In celebration of 100 years of superconductivity research

Dynamics of scientific discovery:
THE HISTORY OF THE BCS THEORY OF SUPERCONDUCTIVITY
With some comments on biology

by
Kristian Fossheim

Physics Department, The Norwegian University of Science and Technology
and
The Royal Norwegian Society of Sciences and Letters, Erling Skakkesgt 47c
7491 Trondheim, Norway

Notation
L: Professor Leon N Cooper
I: Interviewer, Kristian Fossheim

Stockholm 1987

I: Professor Cooper², sitting here in your office at Brown University I am reminded of a previous occasion when we met, … this was in Stockholm in December 1987 when Bednorz and Müller got their Nobel prize for the famous discovery of cuprate superconductors. The day after, in the Physics Department at Kungliga Tekniska Högskolan, there was a session …
L: Oh yes, I remember, there was a panel discussion …

I: That’s right, you were in the panel. There was a tremendous applause in the packed auditorium, and everybody stood up when the laureates entered the room from behind, walking down the stairs, and I was with them. That was kind of a great moment, I felt. And I remember you were sitting in the panel, and we greeted briefly.
L: Do you remember what I said about high-T_c superconductivity?

I: No I don’t. Do you?
L: Sure. It was something about the possibility of the new high T_c superconductors going from pairs with very large coherence distance near T_c to those with a coherence distance so small they are like real bosons. This might not be possible in the present high temperature superconductors, but recently in the Bose-Einstein systems with tuneable Feshbach resonances one seems actually to see the transition between coherent BCS¹ pairs and bosons.

Early experience with science

I: Now about your own work and background, could you tell us how you got into science? Was there anything in your family history that would point towards an academic carrier for you?
L: I don’t think, especially. Maybe far back.

I: Do you know now why you entered into science?
L: I liked it; I guess I was good at it; so I got reinforcement.

I: Exactly.
L: Then I went to some good schools, and enjoyed what I was doing.

I: Which schools?
L: Well, I went to the famous Bronx High School of Science, where actually, I worked on projects in biology, bacteriology.

I: I see … that might explain something you did later.
L: Yes, in fact the project for which I became a finalist in the Westinghouse Science Talent search was to grow a strain of bacteria normally susceptible to penicillin, and make it resistant to penicillin. Or more resistant. And the strain of bacteria was Bacillus Subtilis. Basically I just grew the bacteria in varying concentrations of penicillin. And I took the one that grew in the highest concentration and repeated the procedure. Finally I got variants that grew in higher concentrations. The next project was to figure out why, but I never got to that.

I: This is really a problem nowadays that people are very concerned about.
L: Of course, but I think people have a much better idea about possible molecular mechanisms now.
At that time, I don’t think anybody really knew.

I: But the fact that you were able to do it could be a little warning signal to the use … the overwhelming use of penicillin.
L: Well, it seemed reasonable to believe that there would be variation in the wild type in terms of how it could handle penicillin. And if you kept taking the ones that handled penicillin best, then it seemed reasonable. Actually, it wasn’t so easy to do it because the new strains reverted very quickly to the wild type. But you have to remember that I was just a student, so I had to wash my own test tubes.
I: A limitation, I guess.

Why science?

I: So, you became interested in science and found out that you had talent in that direction. You compared yourself to the rest of the class, and found that you did very well?
L: Well, I certainly did very well.

I: So when did science become a fascination?
L: Well, as I said … probably when I was in junior high school. At that time I had a little laboratory where I would make experiments.

I: A laboratory at home?
L: Yes, it was in a closet. I used to mix chemicals, make magnets and do photography. Actually, when I was in college I loved classics, literature and philosophy. So science wasn’t my only interest, but it was the direction I decided I wanted to go.

I: So it wasn’t a difficult choice for you to make?
L: Well … my father didn’t think it was the brightest thing in the world to do, but it was better than my previous choice, which was to be a fighter pilot.

I: Really?
L: And then when I was in college I had to worry about whether I should go into biology or physics. I chose physics.

