Feynman’s Last Lecture
Feynman, the Josephson effect and superconductivity: a (mostly) unpublished correspondence.
“I remember being distinctly impressed by the boldness and novelty of using quantum mechanics to describe such macroscopic things”. This sentence, contained in a letter Richard Feynman sent to “Dr. Scully” in February 1974, appears on page 208 of The Quotable Feynman, the volume edited by his daughter Michelle, which gathers many others, famous and less so, whether written or merely spoken.
It was tossed in there, without any comment, with no way to grasp the context, in the chapter titled The Quantum World. But what exactly were these “things so macroscopic”? I could have asked Dr. Scully directly, but who knew if he would ever have answered, or if he even still remembered. I think he did — of course he did, it was Feynman! I was even almost certain that Scully wasn’t Dana from The X-Files, who in ’74 was only ten years old, but Marlan, twenty-five years older and, above all, a physicist, by then already a professor at the University of Arizona, working on quantum optics and laser physics. I could really have written to him…
“I’ll start with the Caltech archives,” I thought, “maybe something will turn up and I won’t have to bother him.”
I spot the correspondence right away; it rests in Box 80.17, so I try to rouse it from its slumber. I contact them, and with their usual courtesy, they inform me that there are three letters and ask if I’m interested in all of them. Damn right I am, I reply, and so they send them to me, authorizing me to use them as long as I cite them properly, of course. “Good luck with your article”, wishes Loma Karklins, a staff member of the Caltech archives. It was October 2018, and here I am now, with a draft of this story, finalized just moments before the Nobel Prize in Physics was awarded to John Clarke, Michel H. Devoret, and John M. Martinis “for the discovery of macroscopic quantum tunneling and the quantization of energy in an electrical circuit”. Funny how things turn out sometimes.1
“This lecture is only for entertainment. I would like to give the lecture in a somewhat different style—just to see how it works out”. This is how “The Schrödinger Equation in a Classical Context: A Seminar on Superconductivity” opens — the final chapter, the twenty-first, of the third volume of the Feynman Lectures on Physics2. The lecture had originally been delivered on June 4, 1964, to students in Caltech’s introductory physics course and was later presented again on October 29, under a different title but with virtually the same content, during the weekly Physics Research Conference held in the Norman Bridge Laboratory classroom. It wasn’t a lecture like the others, nor “a last minute effort to teach you something new”, but a full-fledged seminar for people who were already somewhat familiar with quantum mechanics.
Delving into the intricacies of superconductivity allowed Feynman to show how quantum behaviors could manifest in a special way, under particular circumstances, even on a macroscopic scale — in objects visible and tangible, large enough to be held in one’s hand: “the quantum mechanical laws which have been buried in the esoteric works of theoretical physicists who deal only with atoms, must now become the common knowledge of technicians who are going to work with electric circuits and so forth. [laughter]”.3
This exotic state of matter was discovered by Heike Kamerlingh Onnes in 1911, and its properties were both peculiar and extraordinary: in a superconducting material, below a certain temperature, electrons flow without encountering any resistance, while at the same time the material acts like a kind of “magnetic shield,” repelling magnets (you may have seen, somewhere, the phenomenon of “magnetic levitation”? It’s called the Meissner–Ochsenfeld effect, and it was discovered in 1933).
By the mid-20th century, superconductivity had become one of the greatest unsolved problems in theoretical physics4. Explaining the curious properties of these materials had turned into a true obsession, and in the intellectual arena where the finest minds in physics — Einstein included — were grappling with the issue, many expected that Richard Feynman himself would be the one to solve it5. True to his style, Feynman tackled the problem with the most powerful tools in his arsenal: perturbation theory methods, which he visualized through his famous “diagrams.” Despite his efforts, the result was a failure, which he candidly admitted in September 1956: “The only reason that we cannot do this problem of superconductivity is that we haven’t got enough imagination”.6 (5) He would recall it in a disheartened, yet never defeated, manner even in the interview he gave to Charles Weiner ten years later: “Oh, during that period I spent an awful lot of time trying to understand superconductivity. I did an awful lot of calculations and developed a lot of methods, which I’ve seen gradually developed by other people for other problems. But I didn’t solve the original problem that I was trying to solve, which was, where does superconductivity come from? And so I never published anything. But I have done an enormous amount of work on it. There’s a big vacuum at that time, which is my attempt to solve the superconductivity problem – which I failed to do”.7
At the very moment Feynman admitted he hadn’t been able to untangle the knot, John Bardeen, Leon N. Cooper, and J. Robert Schrieffer had already grasped it, feverishly completing their efforts driven by the fear that the “wizard”8 was on their trail. The secret, they discovered9, lies in a subtle but crucial interaction between electrons and the vibrations of the metal’s crystal lattice. At sufficiently low temperatures, this interaction allows electrons to weakly attract and pair up10, dancing the Frug like Bob Fosse’s dancers on the Ed Sullivan Show11. No longer solitary and uncoordinated, they move in a collective dance, capable of moving in unison, “like a single wave”, as one gigantic entity (physicists call this “macroscopic quantum coherence”).
