 

[Nugatory]

My copy of the book doesn't have a figure 24c.

 

[Spinnor]

I think the book is based on a series of lectures he gave,



Your questions my be answered by watching them. The arrows in question spin very fast but also shrink in length proportional to the 1/(length of the path)? If the path length difference is of order the wavelength of the light the phase changes by 2 pi but the length of the arrow changes by a much smaller amount?

 

[Ibix]

As mentioned by @weirdoguy, the book name is QED by Richard Feynman. This is the 2006 printing but I don't believe it matters because the Feynman text is likely the same.

In the 1990 edition I have, figure 22 is just a single arrow and figure 24 does not have any 24c. So it looks like there have been some changes and you'll have to provide some more information.

 

[PeterDonis]

the book name is QED by Richard Feynman

Please note that this is a pop science book, not an actual textbook. As pop science books go, it does a pretty good job of not misrepresenting the science, but it's still not the same as an actual textbook.

 

[PeterDonis]

@photonographer for future reference, if you think someone else's post violates the PF rules (such as the rule about treating other users with consideration), please don't respond in the thread. Use the Report button to bring the post to the attention of the moderators.

All thread participants, please stay on topic. A few posts have been edited to remove off topic content.

 

[TSny]

Figure 22 - Why does Feynman say that the different lengths A to M are so minor that he is going to ignore them but the time difference differ by the same amount and they are not ignored. Was it just the same for the drawing representation of the arrows?

Consider, for example, the arrows corresponding to reflections from C and G in Figure 24. Feynman is saying that the lengths of these two arrows can be taken to be approximately the same. He does not say you can ignore the difference in path lengths S-C-P and S-G-P. The difference in path lengths is significant and leads to a significant difference in time for the photon to travel S-C-P compared to S-G-P. This difference in time results in the two arrows having very different directions.

Figure 24c - Why are different paths A to M vectors added to each other when each path are done independently/in parallel and not sequentially/in series?

The reason is that it works! Feynman’s objective is to illustrate how physicists “count the beans” (page 24) to determine the probability of an event such as a photon leaving a detector, reflecting from a mirror, and arriving at a detector. On page 37, you see the “Grand Principle” and the “General Rule” that are the basis of these calculations.

No attempt is made to explain why these rules work. The “General Rule” states that you should add the arrows for the different paths S-A-P, S-B-P, … S-M-P in Figure 24.

What exactly does the sum of all the A to M vectors represent?

Summing the arrows is a calculational technique for determining the probability of an event. That's all.

To quote Feynman (page 33):
The technical word for these arrows is "probability amplitudes", and I feel more dignified when I say we are 'computing the probability amplitude for an event.' I prefer, though, to be more honest, and say that we are trying to find the arrow whose square represents the probability of something happening.

In Figure 24, the “something happening” is the arrival of a photon at P after leaving the source S and reflecting off the mirror.

What does "This also happens when the total time is the least." mean?

I haven’t found this exact quote. In the description of Figure 24, I see a similar sentence, “This also happens to be where the total time is least.” This is a statement that positions E through I on the mirror correspond to travel times of the photon that are all approximately equal to the least travel time (G).

Vector G is not parallel to the resultant vector sum of A to M so it does _not_ contribute the most to the magnitude in its direction.

The important point is that the length of the total vector (A to M) is largely due to the string of vectors from E through I, roughly. This is because these vectors all have approximately the same direction.

 

[photonographer]

View attachment 362789

Consider, for example, the arrows corresponding to reflections from C and G in Figure 24. Feynman is saying that the lengths of these two arrows can be taken to be approximately the same. He does not say you can ignore the difference in path lengths S-C-P and S-G-P. The difference in path lengths is significant and leads to a significant difference in time for the photon to travel S-C-P compared to S-G-P. This difference in time results in the two arrows having very different directions.


The reason is that it works! Feynman’s objective is to illustrate how physicists “count the beans” (page 24) to determine the probability of an event such as a photon leaving a detector, reflecting from a mirror, and arriving at a detector. On page 37, you see the “Grand Principle” and the “General Rule” that are the basis of these calculations.

View attachment 362790

No attempt is made to explain why these rules work. The “General Rule” states that you should add the arrows for the different paths S-A-P, S-B-P, … S-M-P in Figure 24.


Summing the arrows is a calculational technique for determining the probability of an event. That's all.

To quote Feynman (page 33):
The technical word for these arrows is "probability amplitudes", and I feel more dignified when I say we are 'computing the probability amplitude for an event.' I prefer, though, to be more honest, and say that we are trying to find the arrow whose square represents the probability of something happening.

In Figure 24, the “something happening” is the arrival of a photon at P after leaving the source S and reflecting off the mirror.



I haven’t found this exact quote. In the description of Figure 24, I see a similar sentence, “This also happens to be where the total time is least.” This is a statement that positions E through I on the mirror correspond to travel times of the photon that are all approximately equal to the least travel time (G).



The important point is that the length of the total vector (A to M) is largely due to the string of vectors from E through I, roughly. This is because these vectors all have approximately the same direction.

Thanks for your explanations.

Yes, you found the quote that I meant. I had some typos, "when" should have been "to be where"

I guess I didn't expect Feynman's explanations to be so handwavy, even though the introduction by Anthony Zee talks about how it teaches people to "pour all the pebbles out onto a big pile and count them"

I have taken a couple graduate level Physics and Math courses but that was 30 years ago and I'm a EE (although other sparkys would say that Fields and Optics make me a Physics person). The Mathematical Methods in Physics II was alot of work (that I blame on getting bad advice that taking the part I course wasn't needed)

So, I didn't expect the description to be at that high of a level but that it would have more logic meanings than it has so far.

 

[PeterDonis]

I guess I didn't expect Feynman's explanations to be so handwavy

Again, it's a pop science book, not a textbook.

 

[Nugatory]

I guess I didn't expect Feynman's explanations to be so handwavy,

It's not an explanation, it's an analogy. For Feynman's explanation, you'll want something like this.

As an analogy it is useful: it provides an intuitive picture of how summing probability amplitudes across all paths (an essential concept in some formulations of quantum field theory) can yield the observed behavior of light, without requiring the reader to spend years studying the math first. But it isn't more than that.