I: Did you have any teacher who inspired you?
L: Yes, I remember a teacher in junior high school and … there were other teachers. In particular at the Bronx High School of Science there was a woman who maintained the laboratory where you could do experiments. She was just a terribly nice woman. Probably the reason that I did biology rather than physics was that they had a biology laboratory, and they didn’t have a physics laboratory. So I just worked there every afternoon.

I: Let’s jump to your university studies. What was your thesis on?
L: It was on nuclear physics, mu mesonic atoms. mu meson/lead atoms had an unexpectedly large energy in transitions from 2p from 1s levels. This led Ernie Henley and me to the conclusion that the charge distribution of the nucleus was smaller than had been thought previously. And that the charge radius was smaller than the neutron radius. I did my thesis with Robert Serber, who was Oppenheimer’s lieutenant at Los Alamos. In fact, I teach in a course based on the play Copenhagen, that you may have seen, in which we refer to Bob Serber’s famous introduction to nuclear physics—must reading for all the physicists who came to Los Alamos. That’s what we were working on …

I: Do you remember when you first learned about superconductivity?
L: Well, it probably was mentioned in some kind of course I had, but I don’t remember paying too much attention. I know it was mentioned in a book I studied from, a book on thermodynamics by Boorse. But I don’t think I paid too much attention.

Bardeen³

L: I was really introduced to superconductivity when Bardeen came to Princeton, The Institute for Advanced Study. He was looking for a field theorist who was willing to work on the problem of superconductivity. He had written to C.N. Yang and T.D. Lee⁴ , and they apparently both suggested me. So Bardeen came and talked to me, and I said “You know, I don’t know anything about superconductivity.” I hadn’t even had a course in what we then called solid-state physics. Bardeen said, “That doesn’t matter, I’ll teach you everything you need to know. Don’t worry about it.” At the moment, I felt that I wanted to do something a little bit different, so I decided to try it.

I: And in what stage were you in your studies then?
L: I was a post doc.

Cooper pair⁵

I: But you did your Cooper problem alone?
L: Oh well, yes … I was working with Bardeen at Illinois. At first he wanted me to apply quantum field theoretical techniques. So I started doing that, in September in 1955. I gave some lectures to a small group at the University of Illinois on what were then the latest techniques such as renormalization methods and functional integrals in quantum field theory. At the same time I was trying to apply them to superconductivity. As I learned more about superconductivity I became increasingly troubled. I remember several lectures by Pippard particularly, where he talked about the simple facts of superconductivity: specific heat, Meissner effect, etc. It seemed that in spite of the great complexities and differences between metals there were profound similarities when one entered the superconducting state. Fortunately, we were not aware of or did not focus on the many complexities and variations that have since become evident. But this is the way theories are constructed: First try to capture the new qualitative features. The complication will hopefully fall in place later.
At Illinois we all thought that an energy gap in the single particle excitation spectrum was a key feature that distinguished the superconducting from the normal state. I began to worry that the approach I was taking was too complicated. The problem seemed simple, but baffling. My motto has always been: Don’t solve a complicated problem if there is a simpler one you don’t understand. And so I began to think about the fact that the normal metal was reasonably well understood. But as soon as you put in any interaction between the electrons, then you have this tremendous degenerate situation. And nobody understood that. I thought, “That seems really to be a simple problem in quantum theory.” I remember talking to Joe Wenescer. “Joe” I asked, “is there some way to solve degeneracy problems in quantum theory?”” He said, “Why don’t you look it up in Schiff”. I said, “Joe, I already know what’s in Schiff, but this is more complicated.”
So then I went off on a long tangent trying to think about this problem, which really is a problem of a highly degenerate matrix. I got every book I could find on large matrices, stochastic matrices, etc, Bardeen thought I was out of my mind; he didn’t know what I was doing and began to worry about me. But I had a ferocious stubbornness and I just kept working and working. Everybody asks me “How did you get to the idea of the pair?” What I was trying to do was to find a way to approximate the diagonalization of a very large degenerate matrix. One standard technique is to diagonalize easy sub-matrices first, so I looked for diagonizable sub-matrices. If we have a pair above the Fermi sea, with zero momentum and spin zero, many states are connected to each other. By then I was making simple approximations, such as neglecting variations in kinetic energy. Then I saw that there were these matrices, these big blocks, so that everything connected to everything. And I could diagonalize them. And as soon as I did that, I saw that you have this coherent state with a binding energy independent of the volume. If you estimated the number of pairs the entire energy was the right order of magnitude – one could make it a variational solution. Suddenly there it was; a state that was qualitatively different.

