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Credit: Cornell University Physics Department
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In footnotes or endnotes please cite AIP interviews like this:
Interview of Toichiro Kinoshita by Robert Crease on January 9, 10 & 18, 2016,
Niels Bohr Library & Archives, American Institute of Physics,
College Park, MD USA,
For multiple citations, "AIP" is the preferred abbreviation for the location.
Interview with Toichiro Kinoshita, a Japanese-born physicist who is best known for pioneering the value of muon g-2, the anomalous magnetic moment of the muon. Kinoshita describes his education—Daiichi High School, Tokyo University—how he avoided military service during World War II, and meeting and marrying his wife, Masako Matsuoka. He describes his introduction to quantum electrodynamics and renormalization through papers by Dyson and Feynman. His early research also involved work on the C-meson theory developed by Sakata. After the war, Kinoshita came to the United States to the Institute for Advanced Study, then as a postdoc at Columbia in 1954. In 1955 Kinoshita moved to Cornell. He became particularly interested in making calculations to test the theory of quantum electrodynamics. He describes his introduction to computers at Princeton, using von Neumann’s computer. The interview covers how he became interested in calculating g-2 at CERN in 1966, and his subsequent efforts, the first being the sixth order calculation, where the light-by-light diagram enters for the first time. He describes his efforts doing the eighth order calculation, and his collaboration with Makiko Nio, as well as his calculations of the tenth order. Physicists whom he describes more than briefly include Kodaira, Tomonaga, Nambu, and Nio. Near the end, Kinoshita describes the importance of g-2 experiments, and his recent work.
My name is Robert Crease, and I’m interviewing Tom Kinoshita. And it is January 9th, 2016. I would first like to ask you some questions about your childhood. Can you tell me about your parents?
My parents—let’s see. My father was a middle school teacher, of English.
What kind of education did he have?
He graduated from Waseda University in Tokyo. Actually, he majored in French, but there were no jobs for French teachers, [laugh] so he taught English.
And your mother?
My mother was just a housewife.
And where were you born?
Tokyo, when my father was still a student at Waseda University.
At one point, your uncle came into your life. What happened?
Your uncle. You were adopted by your uncle?
That’s a very complicated story. [laugh] You see, my father was the youngest son. My uncle was the first boy, and my father was the youngest. And their ages, I don’t know exactly, but they were something like more than 15 years apart. And my uncle didn’t have any children. And so, my grandparents decided to sort of—my father becoming the—what do you call—succeed my uncle.
The father would inherit the—the person who inherits everything?
Actually, it’s more complicated. [laugh] See, my uncle probably didn’t have anything beyond a middle school education. And he in the household was a kind of farmer. So, my grandparents owned pretty much rice field. And then they decided to split this land into two, one piece inherited by my uncle, and the other one, by my father. However, since my father was a schoolteacher, the inheritance was supposed to come only after he retired from school teaching. And, of course, that didn’t happen for quite a while. On the other hand, my grandparents worried about what would happens after my father passed away, so I became the heir of both my uncle and my father. That was set-up without me, but somehow [laugh]—and my grandmother wanted to keep me near her, and so after the first six years with my parents—after I went to nursery school and so on— in the first grade of elementary school I was moved to my uncle’s and my grandmother’s house, away from my parents. And then I stayed in that situation through elementary school, which is six years, and then middle school, which is another five years. Then I entered something called high school (in Japan), which is actually junior college (in U.S. terms). That was in, I think, 1942.
Well, wait a minute—’42, you were in college. But what about your secondary school, your high school?
High school is from—five years before that. The system is different from the American system. It’s more like a German system, gymnasium and so on. So, I had six years of elementary school, five years of middle school, and then went to so-called high school, which is actually now part of the Tokyo University. I was supposed to graduate high school in ‘45, but since this was during the war time, the curriculum was sort of compressed, and the first-year of curriculum was taken in a half year, and the second year was another half year. So, I went to Tokyo University in ‘44.
Interesting. This secondary school, which you say was kind of a junior college—
No, no, no. Middle school, secondary school, which is equivalent of the high school here, more or less.
Did you have to take a test to enter?
Of course. Every step, we have to take exam.
And what was the name?
The secondary school and then the…
There are two so-called high school. One is a secondary school, and that’s five years. And then another three years of so-called high school, which is the junior college.
Did they have names, both of these?
Daiichi High School. The first high school.
And the second one?
No, no, that’s the second one.
You see, the secondary school—first of all, I grew up with my grandmother’s family, and this was a rural area. It was in a small village. And my elementary school was a very small school with 40 to 50 students at each grade. Then I entered the secondary school, middle school, for five years, which was actually school of the prefecture, a larger area. The prefecture is called Tottori.
Tottori. How do you spell that?
That’s the prefec…
Prefecture. And actually the city’s name is also Tottori. The population of the city is about 50K, which is not a big city, but it was about 10% of the population of the prefecture. And the city is about 200 miles or kilometers west of Kyoto. It’s not very far from Hiroshima, actually. Now the second stage of high school is a national…
Ah, OK. And that was Daiichi?
Daiichi. Because some national colleges were numbered from Daiichi which is number one, to number eight.
So, Daiichi was Japan’s number one high school.
Highest—most difficult place to get into.
Yes, and you got into it.
Do you remember the test at all?
You see, you can apply to the university after fourth grade in this secondary school. Which I was not clearly prepared for the next level [laugh] so I failed that test. And I still remember the math problem [laugh] which failed me. [laugh]
What was it?
It was a geometrical problem. And it’s—you see, you have some kind of strange polygon, and you want to attach it to a, let’s say, two-meter-wide road outside. And, of course, the shape is very strange, and of course unless you see the answer right away, you waste all the time. The point is at the corner, if you take just a straight line, it’s no longer two-meter-wide edge. You have to make it circle, and then it’s much easier to calculate right away. [laugh] And so somehow this problem sort of threw me over. [laugh] And I failed to pass the test.
But you passed it the next time around?
Next time around, I was very [laugh] prepared. In fact, I was so well prepared I think that I came in at the head of the class. [laugh]
So, you entered there in ‘42. Am I getting this right?
Yeah. That’s right. And it was few months after Japan started the war with the U.S. and other nations.
And what was it like going to school during the wartime?
Tokyo was bombed sometime in, maybe, May of 1942 for the first time. And this is just a few months after I entered this school. Our school was slightly away from the military zone, and so we are spared, I think. But anyway, every so often there was an air raid, and then you had to stop doing something, and go into the shelter, and so on.
Did you have to walk to school and back?
No. There was a dormitory. And, in fact, at this school, everybody had to stay in the dormitory. So, there was no problem as far as getting to school. [laugh] Of course, the other problem was that food became less and less available.
So, you went hungry?
Not that hungry, but clearly the food quality went down.
Didn’t you tell me once that you ate too many pumpkins?
[laugh] Sweet potatoes.
Sweet potatoes. That’s right. So, the only thing that would grow well in those conditions was sweet potatoes?
Yeah. Well, but still, it’s not too bad. It became worse and worse [laugh] as it went on.
So, you went to that school from ‘42 to ‘45.
Yeah, that was the intention. But because of the war, everything had to be accelerated so that they could put the young men into the field as soon as possible. So, the school was actually cut to two and a half years: ’42 to summer of ’44.
So, did you learn any science in the school?
Yeah. The courses were not curtailed. We had a full course load—physics, chemistry, biology, and so on.
And did you know any—had you met Nambu yet?
No, much later.
Did you meet any physicists, people who later became physicists, in that high school?
At this stage, no.
And any good teachers?
Well, I suppose they are good teachers, but—well, let me go back to elementary school. They had a small, tiny library, just something like this stuff [his home bookshelves], in the elementary school. I read a book there—probably I read all of them [laugh]. What I particularly remember is a book on Thomas Edison, and also Marconi, and they were very impressive to me. I wanted to be some kind of scientist at that stage.
So, already in elementary school.
Yeah. And then secondary school. Now, that school was in the Tottori city, and I had to walk about 4 kilometers to the secondary school. Going through the city streets they of course had bookstores, and so I would stop at the bookstores and look at the books, and there was a book by Einstein and Infeld; translated into Japanese.
That’s the famous Einstein-Infeld book.
Yeah. And that was when I was at this middle school. And so, I bought that book in Japanese translation. But anyway, that’s the first serious book I learned from. And then there is another book which is the Dubois (Daniel M.) book on quantum mechanics, translated also into Japanese. So, I got exposed to the idea [laugh] of relativity and quantum mechanics when I was probably in seventh grade equivalent, or eighth grade, maybe. So, I sort of was naturally oriented [laugh] to physics or something. Not very explicitly so, but that’s where my interest was pointing.
You see, our textbooks in middle school were not very sophisticated, so I didn’t pay much attention. The teacher was not very good. [laugh] But on my own, I studied a lot of them. So, I have pretty good idea. I think Einstein visited Japan around that time.
In the late ‘30s, then?
Yeah, that’s right. And, of course, that’s how I got the name of Einstein.
So, when you were in your second high school, the accelerated one, you graduated when? In mid-1944?
Why weren’t you drafted into the military?
I guess I’m not strong enough. Anyway, I had to take the exam to be drafted, and I was fortunately dropped. [laugh]
Do you know why you were dropped?
I don’t know.
So, you didn’t go into the military?
Now, Nambu went into the military?
Yes. I’ll come back to that later, since I got to know him only after 1946.
So, you graduated in mid-1944.
Yeah. And then went into Tokyo University. And then as I probably wrote somewhere, Tokyo University should take three years, too. But because of the war situation, it was compressed into essentially one and a half. And then you would be drafted. Actually, mostly physics graduates were not really bad off, because they are drafted to work in some lab in the army or navy or something of that sort. But my classmates in the other parts of the university or Daiichi High School, specializing in literature and other non-scientific stuff, most of them were drafted into the service, and many of them passed away during the war.
Did you want to go into the military? No?
So, you were glad that you weren’t drafted?
[laugh] That’s right. The chance of being killed was probably better than 50% when you went into army.
Oh, I forgot to ask you—did you have brothers or sisters?
I had one brother, just behind me. He went to—actually, the rest of my family lived in a separate city, because I was in a strange situation for the inheritance problem. And so, I lived in the Tottori city area. Another city in Tottori prefecture called Yonago, was where my father was a teacher, and my brother and sisters grew up there. But my brother was two years younger than I, and he was pretty good, too, and he went into the First High School, too. You see, this is a very competitive—most competitive [laugh] school in Japan. In the entrance exam, usually one person in ten would be admitted. And actually, the quality of applicant was the best in the country. [laugh] So, one in ten is really very hard to achieve.
And what happened to your brother?
In the second year or third year of school, he got TB, and he died soon afterwards.
Oh. What was his name?
So, he never had any children or…
No, no. Not at all. He was still maybe 19 or 20 years old when he died. And then I have three sisters. They all survived, and they have their own children. We send New Year’s cards every year, more or less, but that’s the only contact we have with them.
They’re younger than you are?
All of them are younger. The youngest is probably 15 years younger than I.
So, you entered Tokyo University in mid-1944?
And what was that like in the middle of the war?
As I said, the military wanted to get them to graduate as soon as possible. So, the entire first-year curriculum was taken in the Fall of ‘44, and then the second-year curriculum was taken in the Spring of ‘45. And then it went into summertime. Then the war ended. So, suddenly we had no reason to accelerate the curriculum. On the other hand, Tokyo was very badly bombed out, and so housing was very scarce, and the food rationing system, which was established during the war sort of collapsed, and so you couldn’t get anything to eat. So, you had to survive anyway you could. For instance, many people exchanged expensive clothes with a potato from nearby farmers. And, of course, this doesn’t last too long so [laugh] it’s a really bad situation. Let’s see. And then…
Wait. First, when the atomic bombs went off in Hiroshima and Nagasaki, how far away were you?
Actually, as I said, my parents lived in Yonago, which is right north of Hiroshima, but beyond the mountain range. So, we didn’t see anything. Only on the radio or newspaper we heard that Hiroshima was flattened.
And did you understand what had flattened it?
You understood the idea of an atomic bomb?
I knew what atomic energy can do, so I thought immediately this must be an A-bomb. So, I’m not sure newspaper said that, but I thought it cannot be an ordinary bomb, [laugh] anyway.
So, where were you as that happened? Were you still in Tokyo at the university?
No, as I said, I was visiting my—this is the summer.
Oh, the summer, that’s right. Sorry.
Vacation time. So, I was visiting my parents’ house.
And so Todai was then closed after that, the university?
So, you stayed at your parents’ house, then?
More or less, yes. Yeah.
And what did you do during that time?
I read a lot of books during that time, like Dirac’s book on quantum mechanics, and also Weyl’s book on group theory and quantum mechanics. I read also the book of Eddington on relativity. So yeah, whatever I could get my hands on, I read during this time.
And is this when you said you grew not to like sweet potatoes because they were the only thing that you could eat?
Did I say that? [laugh]
I think I remember you saying that. Was it sweet potatoes or pumpkins? I forget which.
Yes. If you have to eat pumpkin or something every day and night, you become [laugh] sort of—if you have to eat it, you eat it, but you don’t like it. [laugh]
Now, were these the good pumpkins? There’s good Japanese pumpkins called kabocha.
Yeah, kabocha is a good pumpkin, but it’s more expensive. The pumpkins which can be grown more easily are not as tasty.
So, Todai is closed until the end of December. Then you resumed in January of ‘46.
That’s right, January of ‘46. Well, actually it’s more complicated than that. [laugh] When A-bomb hit Hiroshima, I think that’s about August 10th or 11th or something like that.
August 7th and 9th—or 6th—the 7th or 10th or 6th or 9th depending upon what date—where you draw the date.
Yeah, probably 6th or 7th. And I don’t remember exactly why, but I went back to Tokyo very soon after that. Even before the war ended. You have been to Tokyo?
You know Shinjuku Station?
I was at Shinjuku Station to change to the different line, and then they broadcast announcement that said, “Please listen. There’s an important announcement going to be made in a few minutes” or something of that sort. And the emperor gave a talk. So, [laugh] I was at the Shinjuku Station.
Had you ever heard the emperor over the radio before?
So, this was very unusual?
And what did it say, the broadcast?
Well, he said, “Japan surrender, but don’t disturb the order” and so on. And “Accept occupation force” and so on. Anyway, my feeling is that, “Wow, that’s good.” [laugh] So, I don’t have to die. [laugh] And, of course, in Shinjuku Station, it’s full of people, and most people seems to be relaxed after hearing that.
Of course, not everybody does, but some people. Or most of the people that I could see across the station were not particularly mad at anybody [laugh]. Well, they are all tired of the war. That’s true.
So, where were you heading towards, that you were changing stations at Shinjuku? Where were you going to? The University?
No. Actually, I’m going back to the house I’m staying, which is actually a house of a cousin of my father. And I stayed there for, let’s see, I’m not quite sure what—before I graduate from Tokyo University in the summer of ‘47. That means my senior year lasted one and a half years because of the acceleration on the first and second years.
So, you decelerated the last year? The senior year you said took—
No. What I’m saying is that the last year lasted more than one and a half year, which should be normally one year, so I could start working on a research project half a year earlier than normal. And that was a great advantage to me, because then I could start my thesis work or thesis-related work pretty fast. Anyway, I was ready to do something [laugh] at the beginning of ‘46. And as I said, I asked Professor Kodaira to be my advisor.