Feynman’s disappointment at not having understood the nature of these materials never turned into disillusionment, quite the opposite. This is clearly demonstrated by the Caltech lecture he devoted to the theoretical and experimental successes following the discovery by Bardeen, Cooper, and Schrieffer (by then known to all as BCS). One issue in particular had struck him: a “very interesting situation” noticed just two years earlier by Brian Josephson, a young Welsh physicist who, for this reason, would receive the Nobel Prize in 1973.
Josephson had been able to make a theoretical prediction about what would happen between two superconducting metals separated by a thin insulating layer12. What happened between two normal metals was well known: according to the laws of quantum mechanics, a few electrons would be able to pass from one metal to the other, crossing the barrier like “a good old-fashioned ghost”13 could pass through the walls of an old mansion. Nothing more, nothing less. Josephson went further, hypothesizing that the electron pairs in superconductors could make the same passage not as independent entities, but as part of a single collective wave capable of carrying a current even in the absence of an applied voltage14.
For Feynman, this was the clearest proof that quantum mechanics could manifest even on a macroscopic scale. Satisfied but eager to go further with Josephson’s mathematical description, he then moved on to a simple and elegant mathematical derivation of the effect, using as his leverage the standard toolkit of quantum physics: the Schrödinger equation. It was the same equation that governed the behavior of atoms and could write the future of electronics: “These then are some illustrations of things that are happening in modern times—the transistor, the laser, and now these junctions, whose ultimate practical applications are still not known. (…) We are really getting control of nature on a very delicate and beautiful level. I am sorry to say, gentlemen, that to participate in this adventure it is absolutely imperative that you learn quantum mechanics as soon as possible”.
The third volume of the Lectures was published in 1965, the same year Feynman received the Nobel Prize in Physics. The story of superconductivity seemed to close there, albeit with some regrets. His interests returned to focusing on high-energy physics, devoting much of his time to teaching and popularization and less to his colleagues, since the status of “eminence grise” proved unbearable for him.
A small and unexpected twist, however, appeared at the beginning of 1974, when some intriguing manuscripts, some with “Josephson” prominently in the title15, surfaced on his desk. How could he resist? And once read, how could he not respond?
The letter is dated February 116.
Dear Dr. Scully:
Thank you for sending me your papers on superconductivity. I wish I could make some useful comment on the physics contained within them, but I haven’t studied them carefully.
However, in your paper on the Josephson junction you mention equations (1.2 and 1.3) you say are called the Feynman equations. I guess you canmot be blamed for calling them that but I can remember learning them from somebody else. Long ago when somebody told me, for the first time, about the new ideas of a man called Josephson he explained it with equations essentially like these. I remember being distinctly impressed by the boldness and novelty of using quantum mechanics to describe such macroscopic things. I’was under the impression my informant (who, I can no longer remember) was directly describing Josephson’s ideas.
I have never looked in the literature, but I will bet that if you do you will find these equations in Josephson’s first papers.
I am sorry that I didn’t give references in my “Lectures in Physics” but since it was meant to be a pedagogical work and not a report on original work, I didn’t think it necessary.
If turn out to be correct could you please refer to them as Josephson’s equations. It was such a simple and beautiful idea that Josephson had, all credit should be his.
The reply from Scully and his colleague and collaborator Daniel Rogovin came ten days later17. The point raised by Feynman is valid, they stated, but if those equations are not Feynman’s, they aren’t Josephson’s either, because Josephson not only never wrote them down, but also “never identified the macro-wave function.” Their suggestion, then, is to call them “two-level equations (T.L.E.)”, even though some issues remain because they “are not universally accepted”.
“In our experience”, they write, “workers in the field fall into two categories:”
1) Those who think the T.L.E. are written in stone (mostly experimentalists).
2) Those who think the T.L.E. are only of pedagogical value and should not be taken seriously. We have had first hand experience with these experts, e.g., when I gave a talk at Bell Labs entitled “Is the Josephson Junction really just a two-level atom?”, they all agreed the answer was a big NO! (That was a year or so ago - now we think we can convince them it is yes).
They then add:
In some old correspondence with Josephson he refers to ‘the simple theory given in the Feynman Lectures’. In many later conversations (he spent two summers with us at MIT), we never heard of the T.L.E. coming from other than your book. In fact “everyone” calls them the Feynman equations.
and they conclude:
However, we understand your point, and the last thing we want is to cause you embarrassment. In view of the above (sorry to be so long winded), would you please advise us? Do you agree they should be called the T.L.E. or shall we stick with the “Feynman equations” terminology?