Schrieffer

L: The key thing was that the existence of the Fermi sea was serving to make the ground state highly degenerate. I was convinced, but to convince everyone else was another matter. I think Bob was the first one that took this seriously. We both saw that the next problem was to put the pairing idea into a wave function for the many electron system.
I: So you mean Bob Schrieffer?
L: Yes, Bob was Bardeen’s graduate student. We used to talk all the time. He was upstairs, in what they called The Institute for Retarded Studies. He would say “Bardeen, gave me this problem; I’ll never get my PhD!”

I: Quite amusing, considering what happened later.
L: So we used to socialize together, and … so, I think I had the idea of the pair approximately in February ’56, and I first presented it in a lecture … maybe in March or April at Illinois. I wasn’t as experienced as I am now; what I should have done was to embody the pairs in a wavefunction so that we could calculate. I was just proving theorem after theorem, doing Green’s functions above Fermi spheres to show that you got bound states and so on. Bob made the next important step; he wrote down the wave function that embodied the pair and in a way that was consistent with the exclusion principle. As soon as he did that, we could seriously calculate something. And when he showed it to Bardeen, he was convinced. That was what convinced Bardeen. And as Bob said “We’ve turned the battleship around.” This was about January of ’57. I remember that there was some conference that we both went to, and Bob wrote down the wave function, I think he said on a New York City subway⁶ .

BCS paper

I: But when you wrote your paper on the Cooper pair, what was Bardeen’s reaction to that?
L: He was sceptical. But to give him credit, the paper was sent to him to review for the journal, Physical Review. He asked me to change a few things, but then he accepted it, even though he thought it was a too abstract, too mathematical.

I: It is almost surprising that you managed to publish the BCS paper already in ’57, it was a huge step.
L: I think it was at the end of January of ‘57 we started working seriously together. I remember coming in one morning, and Bardeen said “Let’s write a paper together on superconductivity.” From that moment we calculated day and night continuously for the next six months. It was the most intense, unbelievable amount of calculations. But you see, we were really ready for it; Bardeen knew every normal metal calculation. And by then I had mastered the electrodynamics, I had been working on that. Bob had been working mainly on thermodynamics. And we just had to get a few other things into place, the excitation spectrum, how to handle the new matrix elements. There were several wonderful and unexpected discoveries. For example, for a while we would get a London penetration depth with a factor of 1/2, and we were tearing our hair out and started to say “Fine, maybe that’s the way it is.” And suddenly one time at a concert … I mean, this calculation was totally in my head … I saw that you could go from the initial to the intermediate states by two coherent paths. And I remember that I could do the entire calculation in my head at that time, but since there were several creation and annihilation operators with sign changes, I couldn’t be sure of the sign. I could see that the other path would be equal in magnitude, but one sign would give the Meissner effect with exactly the expected penetration depth; the other would give zero. The family fortune was on the roulette table: double or nothing. When I did the calculation I saw it had come out our way.
I recall coming in early the next Monday morning to tell Bardeen. He listened carefully, as usual, showing no emotion as I was excitedly going through the calculation. When I was finished, adding with a flourish, “So you see London’s penetration depth comes out just as expected,” his only comment was “hmmm.” But by that afternoon he had modified all of his calculations to include the new term. Easy problem?
Before we solved the problem of superconductivity, everybody considered it extraordinarily difficult, possibly unsolvable: There were theorems that said you can’t solve it. But after we solved it, it became regarded as easy. One physicist wrote that it was disappointing that the problem of superconductivity was solved just by this inserting a piddling interaction between electrons. This is a pattern that occurs in scientific problems. There is a sequence. Before you solve it, people try but don’t succeed. Then they begin to prove that it is not solvable. Finally someone solves it, and then they say “Oh, that’s trivial, in fact I even … if you look at the footnote of my paper …”

I: Like the famous Columbi egg.
L: Yes.