Kodaira, yes. You said he was the mathematical physicist.
And you said he was very influential on you.
Yeah. In fact, you may not know, but he was first recipient of the Field Prize.
I did not know that. Huh.
So, he was really an excellent mathematician. Of course, we didn’t know that. He received the prize around late 1950s.
So, what did you take that first—oh, so he was your teacher at the university?
This is beginning of 1946 when I return to the Tokyo University.
January of ‘46.
You say there were no more formal courses to take.
That’s right. Because the first two years’ course were already taken.
Were taken. So, you had a year and a half to do a research project without having to—so you got started really early.
And you worked with Kodaira.
And the Kodaira seminar, which is what you talk about here. Now, were you teaching at the same time?
At that point, I was not teaching. I was still a student. But I am not completely sure what—I did in fact do some teaching at a different university. It’s not clear to me when that was. I taught electromagnetism at the university for I think two years, and that’s before—I’m not completely sure, but it may be around the time I graduated from Tokyo University, ‘47.
Because I’m wondering when you met Masa, but you haven’t met her yet.
At that point, in the second year of teaching at this other university, which is called Ochanomizu University, which is actually—at that time, it was called—Woman’s Normal High School was the official name.
Woman’s Normal High School.
It’s the highest school any woman could attend, before the war, because women were not usually allowed to attend ordinary universities. Except Sendai, I think, admitted some women, but not Todai. And so, any talented woman would end up with this particular university. I think in the second year of my teaching, Masa was one of my students. But after my second year, I quit the place, because I got another source of money [laugh], so I didn’t have to do extra teaching. Or in fact, from 1947 to ‘52, for five years, I was supported by a grant-in-aid of the Tokyo University, which was good enough for me to survive.
So, what year did you meet Masa?
[laugh] Few years after I quit her university. But I don’t know exactly—I don’t remember. Around ‘49, maybe. Or maybe ‘48.
OK, so we haven’t gotten there yet.
And what was her background?
She was actually attending Tokyo Woman’s University, probably in 1943 or something. But the school was in a suburb of Tokyo, but next to some military factory. And the chance of being bombed by mistake were quite high. I think it was a factory for making airplanes, [laugh] so the risk was even worse. And Masa’s mother got very nervous, and she forced Masa to quit the university after about a year, I think. So, then the war ended, and Masa wanted to do some more work, and then applied to this Tokyo Woman’s Education University from the scratch, I suppose. So that’s where she was.
And what was she studying?
So, when she was your student, what were you teaching?
As I said, electromagnetism.
What was her last name?
Maiden name, you mean? Matsuoka.
M-A-T-S-U-O-K-A. Matsuoka, yes. OK so you graduate—so tell me about your research project, then, that you did in that year and a half.
I started out, as I said, with Kodaira.
So, you explored field theory in this.
I wanted to learn about the field theory, mainly because field theory was not in good shape at that time. Whatever you calculated, it becomes infinite.
So, you got introduced to the divergences very quickly through that course.
And also, before we got to Professor Kodaira, as I said, I studied a book of QED, on my own. So, when I got back to Todai, I had nothing really more to study except for the new papers.
And how did you get those new papers?
Oh. Did I say that?
I think you said something…
I started out with Dirac’s article. Because when we looked for something new in the library of Todai, there are a few journals which somehow got to Japan, in spite of being under the war. Like some ‘43, ‘42, and even some ‘44 journals were in—not systematically, but some journals were actually in the Todai library. And the first papers we chose for this seminar were Dirac’s paper on indefinite metric and—I don’t remember exactly. [laugh]
You said something about them being stamped top secret.
Oh, that’s a different story. While reading these Dirac papers, I’m not exactly sure we found a statement, but we found that the Pauli mentioned that Dirac’s—no, Heisenberg’s S-matrix theory is a picture frame without a picture in it. This statement is actually made and recorded in some part—I can find it—but in a letter to Dirac, I think, from Pauli, 1943 or something of that sort. There is a collection of letters to Dirac which has this. But anyway, I don’t exactly know how I got hold of this information about Heisenberg’s S-matrix, which was first—I didn’t know that until that time. And we start looking for Heisenberg’s S-matrix theory, which was not in Todai’s library or physics department. But my friend Yamaguchi found out that Tomonaga’s lab has a copy at this time. And this paper, two papers actually, were in one of these books which was smuggled essentially into Japan by a German submarine. Actually, it was brought from Germany to someplace in the Indian Ocean, and then there it was transferred to a Japanese submarine and carried back to Japan. [laugh] Anyway, it shouldn’t have been there, if it’s totally disconnected, but it somehow came in. And in Tomonaga’s office, it probably came to an army or navy office in Tokyo, and somehow Tomonaga was given a copy of these papers. And my friend and classmate Yamaguchi was acquainted with Tomonaga before we knew him, and somehow, he managed to find this paper and made a copy and brought it back to Todai. And then we made a copy of that [laugh] and distributed it among the people there and started a seminar on that.
Oh, this was the Tomonaga seminar that you refer to.
No, no, no, no. It’s still the Kodaira seminar.
OK, so the Kodaira seminar then basically takes place—starts in ‘46…
—and goes on for a year and a half.
Because Kodaira went to—no, it lasted until 1949, I think, when Kodaira went to the Institute at Princeton.
What I’m describing is what happened in ‘47, I think.
So, that’s during the time that you’re still—your last year and a half at Tokyo University.
So, you’re in that seminar of Tomonaga from then on…
Yeah. Which I am not sure. I didn’t know he was there. But my friend Hayakawa, who is two years senior to me, was already working with Tomonaga, and he told me that Tomonaga was at my seminar. [laugh] So, anyway.
So, in Kodaira’s seminar, you learned Heisenberg’s theory.
Yeah. Very deeply. [laugh]
And at the end, what was the end of the—?
Of course, it’s not a physics theory. So, at the end, we have to move on. But the Kodaira picked up the mathematical aspect of the theory and he wrote a paper on the eigenfunction expansion of second-order differential equations or something of that sort. And he sent a copy to Hermann Weyl, probably somewhere in here…
Yeah. I don’t see Weyl’s name, but…
Oh, there it is—Weyl, yes. So, you gave the seminar in S-matrix theory.
Yeah, with my friend Fujimoto. I’m not sure if it was just one seminar or two, but we took turns, anyway. And the room, which could contain about 30 people, overflowed. [laugh]
Anyway, in the Tokyo area, the rumor spread out that we are working on Heisenberg’s asymptotic theory and people came just to—curiosity brought people to our seminar, I think.
So, you graduate then in mid-’47?
August of ‘47. You have to give a talk to graduate [laugh], and I chose Tomonaga’s super-many-time theory as my subject of my talk. You see, do you know why it is called super-many-time theory?
Because there is a paper called the many-time theory, by Dirac.
Right, I remember that.
And in a way, super-many-time theory is an extension or generalization of Dirac’s many-time theory to field theoretical theory.
Ah. So, the super just means the extension.
Yeah. But anyway, Tomonaga did this paper in 1943, and nobody paid much attention to it, so I thought I should talk about this for my graduation talk.
So, you graduated. And by the way, your parents are still—do your parents like your career, like your choice of career?
They didn’t say anything. You see, my father at least is a pretty educated guy, so he used to say, “Do whatever you want.”
And you did.
So, then you go to—then do you enter Tokyo University graduate school immediately for a Ph.D.?
Yeah. Then, you see, during the war, to maintain the future faculty candidate, the government sort of started a new program called special research student or something like that. I don’t know I can translate properly but…
But it’s approximately “special research student”?
And basically, it was a stipend support for graduate students.
And in 1947 to ‘52, I survived with this stipend, which was actually not bad, because of the [postwar] situation, in which people were having a very hard-time surviving until about that time.
How much was the stipend?
I think it was 5,000 yen, but I’m not sure. Something which you can sort of live a minimum life, in a way. At least you don’t have to do some extra work. I could just concentrate on research.
And who gave it? What agency gave it?
I think it’s the Ministry of Education, but it may be Todai. I’m not sure which one. The money actually comes from Todai.
OK, but the government may have supported it. Hmm. So, you enter in ‘47.
‘47 to ‘52.
To ‘52. And soon you get started on publications.
What did you take the first semester there?
What do you mean?
No, no course.
Oh, there was no course.
It’s a research stipend.
Ah, so your graduate education was this research stipend.
Ah. And who did you work with?
You see, I was already working with both Tomonaga and Kodaira, although the work with Tomonaga work was not official. Actually, as I probably said somewhere, Tomonaga assembled the people from Todai and his university, Tokyo Education University, right after the war. And the total number of people in his seminar group was already maybe more than 15. But by the time I joined his group, probably it was more than 30. So, people from all around Tokyo came to come to Tomonaga’s seminar.
By the way, you say here—you begin talking about this seminar that’s in the burned-out ruins of an army facility in northern Tokyo.
And you say “when the exciting news from the U.S. arrived”—what was the exciting news?
Oh, I probably didn’t say in proper order, but the news came not by Physical Review. Phy. Rev. Letters didn’t exist at that time. So, Physical Review is the only real source of physics. However, the occupation force opened the library in central Tokyo, which is open to the public. Mostly, they had journals like Time and Newsweek. Physical Review start coming only few months later, but initially, what you could find there is Time or Newsweek. And around November or maybe October of that year, news about the Shelter Island conference was reported by Time. The conference took place in August, I think. I’m not completely sure. But anyway, so we’d find nothing in the library of Todai, nothing useful [laugh] over there. So, people like us walked from Todai to this part called Hibiya in Tokyo, maybe a three-mile walk, to see publications in the library. And that’s where we found the Shelter Island conference report for the first time.
In where? In Physical Review or independently published?
Time and Newsweek. So, this was not a professional report, but it was good enough to excite us all.
Oh, OK. The Time report was good enough? Huh.
Probably I should add that sentence somewhere.
Yeah. So, then you visit with Yamaguchi, you visit Tomonaga’s lab.
Oh, that’s a different story.
Oh, sorry. It’s right after this one, so I thought they were linked.
Oh. Yeah. I have to…
So Tomonaga is already working with Koba…
That’s near the end of ‘47.
Yeah. And we were already attending his seminar, but this work with Koba was done separately from that.
By the way, Koba is a brilliant physicist, standout among our group from Todai. He became a professor at Bohr Institute in Copenhagen a few years later. Unfortunately, he died soon after that. Because he actually had the TB.
TB, huh? But your first paper is with him.
Yeah. That’s after publication. After this Tomonaga-Koba paper, which found the renormalization.
OK, so after the Tomonaga-Koba paper, then you start working with Koba and…
I think the first paper I published…
Yeah, this paper. I have to explain this. I thought I did explain something there. This is a different…
Oh, this is…
Yeah. It’s—this place.
Yeah, the collaboration with Koba, yes. So, you were dealing with the ultraviolet divergence, and there were two methods. There’s Tomonaga’s method and the C-meson theory by Sakata.
So, with this collaboration, you were trying to figure out how to decide—
How to distinguish experimentally what Koba was working on. And actually, I didn’t explain in more detail, but initially Koba found some difference between C-meson theory and renormalization problem. Because the difference is big enough that you can check experimentally for the elastic scattering of electron of up to few hundred MeV. Turns out that that was wrong. The reason why it was wrong is if you use C-meson theory which is a neutral scalar theory, you also have to apply renormalization to that, otherwise it doesn’t make sense. And when you do renormalization, the difference—the experimentally testable difference— disappears until you get to much higher energy like a TV or something. That’s what we found out.
OK, so that was your first…
Your first three papers, then.
Yeah, I think the first one probably had a difference discovered, and that corrected—when you think more about it, it couldn’t be tested experimentally at that time.
So, those are your first three papers, and your next one was with Nambu.
So, you’ve met Nambu by this time.
And how did you meet Nambu?
It’s not clear. [laugh] The first—I mentioned in the page one—Nambu came back from army service. Yeah, this page.
Still wearing his army uniform.
But he was lucky; he managed to survive the war.
Where was he assigned? Do you remember?
Near Osaka. He graduated from Todai in ‘42, and then he was drafted into the army, but not into the combat zone. He was in charge of some army research facility, which was near Osaka. I didn’t want to say too much more about that, but because of the duty he had to go through, he was not discharged immediately from the army, and that’s why he came back to Todai a few months later. That’s what I say. Now, I think Nambu met his wife while he was there. Or his wife says she got sort of interested in Nambu at first sight. [laugh]
So, she was working there too, or she was—?
No, she was living nearby.
And this is about the time that you meet Masa, then.
Not—no, no. I met Masa a few years later.
Oh, ok, so it’s not ‘48, ‘49. It’s—
This one, you see, war ended in ‘45, and Nambu came back to Todai in ‘46.
And so, it must—earlier than that. During the war, probably.
Right, ok. So, after the three papers with Endo and—
—Koba, you begin working with Nambu?
And how did that start?
That started because in ‘47, people discover the [inaudible] and [inaudible], and renormalization theory was made right after that, by Koba and Tomonaga, near the end of ‘47. And then it sort of was at the beginning of ‘48, and there were still some problems unsettled, and that’s why we worked on this C-meson problem. The first paper came in ‘48, and then a correction appears in ‘49. And then somewhere in my writeup about Yukawa—Yukawa went to Princeton. That’s in ‘49, I think. Or ‘48. Yukawa went to Princeton in ‘48. Oppenheimer invited Yukawa to the Institute in ‘48, and then Yukawa used this opportunity to inform the people in Japan about news from the U.S. And in particular, he sent to Japan the paper of Dyson proving—this is ‘48. So, there was Tomonaga theory, which was based on orthodox quantum field theory. And Feynman’s paper, which was completely different. And Dyson showed that Feynman’s paper and the Tomonaga-Schwinger theory are actually identical. And this information came I think sometime—not too late, but sometime in 1948. That’s how it happened. Now, in particular, you see, what’s interesting is that Feynman’s paper came to us much later, maybe a year later, after Dyson’s paper. So, studying Dyson’s paper, we had to guess what Feynman did, and our guess—by the time Feynman’s paper actually arrived, we knew exactly what he was doing [laugh] from Dyson’s paper. So, Dyson’s paper was a very important development. And so, in early ‘48, people started studying Dyson’s paper very intensely, including the work at Tomonaga’s seminar. And then the question is, instead of just reading Dyson’s paper, why don’t we try to apply this to something else? And I started working on vector meson, charged meson theory, to see whether the renormalization scheme still worked. And Nambu also started the same study at about the same time. You see, the interaction with Nambu is somewhat strange because he has his own ideas, and he doesn’t necessarily come to Tomonaga’s seminar, and so instead, he does his own work. But he is from Todai anyway, so occasionally I see him at Todai. Not at Tomonaga’s place. And we found that both of us are interested in seeing—or no, that’s slightly ahead of my time. What we are doing after renormalization is—that’s the end of ‘47. What we are doing independently is how the same technique applies to charged vector meson theory.
[End Session 1]
[Begin Session 2]
At some point, we found each other and found that we were working on the same problem. In the meantime, as I was going to say, we got Dyson’s paper from the Princeton pre-print, and it’s clear that it’s much easier to apply Dyson’s theory, Feynman-Dyson theory to this problem of vector meson renormalization. And so, we had to really study Dyson’s paper from scratch. And then we decided to reformulate our vector meson theory in terms of Feynman-Dyson theory. That’s what I said somewhere.
So, that’s this paper on the electromagnetic…
—properties of mesons?
