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Does anyone know what Feynman was referring to in this interview which appears at the beginning of The Feynman Tips on Physics? Note that he is referring to something that did not appear in the Feynman lectures.

I didn't like to do the second year, because I didn't think I had great ideas about how to present the second year. I felt that I didn't have a good idea on how to do lectures on electrodynamics. But, you see, in these challenges that had existed before about lectures, they had challenged me to explain relativity, challenged me to explain quantum mechanics, challenged me to explain the relation of mathematics to physics, the conservation of energy. I answered every challenge. But there was one challenge which nobody asked, which I had set myself, because I didn't know how to do it. I've never succeeded yet. Now I think I know how to do it. I haven't done it, but I'll do it someday. And that is this: How would you explain Maxwell's equations? How would you explain the laws of electricity and magnetism to a layman, almost a layman, a very intelligent person, in an hour lecture? How do you do it? I've never solved it. Okay, so give me two hours of lecture. But it should be done in an hour of lecture, somehow -- or two hours.

Anyhow I've now cooked up a much better way of presenting the electrodynamics, a much more original and much more powerful way than is in the book. But at that time I had no new way, and I complained that I had nothing extra to contribute for myself. But they said, "Do it anyway," and they talked me into it, so I did.

Did this approach to teaching electrodynamics appear in any of his later writing?

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I don't know exactly what he is referring to, but one possibility is the QFT way to do it (which for Feynman was essentially a warm up exercise on the way to deriving GR from similar principles). Basically the unique theory of a Lorentz Invariant, charge=0 massless spin 1 particle at low energies is Maxwell's equations. Feynman's way of getting there in his Lectures on Gravitation is to start from conservation of charge and to say that photons couple to matter as $A_\mu J^\mu$ and then by looking at various scattering amplitudes you can end up at the Maxwell Lagrangian. –  Andrew Feb 26 '14 at 10:58
"which for Feynman was essentially a warm up exercise on the way to deriving GR from similar principles" Can you provide some reference for this? Very curious to hear about it. –  Danu Feb 26 '14 at 11:37
may be he is talking about Feynman diagrams –  Hubble07 Feb 26 '14 at 12:42
I find it fascinating that Feynman openly expressed having such difficulty explaining E&M [not saying I can do it, just saying it's very interesting], but such ease with those other subjects. –  honeste_vivere Oct 1 '14 at 15:45

5 Answers 5

I am not sure, but maybe this is about Feynman's derivation of the Maxwell equations outlined in Dyson's article http://signallake.com/innovation/DysonMaxwell041989.pdf (Am. J. Phys. 58(3), March 1990, p. 209). However, my impression was that derivation is deficient.

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This is very interesting, but the article you linked to says that derivation was discovered in 1948, whereas the Feynman lectures were delivered in 1961-1963. So Feynman must've been referring to something else in the interview I quoted. –  littleO Feb 26 '14 at 18:22
@littleO: As I said, I am not sure –  akhmeteli Feb 26 '14 at 18:37
@littleO 1961 happened after 1948. –  arivero Sep 28 '14 at 19:19
@arivero I don't understand your comment. My point was that Feynman's "much better way of presenting the electrodynamics" must have been something he thought of after 1961; otherwise Feynman would have used the "much better way" in his Lectures on Physics. –  littleO Sep 29 '14 at 1:21
@littleO my fault, I misread that you were quoting some preface to the lectures, not the interview. You are right, the "much better way" can not be DysonMaxwell. –  arivero Sep 30 '14 at 1:27

Opening with an aside:

Interestingly, one of Feynman's students, Carver Mead, of VLSI fame, expressed similar dissatisfaction with these EM lectures and actually wrote a monograph, "Collective Electrodynamics", which attempts to reformulate the discipline using the potentials, not the fields, as the primary entities, and quantum systems (superconducting loop, coherent quantum resonator) as the canonical examples.

It's not a difficult read. I'm not qualified to pass judgment on its success, but I do know I wouldn't want this approach to be my first course in EM.

Anyway, all that is only tangential to your question. I believe the interview you quoted is from 1966. Much later, in 1983, Feynman gave a series of public lectures on his theory of Quantum Electrodynamics (QED), which were subsequently published as QED, The Strange Theory of Light and Matter.

The bulk of this book describes the probability amplitudes of interactions of photons and electrons, and their applications in various settings ("calculating the sum of all the little arrows"). Near the end of Chapter 3, there is a schematic argument which may refer to the "1966 approach":

There are circumstances, for example, where the amplitude to emit a photon by a source is independent of whether another photon has been emitted. This can happen ... when a very large number of electrons are all moving the same way, such as up and down in the antenna of a broadcasting station or going around in the coils of an electromagnet. Under such circumstances a large number of photons are emitted, all of exactly the same kind. The amplitude of an electron to absorb a photon in such an environment is independent of whether it or any other electron has absorbed other photons before. Therefore its entire behavior can be given by just this amplitude for an electron to absorb a photon, which is a number - called a "field" - that depends only on the electron's position in space and time.... When we take polarization into account, there are more components to the field. (There are four components - corresponding to the amplitude to absorb each of the different kinds of polarization (X, Y, Z, T) the photon might be in - technically called the vector and scalar electromagnetic potentials.