I: According to the famous anecdote he was sitting dining with some people, and somebody in the party said that “Well, sailing to America wasn’t that difficult.” Columbus said “Can you make this egg stand on its head?” And man tried, but he couldn’t. So Columbus pushed it a little hard, and it would stand. And then the guy said “That was easy.” And Columbus replied “Yes, but I did it.”
L: Well, if you look at problems that are regarded today as insolvable … they go through the same thing, and when people solve it, they say it is easy.

Approximations

L: Another thing, if you’re interested in anecdotes, after we published the paper of superconductivity, for a couple of years I worked on this with Birger Stölan.

I: Yes, my later colleague in Trondheim.
L: I was interested in seeing how you could start from the full many-body problem, and show that in some approximation you would get the kind of pairing that is the basis of the BCS solution. We worked on it for quite a while, and we had enormous numbers of Feynman diagrams. It should have been do-able, but we never really succeeded. I thought that … since the phenomenon occurs for an interaction that is infinitesimal, what you could do is that you take a little shell at the Fermi surface; there is a natural small parameter. Consider that problem, neglect the variation in kinetic energy. And then you could see that the amount of phase available is a strong-function momentum of the paired electrons. Birger and I worked on this for a long time. We hoped to use this as a parameter in which we could make an expansion, and show that somehow the pairing came out; it turns out that it’s not easy. Anyhow, I was giving a lecture on this at some point. And after the lecture a young man comes up and says “I don’t understand why you are working on it, everybody knows that there is a pair condensation.”

I: Really funny!
L: And this was only a couple of years after I was a voice in the darkness myself, so times change.

I: In the expression for T_c you introduced the Debye frequency. Was it obvious that it should be like that? Because that’s sort of a high frequency, and you are at low temperatures where you don’t have formulas of that kind.
L: The reason for using that, is that this was the range, according to a simple field-theoretical calculation, for which the interaction would be attractive. And you see, the intriguing thing was that you didn’t use most of this range because of the exponential factor. So that was one of the things we were qualitatively explaining, why the Debye frequency was the rational parameter. I mean, why are you only using such a small part of that range? Well ok, because of the exponential factor. But the reason for it was that this was the range for an attractive interaction between electrons.

Breaking the news

I: My next question here is: How did you break the news, that you had a theory, the BCS theory? Did you announce it in a dramatic way, so to speak?
L: Well, I think … among the people in Illinois we had lunch every day and told each other what we were doing; so they were terribly excited. And then what happened was that we submitted a post-deadline abstract to the annual March meeting of the American Physical Society. More precisely, we submitted a letter and then a post-deadline abstract. Bardeen wanted Bob and me to present it. And that was just very generous. And then what happened was that I got to the meeting, and Bob had gone to New Hampshire to visit a friend, and he couldn’t make it to the meeting⁷ . I was carrying his slides. So I gave both parts of the talk, both his and mine.

I: What was the reaction at that meeting?
L: Fantastic!

I: It was? So there was a big audience, because people had already heard…?
L: Packed chamber.

I: So they knew.
L: Fantastic reactions. I didn’t appreciate how fantastic it was.

I: Were people standing?
L: I don’t remember. Some things take time. And I had taken so much time on this … but BCS gained instant recognition, instant. But then there were complaints.

I: Gauge invariance?
L: Gauge invariance. I mean our attitude about things like that was that “We’ll clean it up afterwards.” The big fuss was that for the theory to be explicitly gauge invariant we had to include longitudinal excitations. But we knew that longitudinal excitations, because of the long-range Coulomb forces, would be of very high energy. Bardeen and I used to talk about it, and then we just said… “Sure, we have longitudinal excitations, but we don’t have to worry about them”.