And you published “Note on the C-Meson Hypothesis.”
Ah, this is something which I said, also. And that is, you know, C-meson hypothesis of Sakata works in the second order by choosing a coupling constant of the C-meson to electron. I think it was coupling constant square equals two times e square or something of that sort. But the same equation doesn’t work in the fourth order. Naturally. [laugh] In fact this paper says that C-meson hypothesis is actually not workable.
So, it’s paper five, which you do by yourself.
And papers six and seven on the interaction of mesons in the electromagnetic field.
Yeah. Actually, these two are—I worked on them with Nambu. The reason why I have my own name, not Nambu’s, is just convenience of applying for Ph.D. [laugh]
Oh, six. Oh, so was this your Ph.D. paper?
And did you get examined?
Yeah. [laugh] Strange situation. Because my professor, Kodaira, and also Tomonaga, is at Princeton.
So, they’re in the United States.
Yeah. So, we had to import another person to be the examiner, Professor Miyazima at Tomonaga’s university. He became a temporary examiner. I’m not sure whether he read my work or not. [laugh]
Any questions, or were there any problems with it?
[laugh] Well, anyway, so that’s…
And what happened when you were examined? Were there people in the audience?
I don’t remember. You see, also before I graduated, I had to give a talk. And the talk I gave is on Tomonaga’s super-many-time theory. And nobody wanted to ask any question. [laugh] This was before renormalization was found, because the exam was given before 1947, summer of 1947, and renormalization was found at the year-end of ‘47.
By the way, had you seen Feynman diagrams by this point?
From Dyson’s paper or from—?
So, you were introduced to Feynman diagrams from Dyson’s paper.
From Dyson’s paper.
And what did you think of them at that point?
What did I think?
Think of Feynman diagrams?
As I said, studying Dyson’s paper, you learn what a [laugh] Feynman diagram is.
But did you realize what a great idea it was at the time?
Oh yeah, of course. That’s why I’m using it [laugh] all the time.
You’re still using it today, yeah.
It’s a really great idea. I mentioned sometime, not explicitly—[pause]—let’s see. Page four.
Page five. [pause]
I still haven’t put in here—somewhere I need another section. Oh, here. I studied in Tomonaga’s seminar Weisskopf’s calculation of the electron self-energy. Maybe you can read this.
Yeah, ok. Ok, so he had you give seminars on Weisskopf’s paper.
To calculate the second-order radiative correction.
Applying Dirac’s hole theory. And you found that Weisskopf’s result was correct.
And this helped when you read Dyson’s paper later.
So, he found an important result about the divergence—that it’s not linear or quadratic but very weak. Ok. Ok. But you weren’t yet ready to participate in this, in the renormalization work. Yeah.
Ok. Anyway, the point is, this Dirac hole theory calculation of Weisskopf is [inaudible] calculation. In fact, there are quadratic divergences popping up from here and there, and in the end, they all cancel out. Which [laugh] looks like a miracle. But in Feynman-Dyson theory, they appear only as one diagram, and the quadratic never appears on the surface. Just to get the [inaudible]. So, the qualitative difference is totally different. So, in order to do second-order calculation, you still have to worry about a lot of things, other diagrams and divergences—different types of divergences and so on. If you have to do that in the second order, it would become very [laugh] difficult to do fourth order, and sixth-order [laugh] is sort of becoming almost impossible to deal with. But Feynman-Dyson make it possible at the minimum expenses. That’s why I said working on Weisskopf’s paper opened my eyes on why Feynman-Dyson is so good.
But that same year, you do ambiguities and quantized field theories.
Oh, I think that’s a vacuum polarization problem, which is not particularly useful.
Eight, ok. And the infrared catastrophe, is that…
Yeah. This is a two-page note. [pause] Maybe I showed it to you.
I think I saw it in one of your notebooks. I think that you have it there someplace. [pause] Oh, there it is.
Yeah, this is the one.
So, this is paper number nine. “Note on the Infrared Catastrophe”—Ok, yeah.
The point of this paper is if you look at this type of diagram, this is obtained by flipping over—this is a simple program of scattering emitting a photon. However, you can look at this part, then photon is absorbed, and this is scattered into the [inaudible]. So, actually this is not a simple Feynman diagram, but it’s a diagram corresponding to the probability. And if you use this formulation, then you can actually—this electron scattered while emitting photon and after scattering, all these diagrams can be put into this form. And also, each photon emission, this one divergent at K=0. So, it does all these things. But when you put them together in this way, all the divergences disappear. So, that’s a note on that. [laugh]
A note on that, yeah.
In fact, this technique of course is nothing revolutionary, but it simplifies the matter quite a bit. So, this is actually beginning of later work in 1962—I have written—’63 maybe—singularity—yeah.
That’s the Journal of Mathematical Physics, and that’s unusual for you to publish in a mathematical…
This was a mathematical problem. [laugh] So, I thought to publish this in mathematical physics.
That’s number 27.
Now the problem is, nobody saw this paper until about ten years later. And T.D. Lee and Michael Nauenberg worked on the similar problem and discovered this paper only much—after they published their paper. And it is called by the name of Kinoshita-Lee-Nauenberg theorem.
Ah. Oh, that’s what it is. Ok. And that’s why it’s called that, even though you published ten years earlier.
Kinoshita-Lee-Nauenberg theorem, yeah. So, that’s the theorem that you begin here and develop here.
Yeah. Also, there was a further complication of actually this theory because, you see, this paper—oh, that’s from somewhere—with Alberto Sirlin.
Yeah. This paper was written right after the discovery of parity violation.
So, Sirlin was a student at UCLA before coming to Cornell. He had written a paper on radiative correction of [inaudible]. And so, when we saw parity violation, we said immediately that we should also compute the radiative correction to the parity-violating part. And this we did very quickly in a week or two, just before the Rochester conference, and then we published it. Now, the problem is we were too quick and made a mistake. [laugh] I think—I think this is the paper, probably. You see, Feynman and his student Berman worked on the same problem, and they got the answer different from ours, and sent us a pre-print. And when we saw the pre-print, we found immediately that they also made a mistake. It’s a very subtle mistake, but a mistake is a mistake, and numerically, it’s not so small [laugh]. What happened is in the first paper, we calculated the radiative correction by putting a small mass to the photon. Because to maintain covariance, it’s important to have some—make the photon to be a vector meson and then go to the limit of mass going to zero, in the end, to maintain the gauge invariance. So, that’s fine. That’s well-known for many years. But when you combine this with a [inaudible] to compute, the photon [inaudible] emitted photon must also be a vector meson with a small mass. Instead, people usually put mass equal to zero, and emitted photon has a polarization—transverse polarization only. That means you forgot the longitudinal polarization.
Longitudinal polarization, yeah.
And if this is a small effect, seems to be, but if you couple that with a divergence, it becomes quite visible. [laugh] And the first paper, we made a mistake. Forgot that the external photon, emitted photons, need also longitudinal polarization. Ok. So, that was an error which Feynman and Berman found out, too. But they made a mistake—Feynman visited us later and he told me more than ten times he was sorry [laugh] he made a mistake. And the reason he made a mistake is from one page to the next page, copied a formula in the previous page incorrectly. I don’t believe that [laugh] but that’s Feynman’s explanation.
Ok, that’s 1957.
But go back—you have one more paper in Japan, which is on V particles. Paper ten.
Yeah. This is a V particle, which means [pause]—no, this is not very important paper.
This is a very important paper.
Paper number eight—the “Note on the Infrared Catastrophe” you say is the important paper.
Yeah. Eight and ten are not particularly…
Eight and ten are not as important, ok. But by this time, you’ve met Masa.
And how did you meet Masa, again? She was in your class. You were teaching electrodynamics.
But I quit the university job. For probably about a year, I had no contact with her. But her house and our house were not too far away. And one day, she came to our house asking me whether I could teach some physics to her brother. So, ok, I say, I teach. And in some way, then, we got involved. [laugh]
And when did you get married?
And did she have brothers and sisters?
She had an elder brother, younger brother, and a younger sister.
And did she ever work with you on physics?
Did she ever work with you on these papers?
No. She helped me a little bit in the helium problem.
Helium atom problem, yeah.
Yeah. At some stage, early stage, she did work with me, but not much.
So, how did you get to the United States?
I think I wrote something here. Oh, I didn’t finish about Feynman’s. You see, the reason why I saw immediately that the Feynman-Berman was wrong, is their result has a logarithmic dependence on electron mass. And our initial error had a square of logarithmic dependence on electron mass.
The square of—?
It’s finite, but it depended logarithmically on the electron mass. Square of the logarithm. Now, what Feynman and Berman did was [inaudible] square of logarithm term must be dropped. But they left the linear part of logarithm in the form in the final result. And I saw immediately the reason why the square is gone should also apply to the linear term also. So, it becomes really finite as a function of electron mass. So, that’s where Feynman made a mistake. And I think there’s a paper somewhere—“Everybody Makes Mistakes, Including Feynman”—that explains…
Well, there’s more later on in your career with Feynman, but we’ll get to that. So Tomonaga—you sent that paper with Nambu to Tomonaga.
And then you were invited to the Institute.
Yeah. More or less. [laugh]
What do you mean, more or less?
That’s my guess. But Nambu certainly had done quite important work by that time. So, that’s why he was invited, I suppose. So, I’m not sure whether I was his apprentice [laugh] or not.
But there were still very few Japanese people going to the United States at that time.
So, you were special. You were in a special category.
Yeah, sort of special. [laugh]
What was it like? How did you get to the United States? How did you travel?
[laugh] First of all, we were not very rich. Everybody in Japan is mostly—every student certainly was not very rich. So, we couldn’t come by airplane or passenger boat. So, the best we could do is to find a seat on cargo boat, which is somewhat cheaper. So, I took a cargo boat from Nagasaki to Seattle. That’s the best I could find. I would have preferred to start from Yokohama to San Francisco or someplace. But anyway, Nambu was lucky enough to get a boat from Yokohama to San Francisco, but about a week later. So, my boat arrived at Seattle, and then I took a Greyhound bus from Seattle to San Francisco, and then to Berkeley. And I stayed in Berkeley for about a week, awaiting Nambu’s arrival by another boat. In the meantime, I visited Lawrence Berkeley Lab. Actually, the professor at Tokyo, [inaudible] Sagane, he was working with [inaudible] before the war, and after the war, soon afterward, he came to Berkeley again. And so, we had somebody who could take care of us, at least language-wise. Also, he found a place for us to stay in downtown Berkeley. And so, I had no problem coming to Berkeley. But waiting for a week Nambu’s arrival by a later boat, I didn’t want to waste my time, and so I went to Caltech by another Greyhound. The reason why I went to Caltech is before that time, some experimentalists at Caltech measured the electron mass by measuring electron-positron decay into two gammas. And you measure the gamma energy by some device, a clever device called a curved crystal spectrometer. And they found that the energy of the photons didn’t add up to two electron masses. It’s like a 50-electron volt smaller or something like that. So, I was interested—[End Session 2] [Begin Session 3]
—make a theory of why this could happen. Maybe it’s a condensed matter effect, and so on. But before I write the paper, I want to see the experimentalists, and visited Caltech. Found out that they had just found that there was an experimental error. The error is very subtle. You have to move the spectrometer on the rail or something like that. And the rail sort of deforms by the weight of the spectrometer, and that deformation is sort of not instantaneous. It has a residual effect. So, what you thought it was measuring is not the measurement of the right time but at the wrong time.
And who was the experimenter?
I forgot the name.
But it was at Caltech?
So, you went to Caltech, and then you take the Greyhound bus back.
Before that, people at Caltech told me that Schwinger was at UCLA visiting. So, I went to [laugh] UCLA to listen to Schwinger, or to meet Schwinger. And then at that time, Roy Grauber was visiting also UCLA. Turns out he was a very good friend of Tomonaga at the Institute, and he became very friendly to us. To me, I mean. Not to Nambu, but to me. And in particular, he recommended that I take California Zephyr across the continent.
California Zephyr. That’s the train.
Oh, Zephyr, the train. Yes.
You know that?
Yes. The Zephyr train, yeah.
Yeah. So, we took—when Nambu arrived, he and I took California Zephyr and start crossing the Rockies. We stopped at Denver, and went from Denver to Mount Evans, which has a cosmic-ray lab, and stayed overnight at the cosmic-ray lab or some facility, loading-facility, few maybe—at about 10,000 feet. Experimental facility was at 14,000 feet. Now [laugh] the problem was I got height sick. So, while I was up top of the mountain, my head was [laugh] making big noise. [laugh] But when I got down to Denver, I’m back to normal immediately. I didn’t like that. So, I continued my trip to Chicago, on the train, and I visited Fermi’s Lab. I wanted to see his famous cyclotron of 300, 400 MeV, which was the center of the topics at that time. Like something called (3, 3) Resonance. And then maybe the next day we went to Rochester, stopped at the University of Rochester, and met Marshak…
Oh, Rochester. Ok, right. And that’s where Marshak is.
Marshak. And we stayed at the house of French, who was known to us by French-Marshak—no, French-Weisskopf paper. And then we went to New York and Princeton, just a short trip.
Let me go back a minute. Did Masa come with you?
She was staying in the United States?
She was a student, still. So, she came to the U.S. after she graduated from school.
And when was that?
Ah. And you say language—Sagane helped with the language. How good was your English?
Not very good. [laugh]
But you managed to get around?
No problem getting around.
No problem getting around. And how was it to be Japanese in the United States at the time? Did you face hostility?
I didn’t feel any. Maybe I’m not sensitive to that. Well, when we [laugh]—I didn’t particularly feel my English was bad or changing, but one year after I was at the Institute, Abe Klein, I met him—I don’t know you if know him?
He said, “You speak much better English.” [laugh] He saw me at the beginning and then one year later. So, maybe I have improved a little bit!
Then this is 1952. After May of ‘53, Nambu and I went to California, by separate cars. He went on his own. Actually, he was going to Los Angeles, I suppose, to pick his wife and son up at L.A. My wife was with me already. Just like we went across the continent, but in a separate car. And then we arrived at Caltech. We needed a place to stay and found a place in Pasadena. And the landlady couldn’t pronounce my last name, so she invented the name “Tom” for me. [laugh]
Ah. So, until then, you had been Toichiro?
Yeah. Or, it still is. [laugh]
Still is, right. [laugh] Oh, sorry. So, Tom was given to you in 1953 by this landlady.
Yeah. And anyway, so this is the second time I was in that area. A guy named Watanabe; I don’t know if you know…
I’ve heard of him, yeah.
He was a professor at the Naval Lab in Monterey. And while we were—on the way from Caltech to Berkeley, we stopped at Monterey to pay tribute to him. He looked at my car, and he was amazed you could make a trip [laugh] across in it.
Anyway, the car survived the whole trip back to Princeton.
What kind of car was it?
Primous. Huh. Tom, why don’t we break now, and do it later this afternoon? I’m getting tired. I don’t know about you.
I am, too. [laugh]
Can we talk this afternoon?
We talked for almost two hours! [End Session 3] [Begin Session 4]
This is Robert Crease, and I’m interviewing Toichiro Kinoshita and Masa Kinoshita.
Masako is actually…
Masako, right, OK. And it’s January 9th, 2016. We talked this morning about your life before you got to the United States. Is there anything that we didn’t talk about?
Just a moment. [pause] Ouch.
You hurt your finger?