In other words, Feynman is claiming to derive classical EM as a particular limit of QED. Of course that should be possible; the impressive thing here is that, if this approach is indeed what he was referring to in 1966, Feynman felt he could explain it to a "very intelligent person" (or maybe sufficiently intelligent?).

I should emphasize that "QED" contains no more detail on this topic than what I quoted above. It's not going to satisfy someone looking for a detailed exposition.

And maybe his "1966 approach" was something completely different than that of "QED". Feynman was nothing if not creative.

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According to an interview made by the American Spectator with Mead around his book, Mead's idea about the whole subject is somehow revolutionary, although apparently the formulation has nothing really new to the physics world. I guess Mead's idea is from himself, not from Feynman. (Meanwhile, personally, I like his view very much as we already knew it from Islamic philosophy) –  owari Mar 25 at 16:34

I found the following quote on the American Institute of Physics website. It is a continuation of Feynman's quote above. I believe it answers your question about his new approach.

"When I planned it, I was expected to teach electrodynamics, and then to teach a subject which would really be all the different branches of physics, using the same equation — like you use a diffusion equation for diffusion, for temperature, for lots of things, or the wave equation for sound, for light, and so on. In other words, the second half would have been something like mathematical methods of physics, but with many physics examples, so I’m teaching physics at the same time as the mathematics. I would teach Fourier transform, differential equations, and so on. It wouldn’t look like that, though. It wouldn’t be organized the usual way. It would be in terms of subjects, the point being that the equations are the same in so many different fields. So the moment you deal with an equation, you ought to show all the fields that it comes from, instead of just talking about the equation. So I was going to do that. But then I had another possibility. Maybe I could teach quantum mechanics to the sophomores — nobody expects that to be done, that would be a miracle. And I had a crazy upside down way of presenting quantum mechanics, absolutely inside out, in which everything that was advanced would come first, and everything that was elementary would come, in the conventional sense, last. And I told these guys about that, and they kept working on me. They said I had to do it, that the mathematical thing that I was talking about, other people may someday do, but that this thing would be so unique, and they knew that I would never go for another year. I must do this unique thing, you see — even if it kills the kids, they can’t learn it, and it’s no good. I don’t know what the situation is, actually, whether it’s worthwhile or not. I should try it. So I did. And that’s volume 3 on quantum mechanics. But volumes 2 and 3 were really one year, just like volume 1 was."

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The question is about electrodynamics, not quantum mechanics. –  Ben Crowell Sep 29 '14 at 1:02
@BenCromwell: And yet, the quote starts out with electrodynamics, or the expectation to teach electrodynamics. It ends with him saying that he wants to teach Volume 2 (electrodynamics) and Volume 3 in one year... which is not that unusual. I think I had electrodynamics and quantum mechanics I taught to me in the same year (but not in the same semester). There is absolutely nothing in that material that would prevent a good professor from teaching both simultaneously to gifted students (the approach might lose some of the lesser gifted ones, though). –  CuriousOne Sep 29 '14 at 20:26
@CuriousOne While this quote mentions electrodynamics, it doesn't reveal any special way of explaining electrodynamics that Feynman had not already thought of by the time he delivered his Lectures on Physics. –  littleO Sep 29 '14 at 21:58
@littleO: What people think trough and what people eventually do are two different matters altogether. Feynman says that he was trying to go completely rogue... and reality says that he abandoned the idea, because it's not nearly as attractive in reality as it sounds in the shower. A professor of mine tried that for thermodynamics... needless to say, it was a really, really bad class on thermodynamics and we all had to either re-take the class or learn the real thing from textbooks the old fashioned way. –  CuriousOne Sep 29 '14 at 22:01
@CuriousOne Regarding "reality says that he abandoned the idea": Feynman's statement in the interview (quoted in the question above) shows that he didn't abandon the idea of finding a novel way to present E&M, and that in fact he eventually thought of some approach he considered to be much better than the approach he took in his Lectures on Physics. –  littleO Sep 29 '14 at 23:15

He may have been thinking about teaching physics top-down, rather than bottom-up. There is nothing wrong with that. That's exactly what Landau/Lifshitz do in Volume 1 of their "Course of theoretical physics", by introducing a least action principle and deriving much of Newtonian mechanics from it. One could do the same thing for electrodynamics, but the approach would probably lose many of the lesser gifted students along the way.

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It is possible that Feynman was referring to Feynman Diagrams (for which work he received a Nobel Prize). Feynman diagrams offer a graphical representation of particle interactions collectively known as Quantum Electro Dynamics (QED). Feynman's contribution provided a means to analyze quite complex interactions without relying solely on manipulating wave equations or matrices.

As an adjunct analysis device, most theoreticians agree that Feynman diagrams have been quite successful.

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The same remark than for the previous answer [ physics.stackexchange.com/a/100971/16689 ] applies here as well: the Feynman diagrams have been invented long before his lectures. So if he wanted to present the Maxwell equation from the diagram (an interesting program by itself which I'm not sure how to do that) he would have done this already in his lectures. –  FraSchelle Mar 5 '14 at 9:54

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