I: OK, so when did it become formally solved? Was it into the ‘60’s?
L: Various people, Anderson⁸ and others attacked the problem. I think it was solved best by the Green’s function methods. There were various things we did, that had to be cleaned up. A new set of ideas often has initial inconsistencies (consider the Bohr atom). You can have two attitudes: one is that it is inconsistent, so throw it away, and the other is that there is so much in the ideas; the problem is to make them consistent. It’s like a little boy who is an optimist, so optimistic that his parents wanted to teach him what the world is really like. And so for Christmas they gave him a pile of manure. They tiptoe down on Christmas morning, and they hear him singing and whistling, singing and whistling. And they went to look in his room. And there he had a shovel, and he says “In all this manure, there must be a pony some place.”

I: Good!
L: Consider Dirac’s vacuum. With the stroke of a pen, he changed the concept of vacuum from the vacuum as a void,.But the thing to do is to really make it sensible, this happens over and over again. It was something we worried about, but I remember that I talked to Bardeen about it. We knew that were would be longitudinal excitations; they had to be there. But they would be at a higher energy; that’s the current view now. You have gauge type theories, and massive bosons. So it didn’t particularly surprise me, I guess … but everyone else might ask “Why didn’t you work on it?” Well, frankly, I was exhausted. Just exhausted.

I: Do you think that this problem was one reason why it took so long time before the Nobel Prize was awarded to you?
L: Gauge invariance?

I: Yes.
L: No, I don’t think so. That was understood very quickly. The big problem for the Nobel Prize was that Bardeen had already won the Nobel Prize in Physics.

I: Was it?
L: I believe so; he had already won the Nobel Prize in Physics. And I think he is the only person to have ever received the Nobel Prize twice in the same field. That was a problem. I was told the committee thought for a long time if they should have some other combination. But frankly, I think that they did exactly the right thing.

I: Yes, of course.
L: It would have been terrible to leave Bardeen out; he felt that superconductivity was so much more important than the transistor as a scientific problem.

I: Really? He felt that?
L: Oh yes. Superconductivity was the holy grail. So I think the committee did exactly the right thing, but I believe that was what held them up. That’s why there was a long wait.

I: But you knew all the way, from the beginning, that this was the solution? You were convinced about that?
L: After the pairing idea was conceived, I was convinced; I was terrified, but I was convinced. It was a very painful period; because it was very difficult to convince others, and there were some very famous people out there. Well, knew is a strong word, but I certainly believed that the pairs were the basis of a solution. But after BCS there was no longer any doubt.

Other contributions?

I: Were there other experimentalists or theorists that contributed in this process, that helped you get around?
L: Do you mean during the period of calculation?

I: Yes.
L: Charlie Slichter in particular. The atmosphere in Illinois was that everybody helped everybody. We talked at lunch almost every day. Bardeen was interesting in this respect, because with all his talent, he did not have a great capacity to communicate. I remember that we’d spend all morning defining symbols, terms and kinds of stuff. Then we got to lunch, and he would start to talk to the people as if they had been there in the morning conversation. You could see that they were really puzzled. But we’d talk and talk, so there might very well have been suggestions.

I: Yes, I just wanted to ask …
L: Well, Charlie Slichter is one person, because he learned how to do the calculations, and was doing them as fast as we were. I remember he found some errors.

I: In both de Gennes’ book on superconductivity as well as in Tinkham’s book, Hebel and Slichter’s experimental work on nuclear spin relaxation is emphasized. The coherence factors are different in ultrasound attenuation and in nucelar spin relaxation. Both de Gennes and Tinkham considered the way BCS explains this difference as one of the major successes of the BCS theory.

I: Now another subject: Flux-quantization… when did you learn about that?
L: When it happened! Of course. And then the Josephson⁹ junction theory. We were so close to having the Josephson results. Because actually at that time I was working on the proximity effects; the penetration of the wave function into neighboring material But then, you can’t win them all.