He poured tea on his finger. [laugh]
So, what was the question?
The question was—we talked in the last interview about your life before coming to the United States. Are there anything else that you forgot to mention?
As far as physics is concerned, I think I mentioned everything.
Ok. I actually had one question, which is you mentioned people receiving papers from the United States and copying them and then making other copies. How was that done?
In those days, copying was not trivial. They prepare some—I think they have—[laugh]—
Yeah. I was curious but I never knew how it’s done. You make some original copy. [laugh]
Well, that’s to make many numbers of copies, you actually type from the beginning on some kind of special paper.
Mimeograph or something. And so, it takes some time of secretaries or somebody.
So, you have to type it over from the beginning.
But when you said you made copies of Feynman’s paper or Dyson’s paper, is that how you did it?
Yeah, that’s the way it was done.
You typed it all over from scratch?
Including the equations?
If you had enough money, you could make a photocopy, but to make 50-pages of photocopy would be very expensive, so that was not usually done.
There seemed to be always somebody who volunteered to do this kind of job among the students.
Oh, it would be a student job then? Hmm.
Well, anyway, copying is certainly much easier now [laugh] than the old days.
Then we talked about your coming to the United States, taking this steamer to—this boat to Seattle, and then going to San Francisco and then Caltech, and then across the United States to the Institute.
So, you arrived at the Institute when, approximately?
It’s—I think August 18th or 17th—I don’t remember the exact date—but sometime towards the end of August.
And did people meet you? How were you received when you got there?
Do you remember the first day you got there? Did people meet you and show you around? Did Oppenheimer meet you?
[laugh] I don’t remember exactly. I remember the secretary I met, probably the first one, called Miss Winter. She took us around and she told me and also Nambu that our office is here, and so on. I mentioned something about our office, which was a physics building office at one corner of a sort of square-type building, somewhere around here. I forgot to mention Lee and Yang occupied the same building, and when they discussed physics in this room that was opposite our room, it wasn’t very close. However, when they started arguing, they spoke so loudly that you could hear all what they say. [laugh]
Now, you don’t write any papers until 1954, so are you just doing—why is your next paper not until 1954?
I actually mentioned—[pause]—this paper, this paper, and this paper, and this one, are all 1954.
Right. But before that, there’s no—the previous paper was [pause] 1951.
Yeah, but we spend a lot of time on this paper with Nambu. And probably this was published in—and then some small papers here and there.
But nothing between ‘51 and ‘54.
I don’t remember.
So, who were some of the people you interacted with at the Institute?
Of course, [inaudible] became good friend and then Bram Pais was on the staff of the Institute, and we got to know him quite well.
No. He’s too high up. [laugh]
Pauli is an interesting case. He was visiting the Institute when I first got there, and I know that Pauli—Tomonaga showed our paper to Pauli. Pauli was very impressed. And this is my guess, but the reason why Pauli was impressed is that Pauli had a student working on the same problem, essentially, and we outdid his student by far.
Now, he was there…
He would come to the Institute and go back to Switzerland and so on. He did not have a permanent seat at the Institute.
And Oppenheimer? Did you interact with Oppenheimer?
Yeah, sure. I have to say hello to—I had just come to the Institute and so on.
And were you there when—in early 1954, Yang comes to talk about what will be known as the Yang-Mills theory, and Pauli is there. Do you remember that?
No, not—you’re talking about Yang-Mills theory.
That’s somewhat later, I think.
Well, he publishes it in late 1954, but he presents it at the Institute in early 1954.
And Pauli was there, and I was just wondering if you happen to remember that.
I don’t remember that. Pauli is known to make some sarcastic comment on many people.
And what were your work habits? What would you do every day at the Institute?
I just go there every day. [laugh]
Were there regular seminars?
Maybe once or twice a week. Also depends on the visitors. Yeah, another thing I should mention about Einstein—his house was on I think what is called Mercer Street. I lived at the center of Princeton, close to the railroad station. I don’t remember where Nambu lived, but somewhere around there. And then people who lived in town usually took the Institute bus to go to the Institute, which started at Palmer Square. So, we’d go to Palmer Square and take the bus, and the bus would stop in front of Einstein’s house and pick him up. So, I remember that sometimes Einstein sat next to me and would ask me, “What are you doing?” I said, “I’m working on meson theory.” At that time, that was not interesting to him. So, that was the end of conversation.
But Nambu was also interested in relativity, and so Einstein and Nambu talk all the way to the Institute, whatever.
Einstein could sustain a conversation with Nambu?
Now while you’re at the Institute, Masa arrives, right?
Masa arrives in ‘53.
In ‘53. And how did you get to the Institute?
She flew from San Francisco to LaGuardia.
And then I went to pick her up with my friend by a car. So, she had no problem.
Yeah, but the plane was delayed by almost one whole day, because of the bad weather.
In Nebraska or someplace. Well, anyway, I think somehow communication was okay, and I knew exactly when she was coming to LaGuardia. So, that was no problem.
But you had a house, then, near the train station, and that’s where you lived for…
Yeah, it’s an apartment.
Yeah, one-room apartment, of course. But when she arrived, actually Institute gave us an on-site apartment, and so we stayed there for maybe two, three months or—
Yeah. Actually, we stayed in a small house in between.
I don’t remember that.
Yeah. It’s where—I don’t remember the name. It was, anyway—somebody, a very famous mathematician was living in that apartment.
Oh, yeah. On the site of Institute housing, too.
Because he went away for the [inaudible] Institute, and started a vacation. So, that was the only place available at that time, so we lived in that little house. And then other people vacated apartments, a general apartment, and so we moved to the apartment.
And how did you find Princeton? Did you like it?
Yeah, I liked it very much.
And Kay was born there?
One year later.
While you were still at the Institute?
And what did you do at the Institute?
Well, [laugh] so—well, this is—the apartment is in a colony of apartments. There were a lot of ladies who were just about having as much time as I do. [laugh] So yeah, we socialized…
Were you doing the looms then? Were you weaving yet?
No, I didn’t have—well, I really didn’t have any special thing. Well, actually, I was still hoping to continue physics. So, maybe—I attended something…
Some courses. Yeah, right.
Yeah, Wigner’s, and then…
I don’t remember the other…
Yeah. Anyway, I attended a couple of courses in Princeton.
And had you graduated in physics from Tokyo?
Right, in Japan.
And what year, ‘53?
And from where? From which college?
As soon as I graduated, I came here to Princeton.
And which college again?
Ochanomizu. It’s one of the oldest women’s colleges in Japan. It just became a regular college with the change of the system.
It used to be a teacher’s college.
Higher Normal School.
Called Normal [inaudible].
And what was it called again? What was the name?
No, after the name was changed, it became Ochanomizu. Before that, it was called Tokyo High Woman’s University or something like that.
Higher Normal School, yeah.
So, you started working with Nambu, then, on many-particle systems?
Yeah. That was after we got to the Institute. We spent essentially two years working on that.
Oh, ok. So, that’s what you’re doing at the Institute is working all that time on…
But I also did a few more papers. This one is at the Institute.
Fourteen, spinor field.
This one is also at the Institute.
Back to V particles. And is this one—why did you work on the ground state of helium?
That’s after I moved to—actually, it started at the end of my Institute…
Oh, that’s right. That’s ‘57.
Ok, so you spend two years at the Institute.
And then you become a postdoc at Columbia?
How was that arranged?
Well, actually [laugh] I don’t remember I ever applied for a job there. But T.D. Lee was already at Columbia. And someday I think I asked him, “I would like to stay in the U.S. another year.” And he said, “Oh, why don’t you come to Columbia?” He would take care of that.
So, you never applied for a job?
No. As far as I remember, I never applied for the job.
So, you didn’t apply—you didn’t seek positions other than Columbia? You just asked him…
Just asked T.D., and then he told me, “Just come.” Actually, Cornell, I also went in the same way. One day, Ed Salpeter came to give a talk at Columbia, and I asked him whether Cornell had any positions, and then he said, “Well, let’s talk to Hans.” And then sometime in the next week or so, I got an offer from Cornell. [laugh].
Oh, how did you like Columbia?
It was nice. But I would say we don’t really like a big city. And in particular, Masa had a—Kay, as a baby—she had to take out Kay every day to—for exposing to the sun. And, well, I don’t know whether she felt—but I thought—so for instance, Princeton was much nicer, in that sense.
For having a child?
But that must have been intellectually an exciting place at the time.
Samios, Lederman, Weinberg. Where did you live?
No, I know. Feinberg may have come after I went. I’m not quite sure.
Where did you live?
21st. 125th is a big street.
We were told you should never go [laugh]…
North of 125th?
[inaudible] little bit four streets closer to the center. [laugh]
So, you then—so after Salpeter came, you moved to Ithaca.
And what was Ithaca like?
Well, I settled down in Ithaca, and that means I have nothing bad to say about Ithaca. It was very nice.
The head of the department was Smith? The chairman of the department at that time?
Smith or Corson?
I think that Dale Corson was the chairman when I went, but soon afterwards, I think chairman has—let’s see, who…
Oh, I forgot. [laugh]
I know, but I cannot tell. [laugh] The name doesn’t come out [laugh] of my memory.
It wasn’t Smith?
No. Smith is probably before Corson.
Oh, ok. And at Cornell, did they let you work on what you wanted to work on?
Did they instruct you as to what you had to work on?
No. In particular, I was continuing my work on helium atom.
Ah, ok. Before we talk about the helium atom, Paul Hartman remembers that Dyson—you got your first Christmas tree with Dyson? Do you remember that?
Well, that’s when you visited Rochester. Dyson.
This is 1952, December.
There was a conference, one of the Rochester conferences, in December of 1952. And on the way back, we stopped at Cornell, and—actually, we lived in [laugh]—I forgot the name of the guy—it was a postdoc working with Dyson. His wife is a daughter of some Nobel laureate [laugh]. I forgot the name. [laugh] Anyway, they are going on vacation on that day, so they volunteered to let us use their apartment while they’re gone. And then we opened the refrigerator and the refrigerator had a hole in the back [laugh]. It was still working, probably, but not very well. [laugh]
This was Dyson’s grad student? The apartment?
It’s Michel Baranger.
Michel Baranger, huh.
I think they went to MIT afterwards.
Now, so you’re working on the ground state of the helium atom then.
And why was that particularly important?
You see, it goes back to 1954. In the summer at the Institute—the Institute ends at the end of April or something. So, before I went to Columbia, there were four months of vacant time. So, I wanted to do some work or get some money, too, and then asked around the people at the Institute, and they said they had some openings at the Neumann computer center. So, I worked for few months at that computer center, but I needed a research program. [laugh]
So, I looked around the literature, I found that the helium ionization energy theory and experiment disagreed quite a bit. So, I looked at the theory, which was actually in the paper written by Hylleraas. He’s one of the people who worked at the very early stage of quantum mechanics. By calculating the helium atom-ground state energy, he proved essentially that quantum mechanics actually works for a multibody system with two electrons. So, this was an important paper and it was in the middle of [inaudible]. Everybody was quoting it. But an experiment by Herzberg in Canada differed [from the theoretical value] by much more than the numerical uncertainty. And so that’s what interested me.
So, I looked at the Hylleraas paper, in which he used a variational method to evaluate the ground-state energy. And, of course, whether you get a good eigen value depends on whether your test function is good. And actually, I found that his test function was not really that good, but that’s not fatal. If you have too many—many, many terms in a test function, eventually it will approach the right value. But the more important error he made is that the helium atom, when one electron gets close to the helium nucleus, from the view-point of a second electron, it looks like a hydrogen with a charge of one. And this is of course true at the very—if the other guy was very close to the nucleus. And he made a wave function taking this into account. That much is fine. But what was wrong was that he fixed the parameter of this so-called screening charge. I mean, helium atom has charge two, electron has minus one, and if it gets too close to the nucleus, from outside it looks like a charge one.
So that’s a screening, so-called. And Hylleraas assumed the screening parameter, a number of them, maybe—five to ten; I don’t remember how many—and therefore each fixed screening parameter, he did the variation for the other parameters. I mean, [inaudible] screening—wave function can be made more precise by adding more and more terms. So, he certainly took a variational method for [inaudible] varying these other terms, but not the screening parameter. So, this was sort of a reasonable approximation, he assumed, which is not incorrect. But what he did is a variational calculation for each fixed screening parameter, and then interpolated the result, now finding the minimum of the possible screening parameters. But this is not a variational method. If he also varied the screening parameter, then it becomes a variational method, but he fixed that, assuming that he already was close enough. And so, it is not only—it was not close, but in fact it caused a large, quite visible discrepancy between theory and experiment.
So, what attracted you was the possibility of testing quantum mechanics…
—by working on the theory very carefully.
In a paper that seemed to involve a discrepancy with experiment.
Yeah. Actually, I heard from some people—I don’t remember the name—but that Fermi was interested in this problem, and sort of speculated maybe the three-body has a different interaction and is not the sum of the two-body interactions. But my calculations show that this conjecture is incorrect.
By the way, how do you spell the author’s name of this paper?
The name of the author of the paper.
Probably said something in the paper…
Oh, in here, ok. [pause] There we go. Hylleraas. Yes. H-Y-L-L-E-R-A-A-S, ok. Ah. Now, you were using the computer then at NYU?
In the second stage, yes. I started using the computer at Princeton, but [laugh] that’s another story. The computer at that time worked on vacuum tubes.
And every 30 minutes or one hour, some tube would blow. And then your calculation would be back to the starting point. [laugh]
Oh, so when the tube blew, you had to go over—start from the beginning?
Yeah. Then I went to Columbia, and the Columbia Watson Lab had some computer, but I didn’t get much out of it. But then I went—I was at Columbia for one year, and then went to Cornell. After I went to Cornell, the next summer, I was asked to come to Bell Lab, and Bell Lab had a good computer. So that’s where I really got a good value [for the helium atom]. But then for further improvement, I needed the UNIVAC at NYU.
So, how would you get to NYU? Would you drive from Ithaca?
And what was that like?
It’s five, six hours’ drive, and very tiring. But I was young, so it didn’t really bother me.
[laugh] And what was it like working at the UNIVAC? Was it a friendly atmosphere?
You see, the real working program I got at Bell Lab, so it was all tested out and so on. And so, at NYU, it was a matter of running more time and more something and so on. And so afte,r the NYU work, I got a sufficiently good result, and published the paper.
So, was this your first serious involvement with computers, then?
Yeah, I’d say I should think so.
For this helium atom issue?
So, you worked on the helium atom. And then this paper number 16, that we’ve talked about a little bit. The paper with Sirlin.
This is a helium atom paper.
That’s the helium atom paper, number 15.
Then the next problem—actually, timewise, they are overlapping, probably. I don’t remember exactly. But this is very interesting paper in the sense that I think at the end of 1956, parity violation was discovered. And so, it’s obvious right away that it will affect distribution of pi muon decay in this case. And Sirlin was a graduate student at Cornell. Actually, he transferred from UCLA. I don’t know why. But he had written some radiative correction papers at UCLA, so it was very easy for him to compute a part of the parity violation.
Now, do you remember hearing about parity violation for the first time?
Probably within a few weeks.
Because it was—C.S. Wu was working on it, got the results at the end of ‘56. And then there was a famous meeting at the beginning of 1957 on…
No, American Physical Society.
Oh, I see.
And then they were all published in the Physical Review. But do you remember hearing, learning about it? Because it was a very shocking development.