On February 19, Feynman settled the matter in a flash:
Dear Dr. Scully:
OK you win. My memory must be faulty. I guess you can call them anything you like. If “everyone” calls them the Feynman Equations I have no further objection (and, being human, I am more pleased than embarrassed).
Feynman was wrong to doubt himself, but by accepting Scully’s verdict he ratified a truth that the scientific community had implicitly recognized. The “Feynman equations” became such because their formulation, distilled in the Lectures volume, was so clear as to appear inevitable — a work of pure pedagogical illumination that he himself felt more as an obvious derivation than as an original contribution. No claim, then, but a touch of vanity and the awareness that the game of science is worth more than titles and recognition. “The great explainer”18 had thus triumphed once again, in his own way.
Acknowledgments: I would like to thank Judith Goodstein for her kind clarifications, which allowed me to correct some essential points in the text.
R. Feynman, ‘‘The Schrödinger Equation in a Classical Context: A Seminar on Superconductivity,’’ vol. 3 of Richard P. Feynman, Robert B. Leighton, and Matthew Sands, The Feynman Lectures on Physics (Reading, MA: Addison-Wesley, 1963–1965), Chapter 21.
R. P. Feynman, ‘‘Theory and Applications of Mercereau’s Superconducting Circuits’’ transcript, October 29, 1964, Richard P. Feynman Papers, California Institute of Technology Archives, Box 6.14, pp. 1–4
Joerg Schmalian, Failed theories of superconductivity, Modern Physics Letters B 24 (2010) 2679
David Goodstein and Judith Goodstein, Richard Feynman and the History of Superconductivity, Phys. Perspect. 2 (2000) 30
at the International Congress on Theoretical Physics, hosted by the University of Washington in Seattle (September 17–21, 1956). The presentation was published in issue 2 of volume 29 of Reviews of Modern Physics, in April 1957 [R. P. Feynman, Superfluidity and Superconductivity, Reviews of Modern Physics 29, (1957) 205].
Interview of Richard Feynman by Charles Weiner (4 March 1966, 27–28 June 1966, and 4 February 1973). Niels Bohr Library & Archives, American Institute of Physics, College Park, MD USA
Max Kac, Enigmas of chance: an autobiography. New York: Harper & Row (1985)
J. Bardeen, L. N. Cooper e J. R. Schrieffer, Microscopic Theory of Superconductivity, Physical Review 106 (1957) 162
These pairs were named “Cooper pairs” because Leon N. Cooper had already predicted their possible existence in Bound Electron Pairs in a Degenerate Fermi Gas, published in Phys. Rev. 104, 1189 (1956). The journal received the article on September 21, 1956 — curiously, the final day of the Congress in which Feynman laid down his arms.
The analogy with the Frug, a popular dance in America in the 1960s, comes from J. Robert Schrieffer. It can be found in Superconductivity: A Dance Analogy, American Institute of Physics (2017): https://history.aip.org/exhibits/mod/superconductivity/03.html. Here
you can enjoy Bob Fosse’s choreography. The Chicken Dance, from which the Frug draws inspiration, would work just as well.
B. D. Josephson, Possible new effects in superconductive tunnelling, Physics Letters, 1(7), (1962) 251
George Gamow, Mr Tompkins in Paperback, Cambridge University Press (1965)
Josephson was inspired by the work of Ivar Giaever, a Norwegian physicist, who had experimentally studied electron tunneling in metal–insulator–superconductor junctions — work for which he received the Nobel Prize the same year as Josephson.
Presumably D. Rogovin, M. O. Scully, and P. Lee, “Quantum Theory of Josephson Radiation,” Progress in Quantum Electronics 2 (1973) 215; D. Rogovin and M. O. Scully, “Does the ‘Two-Level Atom’ Picture of a Josephson Junction Have a Theoretical Foundation in BCS?,” Annals of Physics 88 (1974) 371, received by the journal in December 1973.
Correspondence between Richard P. Feynman and Marlan O. Scully and Daniel N. Rogovin (February 1–19, 1974), Box 80.17, Richard P. Feynman Papers, 1933–1988, California Institute of Technology Archives, Pasadena, California.
I will not reproduce the full letter from Scully and Rogovin here, but I hope to revisit it at some point to explore the technical and scientific details in depth, especially since these are topics I worked on myself during my time as a researcher.
The Lectures, before their publication, elicited very different reactions among students, partly because the material was conceptually advanced, the explanations often unconventional, and the exercises demanding; as a result, they were not always understood or appreciated as one might expect. I recount this in “Buon compleanno, Mr. Feynman”, Le Scienze 597 (May 2018), but it is an issue I will return to sooner or later.