I: There is an anecdote about that, maybe I can test you on it … I’ve heard that Josephson came over to the US and gave a talk … I don’t know whether it was at the March meeting. Bardeen was sitting on the first row listening, but he didn’t believe it, even protested. Is this correct?
L: It was later than the March meeting. That’s what people say, I don’t remember that. But I do remember discussing it with Bardeen. I believed it, but he had his doubts. I don’t think he really thought of the wave function going coherently into the junction. I’m not sure about his reasons. But I remember talking to him about it. I believed it, because I had been working on this coherence in the proximity effect. If he didn’t believe it at first, he came to believe it eventually¹⁰.

Present problems: Biology

I: When it comes to the difficulty of solving problems, your present problem is even harder than superconductivity.
L: The interaction of many cells instead of the interaction of many electrons. That was one of the things that attracted me in the first place.

I: Is there some similarity?
L: Well, I don’t know … I think that if I have any gift, it is to look at very complicated problems and try to extract some simple essence that contains the qualitative effect.

I: Isn’t that really the nature of good physics, very often?
L: That’s what I believe.

I: When you look at for instance … a very good example is phase transitions, critical phenomena. You literally do this, you throw away a lot. You keep only the essential part, and that does everything.
L: That’s right. That seems to me to be the essence of really good physics. You know, Einstein said “Make things as simple as possible, but no simpler”. You have to take an intellectual risk, because what you throw away might be the essence. And you also take a political risk, because what you throw away might be something that someone worked on for their entire life. And especially in biological problems, you get some very aggravated people. What I focused on is: What is the molecular and cellular basis for learning memory storage? Where and what takes place on a cellular level, when we learn? And at first it seemed like an impossible problem but nowadays I think we’ve almost solved it.

I: So how can you express it?
L: Well, we think we know the systematics of the changes, how the changes depend on receptors and molecules involved and variables such as cell firing rates. One of our earliest formulations—25 years old already, is known as the BCM-theory.

I: What does it mean?
L: It stands for three authors, Bienenstock, Cooper and Munro¹¹ . Most people in neuroscience know me by BCM. Once in Washington someone was introducing me and mentioned BCS. The woman sitting next to me, a very famous neurophysiologist, said “Didn’t he get that wrong?” And I said “No, no, it’s ok, don’t worry about it.”
So I like to say that I have the good fortune of being sandwiched between very gifted colleagues.

I: That’s really a nice way to put it.
L: BCM’s postulates have also been tested experimentally, and confirmed. And some of the very subtle consequences have been tested experimentally. Experiments have been designed expressly to test the consequences of this theory, and they have uncovered new phenomena. It is very rare that this has happened in neuroscience. And to me, if we do this, this will be one of the great achievements … to bring serious mathematical structure into neurophysiology. After all, that is what Galileo did for physics, isn’t it?

I: Indeed.
L: We are now at the stage where we are working on the underlying molecular mechanisms. In fact I am just working on a paper with some colleagues, which proposes a single underlying molecular mechanism to explain synaptic modifications that are known to occur. And we know that there are changes that take place in certain molecules, and in the cell-surface there are so many things going on …so much though, that I would say that this particular problem of cellular basis for learning memory storage probably will be resolved in the next couple of years. The next problem is how this is put together when we do processing. And the hardest problem is how you construct mental states, how we become aware of ourselves, conscious and so forth. And these problems are regarded as so difficult, that as you know, some people say they are insolvable.

I: Do you think it is solvable?
L: Well, you never know until you solve it. But why shouldn’t you try? After all, a hundred years ago people would have said that there is a fundamental distinction between living and unliving. Between organic and inorganic. And then a hundred years before that, between celestial and earthly material. And now, not only have all of these things been resolved, but we see that the distinctions aren’t very good. That there is no clear denotation of living and unliving, or whatever you want. It is a matter of definition. And the same things might be for this situation, we don’t know. But then again you don’t know until you’ve solved it, but when you’ve done that it looks easy.