Certainly, I heard before that. When the parity violation was actually found—do you remember?
It was the end of 1956 when she got her results, and they were published January of 1957.
This is 1957.
Yeah, so this must have been later in the year. But they were published in Phys Rev earlier. I forget which volume.
No, this is our paper.
Yeah, but in Phys Rev, C.S. Wu’s paper was published in Phys Rev along with two other papers at the same tame.
But this particular paper is concerned with muon decay.
Ah. But in the light of parity violation. You knew of parity violation.
I knew about parity violation certainly, as soon as it happened. But this paper was written to present at the Rochester conference.
Ah. Paper 16, yes.
Yeah. So, that means I had to do some calculations in time for the conference. And as I said, Sirlin has done the parity independent part already. So, we added a parity dependent part, and this is that paper.
So, you went to the Rochester conference?
And what was that like?
I don’t remember exactly what it was, really. Parity violation is already well-known, so it’s not particularly shocking already.
And then you did another muon decay paper.
Yes. This is for the general interaction. This is V-Minus-A theory, and this is the general interaction.
So, 16 is V-Minus-A theory, 17 is general interaction.
And then radiative corrections—again, these are all concerned with the asymmetry in muon decay.
Ah, ok. And why are radiative corrections important?
Because it’s not small. So, the measurement has to be accurate to distinguish—to establish the parity violation in muon decay. In particular, low-energy electrons or low-energy positrons would be strongly affected by the radiative correction.
Which is paper 18, yeah. So, you have a series of papers, then, on muon decay, basically.
This is Pi zero decay.
Pi zero decay for 19. Twenty is muon decay.
This is muon decay. Now, I think this is a paper…
Yeah. Correcting the mistake of my first paper.
Correcting the mistake of which paper?
You see—yeah. This paper…
Did I tell you yesterday that if you wanted to compare experiment and theory, you have to deal with the photon as a vector meson, with a finite non-zero mass. Otherwise, people were using virtual photon with an effective mass cut off. But for the real one, they were using photons without a cut-off mass. So, that means in the virtual photon, you have a longitudinal component, but for the real photon, there is no longitudinal component, and therefore they are not consistent.
So, this 23 corrects your mistake here. And how did you realize your mistake?
Oh, this is a different story.
Oh. Which is the correcting paper, 22?
Yeah, this is the one.
And how did you discover the mistake? So, this is the Feynman?
Feynman and Berman redid the calculation and they sent us a pre-print. In the original paper, we had a total decay probability, which contains the square of the logarithm of mass over electron mass. And Feynman and Berman paper has a linear power of this logarithm. So, they found the error, which I just mentioned. However, they made a mistake also. And as soon as I saw their paper, I realized right away that there is no logarithm either. And Alberto and I did the calculation very quickly in a few days, and in fact showed that the logarithm term was completely absent.
So, 22 corrects 16 with Feynman in between. And in between…
I mean, some papers in between may have the same error. Because we didn’t know that there was a problem. And that old error is corrected by that one. After this paper was published, I get at least several phone calls from experimentalists. So-and-so did the calculation and disagrees with our calculation. It’s always the case that these people who did the calculation forgot the problem. It’s a very subtle problem, and on the surface, it looks like an ordinary calculation is okay. But since it involves infrared divergence, you have to be extra cautious.
And then paper 22 is also important. So π-e decays?
Yeah. I think this is one I wrote—actually, the work was done with Feynman.
Feynman was visiting Cornell for one term, and he brought to us the paper with Berman. And, of course, there was an error in that paper, and that’s why Feynman was very sorry that he didn’t see there was an error. It was a different type of error. He said that the mistake they made is copying one formula from one page to the next page.
That’s what you said. But you doubt that. [laugh]
[laugh] Which I don’t believe. [laugh] But anyway…
So, did you work with him on that paper, on 23?
But because he had made the mistake, he didn’t want his name?
He didn’t want to sort of blame his student.
Ah, ok. Oh, I see. So, this corrects his mistake with Berman, but he didn’t want his name on it, because it would cast—he would rather you correct the mistake than Berman correcting the mistake.
And this one, “Radiative Corrections to Fermi Interactions”? You’re back with Sirlin again, 24.
Now, the Fermi interaction is a four-point interaction, and so of course they also need radiative correction. Of course, this is not really relevant, because the Fermi interaction in the standard model is mediated by W, Z, and [inaudible]. So, I think Sirlin and guy at Brookhaven [laugh]—I forget the name…
Theorist. I don’t know the name. [laugh] I don’t remember. [laugh] It’s coming out, but—[laugh]
Theorist. So, not…
Oh, Marciano. Ah. I didn’t…
Marciano was Sirlin’s student.
So, then you’re back to the helium atom in a ‘59 paper.
Yes. Paper 25, yeah.
Number one was maybe—I don’t remember exact number, but something like 18, 17 parameters. And this one is I think 80 parameters. So, the answer is improved significantly.
And again, are you still going to NYU, to the UNIVAC at NYU to calculate?
Yeah, I think so. This is ‘59. I have to look at the paper, but I think that is right. See, this happens on the time scale of about three, four years.
And Cornell still doesn’t have a good computer?
Not at that time. Later on, they had some better computers. But, actually, the Cornell computer was not good enough for my purposes, and I used some at San Diego and a few other places. Well, that’s not for—for g-2, I used different computers, because the Cornell computer was not useful for that one.
And then you have resonances—we talked about this. Number 27. That was the Journal of Mathematical Physics article. That’s the one that didn’t get a lot—the attention it deserved.
Because it was in a…
Yeah. It’s famous now, [laugh] only after Lee and Nauenberg wrote another paper.
Right. So that’s the origin of the Kinoshita, Lee, and Nauenberg…
And actually this [inaudible] is actually related to Feynman’s mistake.
The point is when you made a mistake or made a mismatch of longitudinal mode, you get the dependence of log. And only if everything is done correctly, this log term goes away.
And then can you explain the enthusiasm for Regge poles?
Hans Bethe shows up here for the—[laugh] the only time I collaborated with Hans. He knew a lot of mathematics as a well-trained German physicist usually does. And so, he was very happy to deal with Regge poles, and we had some discussions. But, well, this is just a mathematical theory, and not really a physics problem.
And is this one a physics problem?
Yeah. This is the first paper I wrote at CERN.
Right. Tell me how you got to CERN. You were a Ford Foundation fellow?
In 1962, I went to CERN.
And how did you do that? Who encouraged you to go? How did you think of going to CERN?
Oh, I guess this was more or less close to my sabbatical year. And so, if I go away from Cornell, the only place worth going to is CERN. [laugh]
In fact, I got a Ford Foundation fellowship and went to CERN.
Now, wait, back to personal life for a minute. By this time, Ray and June are born?
Yeah. That’s right.
So, do you take them all to CERN?
And how did you like CERN?
Did they like CERN?
Did you like CERN?
Oh. It’s nice to be there. In particular, I become a very good friend of André Martin. And so, I liked [laugh] him very much. He’s a very good mathematician and also has a good sense of physics. In fact, we wrote a paper together. This one.
Martin and number 30, yes. So, at CERN, you wrote this one on Regge poles.
Twenty-nine. Thirty—the upper bound for high-energy scattering amplitude.
This is written later, but it’s following the idea explored in this.
So, this was the first time you had visited CERN.
Is ‘62 to ‘63. And what about Brookhaven? Had you been to Brookhaven during the summer months?
Several times. I don’t remember how many times. [laugh] Probably three or four times. Because I took off from Cornell to Brookhaven.
So, this paper too, you wrote with Martin. And here, Khuri, this wasn’t at CERN then?
No. Khuri I knew from before that. In fact, I should have known him when I was at Princeton. He was a graduate student at Princeton at that time. But around the time when I got involved with Martin, Khuri also was interested in the things that we were doing, and quite often we worked together, and this is one of the things. You see, I wrote three papers with Khuri.
And you’re back at Cornell, then.
Yeah, I’m back at Cornell. And then I went to CERN again, 1966, I think.
Yes. Now, wait. Before you get to CERN again, the Ken Wilson—Hartman says that you were responsible for Ken Wilson coming to Cornell.
Actually, this was before my first visit at CERN, which was ‘62. And he already decided to come to Cornell. I think I wrote a very strong letter to Hans, and Hans decided immediately, “Let’s take him.” [laugh]
Oh, ok, because Hartman said that you were the person who was responsible for him to come.
Not exactly. I’m not in the position to make an offer. But maybe when I went to CERN in ‘62, Ken Wilson also was there.
And we interacted to some extent. Particularly whenever I asked Ken some question, he’d say, “Wait a minute” and pull out some paper from his drawers, and say “Here’s an answer to the question.” [laugh]
So, that’s the way—he has thought about many, many things concerning with Regge poles related problems, and so I was very impressed, and reported back to Hans that we would be lucky to have him.
And then Hans—so Hans, then, was in a position to ask him to come?
And who was the chair then? Was Corson the chair yet?
At that time, I’m not—Corson was not the chairman one or two years after I went to Cornell. So, some other person was the chair. Name is also almost to here, but I cannot quite…
So, you come to CERN in—here, ‘66 to ‘67. So, you work with Khuri. And these papers too—36, 37, 38—are probably before CERN.
On forward scattering amplitudes.
That’s sort of an after effect of the first visit with CERN. All these are related topics.
This one also is related.
Which one, 39?
And probably this. Probably 40, too.
Ok. Now, so you get to CERN in ‘66.
‘66. And within a few weeks of our arrival at CERN, the theorists were invited to visit the experimental groups. And the first experimental group I visited was actually doing a muon g-2 experiment. And they had a picture of measurement in which muon detection has a decay structure superimposed by spin orientation stuff. And looking at that picture, I sort of thought, well, how beautiful it is. [laugh] And it must be possible for me to do something for muon g-2. And that night, in my bed, I figure out how to solve the problem [laugh]. And the next morning, I went to the experimental group there, and, “I know the theory of how to solve the problem.” Turns out that was probably written somewhere here.
They are not published here, but it was reported at the Cargés summer school or something.
I’ve seen that, yes. You gave a paper at the Cargés summer school about it. And what was that paper on?
That is a paper on my struggle to solve the problem. [laugh] The first part was very easy. You see, when I saw the experimental curve, I recalled that there was a paper on muon decay in the fourth order, mu’e decay in the fourth order. No, not mu’e decay; muon g-2—in which Wickman and Suura…
Wickman and Suura.
Suura. They computed this diagram. A very simple diagram—mu and e. And it had a term of rho and mu over m_e. And they published around 1957 or ‘58. And this was a very small and simple calculation, and they reported the number like that for muon g-2, fourth order correction. So, that was it.
And why is this called fourth order?
One, two, three, four interactions.
Four interactions, ok. So, the orders refer to the number of interactions.
And they always go up by two because you have the—this is the electron, and this is the…
Second order is something like that.
Now, the question is, how you got this. And at the time when I saw this paper by Wickman and Suura, I just thought, “So what?” But when I saw the experimental curve, this problem came back to me and I suddenly understood why it was. And that is this factor comes in from the renormalization group. Which I didn’t really know at that time, but some people after they saw my paper, they said, “That is all the applied renormalization group.”
Applied application of—
Oh, applied renormalization group. Oh, ok. So, you saw this paper when it was written? The Wickman and Suura paper, when it was written?
When this was published, it didn’t connect.
But you saw it, but you didn’t…
I didn’t know what it was. Then as soon as I understand that, you also see what this sixth-order term would be like. Or this is even eighth-order. All these can be related to the rho [inaudible] order diagrams plus a [inaudible] which you can fix by renormalization group technique.
So, you saw this diagram on the wall…
No, no diagram. Experimental curve.
Experimental curve, right. But you had been working on related issues to that. I mean, a lot had prepared you to understand that curve.
Such as all of these papers on polarization in mu decay, and radiative corrections.
No, no, it’s not there.
Because this is the first time I got interested in g-2. And the interest came from the experiment and understanding this particular problem of Wickman and Suura. And then once you understand that, you actually can compute a sixth-order correction without doing any work. Just go to the library and print out necessary formulas from the publication. So, that was very exciting.
And which publications were those, then? Oh, that—we’re on the wrong page.
I think this is the paper.
Forty-one. Nuovo Cimento.
So, you go to the library. You find what’s needed to be added.
Well, this is…
—probably summer school at…
This is summer school at Cargés you think?
That is likely to be the case, because it’s published in Nuovo Cimento. Now, that is not the end of the story. [laugh] Actually, there was another diagram like this, which I wanted to evaluate in the same way. But it didn’t work. And the reason—and also, you see, this diagram is known as the Euler-Heisenberg in the light-by-light scattering problem.
The light-by-light scattering?
The light-by-light scattering. It was studied by Euler and Heisenberg before the war.
How do you spell Euler?
But he was much earlier. The mathematician?
Oh. The Swiss mathematician, Euler.
No, no, this is a physicist. Euler is another famous mathematician with the same name, but this is a…
Heisenberg was his student, probably. Now, the point is this at low energy, this is proportional to [inaudible] force of the photons. And at the low energy, therefore, it’s very small. So, I saw that at the beginning this also would be very small, and I tried to prove that, without doing any calculation, that this is a very small contribution and therefore you can ignore it compared to this. Which is wrong. Euler-Heisenberg showed that thirterm is very small near the threshold. But this is not near the threshold. This is a muon. This is electron. And the momentum here is the muon momentum. So, this condition is not satisfied. And so, this could be large. So, this was computed analytically much later, but at the time it was a very difficult calculation to do. So, I decided to do a numerical work. Write the program and evaluate the calculation by a numerical method. Turns out, it is huge. Like in alpha/pi to the cube times factor 20. And that was a really amazing discovery that we—oh. This numerical work I started for the first time on g-2, my teacher was Stan Brodsky. Actually, he was working on the same problem, and we worked together.
Was he at CERN?
Oh, ok. So, he’s at Cornell.
I was back to Cornell.
You were back at Cornell, yeah.
Must be other ones. Ah, this one.
Here’s Brodsky. Yeah, it’s 45.
This is the paper.
Oh, so this is light-by-light scattering, 45, yeah. So, you work on it with Brodsky, Dufner, and Aldins.
Aldins is my student, and Dufner is Brodsky’s student. And this is a paper discovering a huge contribution from this diagram.
Are both of these—44 and 45?
Yeah, that is the announcement, and this is the actual calculation.
Forty-five is the actual calculation, yeah. Forty-four is the announcement. So, this is a big discovery…
—in calculating, again, the sixth-order of g-2—
—which didn’t show up in the fourth-order calculations.
That’s right. It’s a completely new diagram.
So, when we found this is large, we talked to some people at CERN, and T.D. Lee was at CERN at that time. [laugh] He was very excited. And he announced that to everybody over there. [laugh]
When was he at CERN?
Probably 1970, ok.
So, that’s how actually I started using the computer. Helium atom was also a computer work, but it’s completely different.
How was it different?
Well, the helium problem is actually a variational method, and you have to compare it with the measurement and then see how they move around with you as you change the parameters. But this one is a QED problem, in which there’s no free parameter, and you just have to evaluate the integral, which in the sixth-order case, is probably a seven-dimensional integral. And then by the time you go to the tenth order, you have a 13-dimensional integral. And the usual method of numerical integration may or may not work on higher dimensions. In fact, practically speaking, the number of terms increase like n factorial, so by the time you go to ten, it’s enormous. And another thing—each—this is [inaudible] with different integrals, and then each integral itself grows up like n factorial. So, we are lucky that we used a program called Vegas, random number sampling program written by Peter Lepage, who is at Cornell.
Peter Lepage [sic]? B-A-R-G-E?
Ok. So, by this time, you were using computers at Cornell?
Not necessarily. [laugh] The Cornell computer was not useful for this purpose. I probably tested something on it, I remember. But I sort of had to use a national computer.
Where is that?
San Diego, for instance.
And would you fly to San Diego to use it?
No. That is not necessary. You send the program and somebody—the program writing has to be done by yourself.
And where was the computer at San Diego?
I don’t know. I mean, I send it to San Diego, and somebody takes care of that. Even that, I no longer used after few years.
So, let’s see. You have a—oh, hadronic contributions. Number 42. Is that a special paper?
Forty-two, with Oakes.
Oh, this was at CERN. I think this is not particularly useful, because hadronic information was not very good.
Oh, ok. But the really important thing was 44 and 45, the light-by-light scattering?
And then 49, you do vacuum polarization contributions, with Brodsky.
Oh, yeah. This is actually a small calculation.
You mean 49?
Yeah. Diagram—say, something like that.
This is a sixth-order diagram. And this can be estimated using the renormalization group method, however, that also [inaudible], and it doesn’t give us the exact result. So, to get the exact result, either you calculate analytically, or numerically. This was analytically calculated by many people later on, but at the time, the numerical method was the only way to get the finite part, and that’s what we did, Brodsky and…
So, all through here, you’re working mostly on g-2, but you have other concerns?
Yeah, this is…
[inaudible] with scattering amplitudes, 50, 51, on particle production?
Oh, yeah. This is something…
—which Brodsky, I, and Terazava—the process is something like that you scatter two particles, and then it creates something, and it creates something. So, light-by-light scattering cross-section is involved here. So, this is experimentally useful information. And we did calculate something of that sort, and that is this paper. Yeah, two-photon mechanism. Because the two-photon on the incident particles.
Two-photons released by the incident particle.
And is this a related paper? Fifty-two?
Yeah. I think this is a few years later. I’m not sure whether the order is right. It’s related.
Oh, right. ok. And now you do another sixth-order radiative correction paper.
And this was my graduate student.
How do you pronounce it?
And this is the beginning of the serious g-2 work.
Why do you describe this as serious as opposed to the other papers?
Because the other papers were approximations. These are all approximations. You cannot be serious. So is this. If you use the renormalization group technique, you only calculate the leading term, not the complete calculation. But this is the beginning of a complete sixth-order calculation. And he was a very good student.
Where was he from?
From Yugoslavia, or whatever that…
Where is he now?
He’s at Georgia Tech or someplace in mathematics. After writing this paper and a few more papers on physics, he decided not to work on physics. [pause] To work this, we wrote several papers with Cvitanovi?. These are all different parts of the same problem.
But here you’re working on the magnetic moment of the electron, 57.
Yeah, yeah. This is the same as mu except that mass scale is different. And in the muon case, you still can use this renormalization group idea, but for electrons, it doesn’t work. Because what you have is either—it’s electron and equal one, so it doesn’t affect [inaudible] or otherwise, if this is an electron and this is a muon—or no, the other way around—this is a muon and this is an electron, the mass dependence becomes m_e over m_mu squared, which is very small. And now, here is the charmonium.
Yes. Why do you get interested in charmonium?
This is the experiment—I think the experiment discovered some state, hadronic state, which could be interpreted as a kind of charmonium or something. And—well, anyway, as soon as that information became available, a bunch of us—Eichten, Gottfried, Kogut, Yan, Ken Lane—got together—
—and made a picture of charmonium-quark anti-quark bond state, and applied some potential, which is called later by other people a Cornell potential, which is the Coulomb potential plus linear wall, because of the confinement. Well, anyway, we computed charmonium—I mean, quark anti-quark bond state spectrum using this Cornell potential in a very naïve way, but it reproduced all these spectra of charmonium state. So, in fact, this is still quoted by many people, and it’s an important paper understanding—
Again, 58 paper?
The Cornell potential, it’s called.
Yeah. We didn’t call that way, but—
And you have a number of related papers, so 60 and…
Yeah, this is still related to—yeah. This is back to the QED paper.
Small details, but the idea is not new.
Sixty-one, yes. But you have a charmonium, the model paper. This is a—in Phys Rev, 64. Is this a summary paper?
Yeah, this is all related to this. This is a short paper, so it’s announcing. And this gives you the details.
Sixty-four. Phys Rev Letters is 60, and 64 is this. And then you do a paper on comparison with experiment. Where were the experiments done? SLAC?
Let’s see. SLAC certainly is one group of experimentalists. And then people in Europe also found something that way.
At CERN or at—
Now, you said this is the beginning of the serious g-2, sixth-order.
When is the end?
You may not know Lindquist.
Yes, I remember Lindquist.
He was a student of mine. Worked on g-2, eighth order.
But when do you announce this—when is the final sixth-order paper?
This was ‘81.
But that’s eighth order, that is paper 66. When is the sixth order?
Sixth-order was this one. Oh, this is the letter. Oh, yeah, and as I said, there are [inaudible] papers.
Here we go, here we go—“Sixth-order Magnetic Moment of the Electron.” Fifty-seven.
So, this you would consider the definitive sixth-order calculation?
[inaudible] formulation. You see, the point is that numerical integration is never finished. You simply approach [laugh] the correct result. So, if you get a value better than the experimental precision, then you say theory went that far. But if the experiment improves, you can recalculate, and you can put the theory ahead of the experiment.
Now at about this time, isn’t the second or third g-2 experiment done at about this time, in the ‘70s?
The second—you mean—the first experiment is done by a group at Columbia, Foley and…
No, no, that’s different. G-2 is done in ‘47.
You could do it without parity violation?
No, before parity violation. Well, anyway, the guy got a Nobel Prize for that. [laugh]
Hmm. Who was…
Again, I tend to forget names. It’s sort of coming, almost.
Let’s see if we can find it.
Oh, yeah—Polykarp Kusch.
That’s 47. And then his experiment was on the Zeeman effect, but then—that was atomic physics. And then within ten years, some other people did another atomic experiment which improved the precision, maybe by an order of magnitude. But then people realized that atomic experiments have a limitation. And so, in particular people at Michigan did the experiment by circulating electrons in a magnetic field, and the precision of the spin at the big magnetic field.
Right, that was Farley’s experiment and…
No, I’m talking about electron.
Oh, the electron. Ok, right.
And Farley’s experiment is simply a copy of that experiment, for the muon. Of course, muon has a different problem, but for the Michigan people, got a pretty good result for the electron by this method—the spin-precession method. Because an electron never dies, and therefore you can circulate as many times as you want. On the other hand, the problem with the electron is polarization, and the detection of polarization is not easy. For the muon, polarization is natural.
It’s a gift. Parity violation is a gift to the…
Yeah. But for the electron, that doesn’t take place. So anyway, Michigan people probably improved by three orders of magnitude over Kusch’s experiment. And then Dehmelt at the University of Washington had a different idea. A magnetic bottle, which is called a Penning trap. You can trap the electron in the Penning trap and let it go around anytime you want, like for a few days or even for a few weeks or so. And in the meantime, you flip the spin by applying an RF field. And this gives you a very precise measurement of g-2, another three orders of magnitude. And then Gerry Gabrielse at Harvard, who was actually a postdoc with Dehmelt, he improved on the method of Dehmelt and got another factor of 20. He’s still working on it. Because [laugh] theory is about an order of magnitude ahead of experiment right now.
But for the g-2 of the muon, the third experiment is published in about 1979, so it’s published about this time.
And it confirms the theory to a precision of seven ten-thousandths.
Eighth-order calculation, there are several papers.
You start the eighth order. But why don’t we talk about the eighth-order tomorrow?
We’ve gone up to the sixth order. So, should we talk about the eighth-order tomorrow?
No, eighth-order already has been published. Here is the work. Eighth-order g-2, you have to compute 891 Feynman diagrams. And you cannot hold all of them in a single paper, so that’s why there are several papers. [laugh]
But should we talk about this tomorrow?
Oh, yeah. Sure. You look tired.
I’m tired again, yeah. So tomorrow, can we…
What’s good for you? Nine again?
Nine is fine. If you like, ten is better, probably.
OK, let’s do ten.
Ok. I’m tired, too. So, anyway, there are still quite a few papers to talk about.
Yes. Ok, good. [End Session 4] [Begin Session 5]
Yes, this is Robert Crease, and I’m talking to Toichiro Kinoshita, and it’s January 10th, 2016. Now, yes, I had asked some of these questions, but you sort of answered them—that you decided to already—the answer to this is…
Undergraduate education—again, school system is slightly different, and this university level, you see, I attended at the post-secondary level, which is Daiichi high school. That means first high school, which is actually—it’s equivalent to the undergraduate education here. At that point, there are only science-oriented course, and otherwise. So, there are two broad separations. And so not specifically for physics.
But by then you had decided—you enter the science track.
No, at this point I chose scientific course. So that more or less answer your question. But not in physics in particular.
But just in science, yeah.
Yeah. So, it’s more like that. Science and technology, maybe. I was not particularly impressed by any of the teachers. They are ok but [laugh] not very inspiring.
Not really until your math teacher at the university?
Oh, yeah, the math teacher was more interesting. You see, at this level, which is the beginning of high school—equivalent to the college here, but the curriculum is slightly different, shifted. And the first year of this first high school, so-called, the math teacher was quite interesting. Also, he went so fast, so his first one-hour lecture covered 30 pages of the text of what he means by continuity, which was not a concept I got used to in secondary school. So [laugh]—but, well, I had to catch up, working hard, on what that meant. But after that, it was much easier. So, that’s math. There was no particular impression with physics or chemistry. It was sort of dull. I mean, I knew much more than what the course was teaching. Again, when I entered Tokyo University, that’s three years of undergraduate at Tokyo University, and then all the rest is graduate. How many years depends on [laugh] how long you work. So, at least when I decided to go to the physics department of Tokyo University after first high school, certainly I decided to take physics. Well, actually, this math teacher I mentioned few moments ago, I had a pretty good contact with him, and some of my friends got together and got special tutoring of mathematics, like group theory and so on. It was not in the curriculum, but we knew that mathematics has a lot more stuff to cover. And one of the topics we asked this teacher to help us was to understand what is meant by group theory and so on.
But you had already read Weyl’s book, hadn’t you?
No. Group theory in a formal sense. Weyl’s book is group theory specialized to quantum mechanics. Well, anyway, I had some general idea of what group theory should be, but this tutoring by this professor, an extracurricular activity, it was quite helpful.
And you did this extracurricular activity by yourself or with other students?
A few of my classmates got together and asked this teacher to give extra-curricular textures. And I think at this point he realized was not really good for mathematics. [laugh] So, when I asked him something about that—he said, “You should go to physics,” or something like that. So that—whether he influenced me or not, I’m not quite sure. Because I was already very oriented [laugh] to go to physics, anyway. Question here—it’s not—I cannot really answer this way. I just got interested in physics as a subject. Doing research is part of it, but not—I don’t know.
So, you didn’t in particular want to be a teacher or a…
Being a teacher actually seemed pretty dull, [laugh] actually.
But did you want to become a teacher, or did you want to become a researcher? Or an experimenter?
I wanted to be a theorist.
Oh, you wanted to be a theorist? Ok.
Yeah. So that’s what I wanted to be. It was influenced probably by Einstein or something, which I mentioned yesterday.
You had read Einstein and Infeld’s book.
And also, at that rate, before I—this is undergraduate level—I knew that Yukawa did a lot of great things, and certainly I was very much interested in his work—I read his book also.
Read Yukawa’s book?
Yeah. Which is not only particle physics but nuclear physics in general.
And this is an interesting question. After you graduated, what did you expect to do?
This is at undergraduate level, right?
Graduate training comes later.
But what did you think your career was going to be like as a scientist, as a physicist?
Oh, probably university professor or something like that. Although some of my friends became [lower level] teachers. Some of them went to industry and so on. So, at this point really it just depended on the opportunity. If something opens up, then you tend to go in that direction. In my case, I was going into graduate training, so this question of what I would do in the future didn’t take place for a while. Ok?
How did you choose to go to Tokyo University? Graduate school, you mean?
Well, this is the best place to go in Japan. [laugh]
And you were already there at the undergraduate level.
And here, how were you supported? You referred to this fund.
Yeah, I got this fund. That’s after that. I think I was supported partly with my family’s money, and then also I got some scholarships from some Japanese newspaper, maybe for a year or two. I don’t remember how long. These of course helped…
From a newspaper?
Yomiuri is one of the—there are Asahi and Yomiuri and a few more papers in Japan. Yomiuri is one of the big major papers.
And why did they support graduate research?
Oh, I don’t know. [laugh] Anyway, they tend to support some people from university area for a year, maybe. More precisely, I think some of my teachers at Tokyo University probably made a recommendation. Who did that, I don’t know. But unless somebody does that, they’ll never know who should be supported. So, it’s like being supported by the New York Times.
But the New York Times doesn’t support anybody.
No, no. If they would.
So, it would be interesting to know the logic behind it, the reasoning.
I don’t really know the reason. I was happy that I got the money. [laugh]
Anyway, when I became a student in Tokyo University, again—see, the system is different from the American system. We’re talking about the graduate part, right?
Now, as I said yesterday, the undergraduate part stretched over ‘44 to ‘47 and was interrupted by end of the war. So, it’s not very simple. [laugh] You see, one and a half years after the end of the war, I was still an undergraduate student, but I started working on some research.
Because you had that one-and-a-half-year period when there were no courses you could take.
You just could devote to research.
So, I had a great freedom and could do everything I wanted to do. And my teacher was actually a mathematician. Kodaira, Kodaira.
Now, Kodaira if I understood, is the first teacher that you really thought was a really great teacher.
Yeah. No question about that. He was very clear. His lectures were so impressive. I’m really happy that he was my teacher. And I started out the research project under his guidance, but he was not a physicist, so essentially my classmate and I generated curriculum for—as I said yesterday, I think, we wanted to start from the latest publications. And looking at the library, I found that a few papers of Dirac were in the library from 1942 or maybe ‘43, and these were something which we never had before, so we started with these papers of Dirac. And then somewhere along the way, we found that Pauli criticizing Heisenberg is work as a picture frame without a picture. So, we started looking for Heisenberg’s paper. Then my friend Yamaguchi found it in Tomonaga’s library or something. And it was published around 1943. No journals were coming anymore from abroad to Japan during the war. But these particular journals were there, and they were brought by German submarines to somewhere like the Indian Ocean, and there it was transferred to Japanese submarines and came to Japan.
And how did you learn about that?
That’s what Yamaguchi told me. And that’s what he probably heard from Tomonaga. And Tomonaga probably heard from the Naval officers.
The Naval officers, yeah.
Anyway, those papers were not supposed to be in Japan at that time, because there was no communication and so on.
And have you kept any of those papers that you used in the old days?
Have you kept any of those papers?
No, unfortunately not. When I moved here, I threw away most of the things. [laugh]
Oh. Huh. Hmm. And you said these were copied by people actually typing the papers over again?