Prions

I: Would the prions be examples of something in between living and unliving?
L: I think I would classify a virus, as more clearly something in between. Something that can reproduce when it captures cellular machinery, but without that cellular machinery can’t do the job by themselves. It seems more likely that a prion is a protein gone bad. In fact, when you think about it, it is somewhat miraculous that with all the proteins floating around, they don’t get in each others way very much. Well, of course if they got in each others way things wouldn’t succeed, so part of the process of evolution is to sort that out. But you can ask conceptually, suppose there is a protein that interacts with another protein in a devastating way; that would be highly poisonous. And if it can interact with the protein in such a way that makes the protein make a transition from its initial folding to another folding, which then makes the prion duplicate itself. Then you would have a very deadly possibility. We have been thinking about this a lot—trying to find a model. But I don’t think that that really should be classified as a living thing. You know, that’s just a question of definitions. You can say that a living thing is something that can reproduce, you can say that a living thing is something that can speak, or … I was once having a discussion at a dinner in London with a lady. I said “It’s a continuum, because you can teach apes language.” And then she says “Oh no, an ape can’t quote a line of Shakespeare”. And I thought to myself that there are many human beings who can’t quote a line of Shakespeare.

I: Indeed!
L: So you can make the distinction as you wish, but my own opinion is that it’s a continuum. And maybe that goes for consciousness. That the transition between conscious and unconscious in phase transition language is second order—consciousness comes out of the shadows and we gradually become conscious. This might very well be the case for every human baby. But the heart of the problem, as I like to put it, to paraphrase Santayana who once said “All of our sorrow is real, but the atoms of which we are made are indifferent.” To my mind, the problem can be stated very simply: How do you make real sorrow out of hypothetical atoms? That’s an unsolved problem. And that is the problem that some people think is unsolvable. The use of words such as consciousness is subjective. My answer is: Give us a couple of years. Everything is unsolvable, every hard problem has been unsolvable, but then it is solved and then it is trivial. It’s like we talked about just a minute ago. Well, that doesn’t mean that we will always find solutions in the usual way. I can’t prove that you can find solutions, but personally I think that throwing up your hands and saying you need another law of nature and so on … why give up so fast? But then you see here I am just a card-carrying, working day scientist. A “no nonsense physicist” as one reviewer of my elementary textbook wrote some time ago. That’s what I believe.

I: Professor Cooper, thank you very much for sharing your memories and thoughts with me and with present and future generations of scientists!

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¹ For the non-specialist: The acronym BCS is formed from the initials of the theory’s three inventors: J. Bardeen, L.N. Cooper, and J.R. Scrieffer, Phys. Rev. 108, 1175 (1957). The three shared the Nobel prize in physics in 1973.
² Professor Leon N Cooper, Nobel laureate in physics 1973 for his contributions to the BCS theory of superconductivity, born in New York City, 1930. The interview took place in Professor Cooper’s office at Department of Physics, Brown University, Providence, Rhode Island on April 9, 2001. The interview was videotaped. Some editing upgrading of the transcription was later performed for the sake of precision, easy reading and concentration of textual material. The resulting text was approved by Professor Cooper in august 2011. Due to Professor Cooper’s later change of scientific direction into biology and neuroscience, this subject is also touched upon towards the end of the interview, including comments on the nature of life.
³ John Bardeen, twice Nobel Laureate in physics, in 1956 for his contribution to the discovery of the transistor, and in 1973 for his contribution to the BCS theory.
⁴ C. N. Yang and T. D. Lee shared the Nobel Prize in physics for 1957
⁵ L. N. Cooper, Phys. Rev 104, 1189 (1956)
⁶ This statement was later confirmed by J R Schrieffer in an interview at National High Magnetic Field Laboratory in Tallahassee, Florida in 2001, to appear in a collection of interviews of Nobel laureates on Springer Verlag in 2012
⁷ Schrieffer later confirmed this to the author. The reason was that he had got stuck in New Hampshire due to heavy snowfall.
⁸ P.W. Anderson. Receipient of the Nobel Prize in physics 1977
⁹ B.D. Josephson, Phys. Lett, 1, 251 (1962)
¹⁰ This event has been confirmed by Josephson in a later interview with the author, to appear in the Springer book mentioned above.
¹¹ Bienenstock, E. L.. L. N Cooper, P. Munro (January 1982). “Theory for the development of neuron selectivity: orientation specificity and binocular interaction in visual cortex”. The Journal of Neuroscience 2 (1): 32–48.