Yeah. At least some papers were actually typed and mimeographed, and these were distributed to whoever was interested in it. I also remember some papers, photocopies of originals. Again, I don’t remember who did photocopy, but certainly I remember using some of them. So, unfortunately for you, [laugh] when I moved [to the U.S.], I threw away most of the things. I thought I’ll never use again. Including my own—many, many research papers and tapes.
Used to be tapes. Remember that?
Tapes of—what do you mean, tapes?
Oh, computation tapes, yes.
Oh, those big ones you had in your office. The piles of tapes, computer tapes you had in your office at Cornell.
These are all gone.
If you had told me to keep it, I would have kept it. [laugh]
Do you have any old notebooks?
No, they’re all gone. Once the work is written as a paper, anything that supports it is usually so bulky and occupies so much space, and I threw it away. All the important information is put in the paper. [laugh] So, anyway, unfortunately I should have kept them but, moving here was a big deal.
That’s too bad, yes.
You have to realize that in ‘47—end of ‘47, Tomonaga and Koba discovered renormalization. And it excited all of us. [laugh] You could do a lot of things which were impossible previously. And so, people became very busy working on many aspects of the renormalization theory. I was one of them.
Ah, ok. So, that’s what drew you immediately into this area.
Yeah. Actually, even before that, I was aware of Tomonaga’s super-many-time theory, published in ‘43, in Japanese. So, I studied that paper rather in detail, and in fact I used that as the topic of my graduation seminar speech. You have to give a talk to the people—the professors and the friends—about what you have done [laugh] to graduate, and I chose Tomonaga’s ‘43 paper as the text for my talk. So, that is ‘46. No. Graduation is the summer of ‘47. And so that was ’47. Certainly, I knew what Tomonaga has done, except the renormalization part. So, I said, “This paper is beautiful, but it cannot calculate anything.” [laugh] It’s infinite. Oh, that was the kind of talk I gave. And then a few months later, Tomonaga and Koba found that it can be made useful by renormalization.
And again, Koba was his student?
No. Koba was actually a special case, because he was probably ten years ahead of me at Todai, and he delayed his career because he had TB or something, and he was sick for many, many years. That’s why he didn’t go to the war, either. But when I started working in ‘47—’46—he was the best person in the Todai group. And that’s why Tomonaga picked him up. And, actually, Nambu also was very good, but he was ahead of me by two years, and he was in the army. And he came back to Todai after I came back to Todai in ‘46.
By the way, just to make sure I understood, you said the reason you didn’t go into the army was that you failed the test?
But you don’t know why you failed.
[laugh] I don’t know. Maybe they took into account that I was a physics student at Todai, and so probably they postponed drafting me into the army.
Oh, so it’s not just that you failed a test, but that they postponed—
I don’t remember, because I was in pretty good health. So, I don’t know why I failed.
But they decided not to take you in.
They decided not to take me. I was very [laugh] grateful for that.
Because my classmates at the high school, probably more than 10% of them were drafted and died in the war. So, I could have been easily in the draft, and these are the people in non-technical areas. The technical people were spared, at least for a while, until they finished university training. So, that was the case with Nambu. He graduated in ‘45, I think, or ‘44, or maybe even—maybe ‘44. I have it written somewhere. I forgot to mention in section one when Nambu graduated. Oh, he graduated from—I think this was undergraduate—1942. And he was about three or four years older than I. And he was drafted into the army as soon as he finished his training in physics. Understand—this was not really—the army research lab, that’s what he was drafted to serve in, not in the front.
Right, so he stayed in Japan.
Yeah. And then he had to be there for a few more months after the war to close down the facility he was assigned to. So, anyway, I think the situations of science-student university graduates, they were actually more favorably treated than those in a similar situation in the U.S. I remember some of the people in the U.S., scientists, were actually drafted before they graduated. Ok, well, that’s so you understand the situation.
And you talked about Feynman diagrams. You learned about them first from Dyson’s paper.
Yeah. That came to Japan—I think I mentioned that—in 1947. Oh, or ‘48. ‘47 is where the Newsweek and Time magazine began to come to Japan, and then we learned about the lamb shift and the magnetic moment anomaly from these journals. Not Phys Rev. And the Feynman diagram from the—Dyson’s paper, which Yukawa sent to us in Japan—did I say this? Somewhere, I said that.
I think so. So, Yukawa was in the United States, then.
He was invited by Oppenheimer after ‘47, or no, ‘48.
Oh, here it was. “While our work was in progress, we received from Yukawa a brand-new pre-print of Dyson’s paper.”
Yeah. That was it. So, actually, Nambu and I started this renormalization possibility of vector meson theory before we heard about Dyson’s paper. Before we made big progress, Dyson’s paper appeared in Japan. And so, we reformulated our problems using Dyson’s paper as our prototype. So, that’s…
And you came in ‘52.
Now, Tomonaga went to the Institute, I also wrote somewhere, in probably 1950—’49 or ‘50, I’m not quite—it’s in there.
Oh, here. “In the summer of ‘49, Tomonaga and Kodaira were invited to the Institute.”
Yeah. Ok. And Tomonaga stayed at the Institute until—just one year. Kodaira stayed in U.S. for maybe 20 years. Then we sent our paper to Tomonaga at the Institute. He showed it to people like Pauli, as I said yesterday. And Pauli was very impressed by the quality of our paper. [laugh] Anyway, Tomonaga recommended to Nambu and I, Oppenheimer, very strongly I think, and that’s why we went to the Institute. Now, I don’t remember writing any application letter to Oppenheimer. I think somewhere I have a letter from Oppenheimer inviting us to the Institute.
Do you still have it, do you think?
[laugh] If I work hard enough, maybe.
If you find it, let me know.
Yeah. And this was ‘52.
Of course, working at the Institute, it was very nice, because you don’t have to worry about how to feed yourself and so on. That part of the life became very stable. So, you can just focus on what you do—research. I had some interaction with Pais. In particular, the paper I wrote on the C-meson, Pais wrote the same paper but called it the F-Meson. [laugh]
Ah. That’s what that’s about. Yeah.
And I sort of proved both of them wrong.
So, that’s the beginning of my interaction with Pais. Pais was a staff member at the Institute, and he sometimes invited us for after-dinner talks or something. So, he became very friendly. Even after he moved to Rockefeller, he was very friendly to me. And [inaudible], we used to go to a Chinese restaurant in Princeton, I think Witherspoon Street, or something, to have dinner with them and their wives. But our interests were somewhat different, so I didn’t talk physics with them. Einstein, I mentioned yesterday. Pauli, I mentioned yesterday, too, I hope. I thought. Because I had just one encounter with Pauli, and I was frightened by Pauli. [laugh]
No, nothing happened, but he was so—I mean, he’s known to frighten everybody. [laugh] At many seminars at the Institute, Pauli was so critical of speakers. Sometimes the speaker couldn’t continue. That happened—I saw—Pais just standing in front of the blackboard and unable to talk. And then Oppenheimer told Pauli, “This is Pais’s seminar. Let him keep going.” So, Pauli quieted down. But anyway [laugh] it not only happened to Pais, but I know it happened to Yukawa. It happened to Klein.
And to Yang?
Yeah. And this I talked—I don’t remember—I must have heard his talk, but it doesn’t—my memory doesn’t cover his talk.
Yang-Mills talk, yeah.
So, then after Institute, I went to Columbia from 1954 to the summer of ‘55 as a postdoc. T.D. Lee found—I asked him—they had some position at Columbia, and T.D. Lee found some scholarship—I forgot the name of the scholarship, but it was a very prestigious scholarship at Columbia. It’s probably written somewhere, in my career. [pause] Oh, it doesn’t say. Well, this postdoctoral fellowship, I don’t remember the name, but for instance, Mandelstam was a recipient of the fellowship after me. Being postdoc at Columbia is very nice. I met many people like—let’s see—I can’t remember the name. The old gentleman. I should know his name very well.
Rabi! Yes. He was still active and would come to afternoon tea or something of that sort, and he had his opinion on all sorts of things. So, it was very nice. And at Columbia, I kept working on helium atom, which I started at the Institute as a summer job. So, I had some contact with the Watson Lab.
And you used the NYU computers?
That’s somewhat later.
Oh, that’s later. Ok. But for the early helium paper, you used the Watson computer?
Maybe I had had some introduction to that, but I don’t remember using it any real way. Probably I was still at the stage of writing a program in Fortran or something. Pre-Fortran type of programming. Because I started using Fortran heavily only after I used the Bell Lab UNIVAC or something. And then I went to NYU to use their computer. The order may not be quite right, but anyway, it took some time to write a workable program, and then more time to run. And the really good data begun to appear on the Bell Lab computer, which was much better than anything else.
And you used that when you were at Cornell or Columbia?
Bell Lab computer is after I went to Cornell.
Oh, ok. And the language you were writing in was Fortran?
Probably I started out writing using some other language, but I started using Fortran at some very early time. Again, I had some box full of programs [laugh] I wrote at the Institute, but they’re all thrown out.
Unfortunately. [laugh] But you see, after a few years, some visitor to my office at Cornell looked at the shelf filled with [laugh] computer programs, and in fact, the shelf actually collapsed, and everything came down to the floor.
Fortunately, I was not in the office.
When was that?
I don’t remember, but certainly not very late. Because afterwards, I never used punch cards. All the information was put in a tape, round stuff around this size, which didn’t occupy the big shelf.
So, the shelf that collapsed was full of punch cards?
I suppose that was the case. I’m not completely sure. Ok. And I think I told you yesterday that I didn’t write to anyplace, but since Salpeter came to Columbia to give a talk, I asked Salpeter about the possibility of Cornell. And he talked to Bethe, and Bethe said ok. Now, were you encouraged to work in a certain direction? I think experimentalists at Cornell wanted for me to work on some of their problems, but I was still in the middle of the helium atom problem, and I didn’t want to divert my energy to something else. So, I probably was not too happy with—some people were not too happy with me. [laugh] Anyway, I was not told directly to do anything for that purpose. You see, you have Hartman’s memoir or something?
He must have mentioned the chairman of the department at that time. It’s coming almost to my head but [laugh] I can’t remember. He was a chairman for many years after Corson. Anyway, if I remember, I will tell you. I said Phys Rev and…
Dyson took Nambu and you to get a Christmas tree?
Oh yeah, that’s a—before I went to Cornell. But in the spring of—no, winter, around December, Christmas time, just before Christmas, I suppose, there was a conference at Rochester, the famous conference, and I attended the Rochester conference with Nambu and a few other people. In fact, five or six of us drove to Rochester from Princeton in some car, like T.D. Lee and Yang and some Europeans, and we all went in the same car to Rochester. After the conference, we wanted to visit Cornell, and either Dyson or somebody from Cornell gave us a ride to Cornell, and we stayed overnight with Dyson’s student apartment—I told you yesterday. And then Dyson took us to some hill near Cornell to cut down the Christmas tree.
Oh, that’s what the story was about? Ok. And the journals you read were Physical Review—
More or less. Also, Progress of Theoretical Physics. But the point is that Progress of Theoretical Physics was actually a very active journal right after the Tomonaga-Koba paper. In fact, people say that they read Progress rather than Physical Review because it had more information about the new development. For at least three or four years, that was the situation. But by the time I got to the Institute, there were no new interesting papers in Progress of Theoretical Physics anymore. You had to look at the Physical Review or something. So, unfortunately, the importance of this journal sort of went down. Let’s see. This, I think I told you yesterday.
Yes, because you were working at the helium atom at this time.
No. This time, I was working with Nambu and…
Oh, Sirlin, or…?
This paper, ‘54. It is a sort of field theory with a theoretical treatment of a many-particle system.
With Nambu. This was in ‘54. And ‘55, ‘56—
Yeah, between ‘54 and ‘57—
Oh, yeah, that’s a gap. There’s a gap here. But this paper takes a lot of work to write, to calculate and formulate.
Paper 15, the helium atom paper.
Yeah. That started work on this in ‘54. And to write that took two, three years. So, that’s why. Ok. Well, actually, this paper—
—is one of my most elaborate works. And I heard that Eugene Wigner loved this paper very much.
Paul Hartman also mentions it.
Is that right?
In his memoirs, yes. Sorry, what did you describe that as? Your most elaborate work?
One of the most elaborate [laugh] works.
Elaborate. [laugh] Because you have to write down all the formulation to start with. I think the next paper for this one, too.
Oh, here it is—paper 25.
Yeah, number two. This is the more detailed computational result. That paper was a starting point of this work.
And again, what does the paper do?
As I said, it’s a simple matter of computing the ground-state energy of a helium atom, except that the theory and experiment available at that time disagreed by a big amount, like 0.1% or something of that sort. I don’t remember the exact number. So, you had to check the theory from scratch. And the first paper is a formulation of how to do it, and also some simple calculations, maybe six- or seven-parameter calculations. And this next one is the finishing paper, with a higher precision. After all this is done, actually, I found that some astronomer in Chicago, if I can tell you the name—I forgot—famous guy who also won the Nobel Prize in something—if I cannot—I’m so forgetful of names now—but anyway, he was an astronomer and checking some astronomical problems, and he also calculated the same calculation and came out with my—in agreement with me. So, that’s finished.
And that was before you or after you?
Independent of me. In parallel. I don’t know whether he’s first or I’m first. Well, actually, there is a third guy who worked very hard on the Israeli computer, and he used the trial function with 1,000 parameters or something like that. Clearly, he had a better result, but I think his came out one or two years later. Also, he may have started earlier. I don’t know. Well, anyway, that was a problem which attracted several people. So, that’s the situation. Then before I got to the g-2 problem, I spent some time on weak interactions. This is motivated by the parity non-conservation experiment. And that occupied me until probably around the end of ‘50 or…
So, why did parity violation direct your attention to the weak interaction?
Parity violation occurs in the weak interaction. But also, the experimental precision has to be very good to see some subtle effect. And to compare that with the theory, you have to include radiative correction. Since I was very familiar with radiative correction, it was immediately applicable to the radiative correction to weak decay.
Right, and you’re incorporating the radiative corrections into the theory to help make it experimentally—the comparison with experiment.
Yeah. Also, experimentalists were trying to improve the precision as much as possible, so they needed the radiative correction to the weak interaction. So, does that fully answer this question?
And this question also, I think I told you yesterday, Sirlin was a Cornell student. Actually, a student of Salpeter. But he had worked on the radiative correction before he came to Cornell, at UCLA. And so, when the parity-violation problem arose, he was right there to—could start working on radiative correction of the parity violation immediately. So, we worked together. For the Ford Foundation fellowship I was given by CERN, I think they gave it to CERN and CERN distributed the foundation fellowships to several people. The best thing I did at CERN at this point is that I found André Martin, and we did collaborate on several topics on scattering amplitude at high energy. That’s several papers.
And this was your sabbatical. This was your first sabbatical at Cornell?
It may be one year ahead of sabbatical or something. I don’t remember. ‘62. I went to Cornell in ‘55. So, that must be a sabbatical.
But then your next trip to CERN is in ‘66, which is early.
Yeah. It’s nothing to do with the sabbatical.
Oh, it doesn’t have to do with sabbatical, ok.
If this is a sabbatical, I cannot have two sabbaticals in—
I think the next trip to CERN may have been the Guggenheim.
Your Guggenheim is in ‘73, ‘74.
Oh, that’s much later.
Yeah. So, your next trip to CERN is ‘66.
Yeah. So, I don’t know how I managed to finance—
Visiting scientist. Well, maybe CERN paid you.
Yeah, possibly. The first visit was as a Ford Foundation fellow, but this was not the Ford Foundation. It must have come from CERN. And then I have of course other later visits, not the whole year, but just a few months, the summer, or something like that.
Now at one point in one of your trips, Kay worked at CERN?
Yeah, that may be.
That’s much later. I think that’s maybe in ‘73.
Let’s see—’81 and ‘88. This is a short period work. Kay was a student probably at Harvard. Let’s see, Kay was born in 19—
—’54. And then 1988—’81 is—well, 27—this is much later. [laugh] You see, Kay went to Harvard, graduated from Harvard, around 20 years, or 19 or 20. I don’t remember. And then—that’s undergraduate. And then she attended Berkeley as a graduate student, maybe four or five years. I don’t remember exactly. Then she came to Cornell, worked at CLEO as an experimentalist for quite a while. So, I’m just wondering, it was during her work at CLEO, when probably she’s around her late 20s. Anyway, just a few months in the summer or something like that.
Oh, ok. Because Ray was telling me that you didn’t get enough money in Geneva, and her working there helped support the whole family.
Oh, that’s nothing to do with that. [laugh]
[laugh] That’s what Ray thought. [laugh]
Ok. What about summers at Brookhaven? Was there anything that you remember about the summers at Brookhaven? Would you go to the beach?
Yeah. Some summers at Brookhaven, we go to the beach, as you know. Feynman was also there. And that was just before parity violation discovery or something like that, I think. But mostly on the beach, you relax. [laugh] Swim and so on. Occasionally, he writes something on the sand, some formulas or something like that. But I don’t remember what it was about.
And did you write in the sand, in formulas?
Sometimes. [laugh] Well, I spent several summers at Brookhaven.
Ray remembers you socializing with the Khuris at Brookhaven.
You know, Khuri was interested in what André Martin and I did on analytical prosperity of scattering amplitude. And so, he may have invited me to Rockefeller at least several times. When it happened, I don’t remember. So, it’s possible I knew him and his family even before this Brookhaven summer stuff. But it was more or less about that time.
Now, Ray remembers a summer at Argonne.
[laugh] She remembers a lot of things. I spent one summer at Argonne. I don’t remember what I did there. Which year. Also, I spent some summers at Madison, Wisconsin.
When you worked with Feynman, there was one story I remember you telling me once where you and he are working on the same calculation, and he’s playing the bongos and you’re working at home, and you achieve the same result?
Was that at Ithaca?
In Ithaca, yes. That’s the year when Feynman visited Cornell for the fall term.
Where you were correcting the paper with Berman.
But the story is that he was playing the drums while he was calculating?
Yes. I wrote down the problem the standard way, the decay amplitude and cross-section and so on, step by step. Took quite a while to get the final result. But in the end, Feynman and I agreed with the same result, except I had the paper piled up like that; Feynman had one page. So, he was very efficient. And all the time, he was trying to find out how you make it efficient. Yeah. One trick which was very interesting due to Feynman—and probably it’s not known to many people—that is, you see, the problem was pion decay into e-neutrons plus photon. So, it’s a four-body problem. And the algebra gets very complicated, because which way the photon goes and so on. So, what Feynman found after a few months of writing this way or that way is if you go to—you see, when you do some such calculation in a standard text you certainly choose some reference system which is normally a center of mass or something like that. What Feynman did was if the formulation is completely covariant to start with, then actually you can also apply center of mass of part of the diagram. And then the integration can be made very simple and the whole result becomes [laugh] much, much easier. This trick of choosing transformation of the coordinate system in the middle of a calculation probably doesn’t occur to many people.
And that’s what Feynman was trying to do. And it was very [laugh] impressive…I had so much paper [laugh] and he has one piece.
It was impressive, huh? [laugh] And was his office right next to yours?
No. Then I ask him to put his name on the paper. He refused, because he doesn’t want to hurt his student.
But were you working in the same office?
Next door. I have an office at 310 Newman, and he had an office next door, which is probably 308, which is the office of Bob Wilson. He was on sabbatical leave or something, and it was empty, and so Feynman worked at Wilson’s office. And now, what he does—he used a heater cover as a drum.
He used the heater cover as a drum.
Yeah. And so, he did this all the time. But his heater cover was connected directly to my heater cover. [laugh]
So, I could hear [laugh] what he was doing.
[laugh] Now, at Ithaca too, what was the social life like of the physicists? I mean, Ray for instance remembers a yearly picnic?
You would have a yearly picnic at Ithaca?
Yeah, yeah, yeah. And what?
What was it like?
Oh, it was nice to go out for a picnic. And in particular, you get to know the families of my friends. Your friends, you see every day, but I don’t see the families more than once or twice a year. But you get some idea what is the family they have and so on. So, it was nice. About ten years ago, more recently anyway, this habit was forgotten. So, the annual picnic is now done in the lab. Families are not invited. So, I don’t know what their families are. So, in a way, it’s too bad. Some chairman probably forgot, or some secretary thought it was too much work to do.
And you also—Ray remembers you inviting your grad students for dinner once a year.
And what did you do then?
He was working on my project and—
But all of your grad stu…one grad student, or all of your grad students?
One or two. Or postdocs, occasionally.
So, now we’re up to—
You asked me yesterday about this.
Right. You talked about this. But what about Regge poles? Can you explain the enthusiasm for Regge poles at the time?
Well, Regge pole—did I say this—what is the background—oh, that’s because I thought it was a mathematical paper?
Right. And this was the one that turned into the Kinoshita-Lee-Nauenberg theorem.
Yeah. Yesterday, I told you that.
Because they didn’t see my paper. [laugh] The Regge pole was—a paper by Regge appeared probably a year or two before this—’60 or ‘61. I don’t remember. And so hadronic processes could be understood more systematically using the Regge pole ideas. The Regge pole is not a fixed point, but it’s a trajectory in the energy and momentum plane or something like that. And the interest in Regge’s paper continued maybe until ’62, when I went to CERN. And that’s why I wrote some paper with some people over there about Regge poles. And even Hans Bethe was interested in Regge poles, so I wrote a paper with him. But then after a year or two, the general interest in the Regge pole sort of faded away. Maybe experimentalists were still using it for their analysis of experiments, but not the theoretical problems. Except I think Ken Wilson also worked on the Regge pole. At the time, ‘62, when I went to CERN, Ken was also over there. And I told you yesterday, whenever I ask some question, he says, “It’s written.” In his drawers. [laugh] That’s about the Regge pole, I think, most of—
And that was at CERN, when he said that?
He was at CERN at the same time. And so, I got to know him pretty well, because I spent the same time over there. I talked about and—I think—but the Feynman’s error, I talked to you yesterday.
As I said, my introduction to computers was at Princeton, von Neumann’s computer. And my experience except for writing program for that computer, which was in a box like that, which I lost, is that it didn’t work. [laugh] I mean, the computer broke down every 30 minutes, because the vacuum tube broke. [laugh] And anyway, for a period of two, three months, I couldn’t do much except for writing my own programs. And this kept going on at Columbia. Now, I started using the Watson Lab computer occasionally, and made some progress, but not much. When I went to Cornell after that, in ‘55, the Cornell computer was very primitive. It was a punch card machine, and you fed a punch card to the feeder, and so on. So, I couldn’t really do much work. And then in the summer of ‘56, I was invited to Bell Lab’s in Murray Hill for the summer. And that’s where the real work started. I think that’s where I really started using Fortran. Fortran, of course, it’s maybe obsolete by now, but it’s still used. So, what else do you want to know?
Well, now we’re up to about the time of g-2, and we talked about your visit at—
Oh, on computers, you mean?
Oh, also computer is still preoccupied with helium atom.
G-2 came in after I went to—the second time I went to CERN. That’s ‘66?
Yeah. Ok, so that’s later.
Well, anyway, the Cornell computer at that time was very primitive, and so I had to go to NYU.
NYU. And you would drive down to NYU and use that?
Which computer was the one where the vacuum tubes would blow?
That’s a famous computer, I think. [laugh]
The ENIAC computer?
I don’t remember the name. I think it’s either the first or second computer von Neumann built.
But the vacuum tube—that was a vacuum tube computer.
Oh yeah, it was dependent on vacuum tube. It had no transistor at that time or something.
And you’d have to start all over when they blew.
Yeah. Anyway, I guess that it worked only for pretty simple programs, but as soon as it got more complicated, probably it doesn’t do [laugh] any work.
So, you were testing the limits of the computer?
More or less, yes. Even now. [laugh]
Even now, huh? And did you work with von Neumann at all?
No. I saw him at a distance, but he’s such a [laugh]—guy who is hard to approach. [laugh]
So, then when you get to CERN in 1966—
The second time.
The second time, yeah. And you start, and you see the results on the wall.
And you start working on g-2.
But not with the computer.
Oh, the first round was not with the computer.
Yeah, the first round is looking at the chart and saying, “I think I know how to compute the leading term of muon g-2.” Just result computing. I think I talked to you yesterday—after I saw this graph or like this, thinking about g-2, I certainly recalled that Wickman and Suura paper on second-order—what was—diagram. That can be calculated—the leading term of that term can be calculated without doing any actual work, you only have to know what the renormalization does to this amplitude. And once you understand that, then the sixth-order diagram can—the leading term also can be calculated without actually doing anything. You just go to library and find some relevant reference. That’s what I did. So, the next morning, I went to the experimental group and said, “I know how to compute the sixth-order term.”
And were they happy?
Of course, they are surprised. [laugh] But then after trying to compute, or to find out the light-by-light scattering contribution, which I wrote down—this is a mu—this is an electron, and this is a magnetic field. And then three photons exchange between a mu. And this gives you—as I told you yesterday, I thought this was very small because of the Euler-Heisenberg paper in 1930s. But that was wrong, because in the Euler-Heisenberg calculation, which is something like this, momentum k of all the photons are very small, much smaller than the electron mass. And then this is proportional to k to the fourth. But in this picture, here is muon and here is electron, and the momentum of these photons are not small. So, this argument of Euler-Heisenberg doesn’t apply to this. You have to compute this directly. That’s the first time I used computer in the g-2.
Ah, so the first time you used it was in connection with the light-by-light diagram calculation.
Ah. And you were back in Ithaca by then?
Yeah, I was back in Ithaca by that time, and found that Brodsky was also looking at this diagram. And we worked with—Brodsky, of course, knew how to use the computer. So, I learned using the computer and writing Fortran programs for this from him.
Now, when you started working on this, did you have any idea that this g-2 calculation would wind up absorbing the rest of your career?
This is the sixth-order. So, my aim at that time was to finish the complete sixth-order calculation. And then experiment went ahead of the sixth-order calculation. So, you had to do eighth-order to beat the experiment. And the experiment went better than that. And so, I have to go much further—tenth-order. The idea is—my feeling is that any theory must be wrong somehow. You see, I started out working on C-meson with Koba. So, the theory must be—have some limitations. And if you push hard enough, you will find some error or some failure of the theory. And in the case of the C-meson, it was easy to find what was wrong.
What about the helium atom?
Helium atom, I found out that if you do the correct calculation, in fact the theory available at that time was wrong. The theory was wrong. So, the question then is, is the Feynman-Dyson theory right? How do you know if they are wrong or right? By pushing the Feynman-Dyson theory to the limit.
And are you talking about the helium atom or g-2?
I’m talking about the g-2. Feynman-Dyson theory has nothing to do with the helium atom.
So, push Feynman-Dyson theory to the limit.
And in 1966, this—well, you succeeded to the sixth-order calculation.
Or you started on the sixth-order calculation. And then the theory—
Theory was ahead of experiment for a while. But then experiment improved. They are now ahead of theory. They still agree, but you have to know the eighth-order to see whether they really agree or not. And they are on the tenth-order by now. [laugh] But the nice point at least as far as formulation is concerned is that—the Feynman-Dyson theory is somehow in some form that can be pushed. At least as it is written down, you can push it to any order you want. Eventually, its expansion may diverge. Then, that’s something to find out, too. Tenth order, we pushed to—there’s no indication that the diagram expansion is diverging yet. Questions are still going around. But eventually, it must start growing. That’s what Dyson actually made a sort of heuristic proof that the convergence of the perturbation theory is not the convergence but asymptotically divergent. So, I sort of think that is true. But beyond that, there might be something experiment definitely disagrees [laugh] with the theory of Feynman-Dyson theory in that case.
And for a muon, of course there’s three standard deviation at the moment between theory and experiment. I don’t know whether this is an indication of something—whether the theory is breaking down or not. One popular candidate is the dark matter. But dark matter itself is a very nebulous concept. I, to some extent, and I can’t believe any of the statement. [laugh] In particular, much of the argument of the dark matter being 70% of the universe is made of dark matter, something like that, is based on the observation of ordinary matter. For instance, you find a paper from time to time in recent months that you point out some detector in one direction of the space, cover some very small area, but with an ultraviolet or X-ray-sensitive detector. Then they find that where they see nothing with ordinary telescope or—they see the source of x-rays beyond the cloud which obscures everything. Now, this may be an exceptional case, but I think it is probably not.
And then the cosmologists think that dark matter occupies 90%—ordinary matter is only a few percent, and so on, based on the previous obviously. But the matter behind this obscuring cloud may make a big difference in the overall—on regular matter density. Because even though these experiments, these white dwarves, and the matters behind that is quite enormous. Not as big as the universe as a whole, but it can change substantially how much ordinary matter you could have. You see, the point is, the cloud in front of this other galaxy or whatever is quite interesting, because it blocks the regular, ordinary low frequency light, but is penetrated by an x-ray of some frequency. That means these clouds are not dark matter. It’s ordinary matter. Because—or at least in the sense that it interacts differently for low-frequency light and high-frequency light. If it’s a dark matter, which has no interaction with light, it should be transparent to not only the regular light but also ultraviolet and X-ray. So, there is no blocking of sunlight. So, this is one example. Many other examples seem to be coming up from new observations that your understanding of the universe is not really finalized.
And what are you working on now?
I am not working on that in the sense of trying to find something new. I am sort of looking at the literature to see whether the existing theory is reliable or not. And I sort of feel that the existing theory is not very good. [laugh] If things are more settled, then I begin to see what is working, what is not working. But, at the moment, it’s a mess.
Now, do you still go to an office every day during the week?
More or less in the afternoon only.
But every weekday?
Yeah. Oh, one reason why I go is to maintain our health. [laugh] If I stay here in a room all the day long, I probably—my muscle will degenerate, and I’ll collapse eventually. [laugh] But going into my office and talking to friends and so on keeps me awake. [laugh]
So, your last g-2 result was the one you reported in April at the university?
Yeah. And also, it’s published in Phys Rev.
Oh, it’s published in Phys Rev now, ok.
And also, my collaborator, Makiko Nio, she’s the only one working on that subject right now, because she has a computer in Japan. And other people already left to [inaudible]. So, she is still working on improving the tenth-order calculation. It’s not easy work because there are several hundred or even a thousand of Feynman diagrams to deal with, and each one is, say, compared to the eighth-order diagram, it’s more than a factor of ten, maybe a factor of 20 or 30, larger, as a Fortran program, and it takes that much longer to run. And there are so many more diagrams to deal with. So, to make good progress takes a long amount of time. But the factor two improvement may take, say, a year or two, but that’s worthwhile, because it’s still well ahead of experimental precision. So, the real work is being done by my collaborator Makiko Nio.
Nio? How do you spell Nio?
And where is she?
She is at RIKEN in Tokyo. So, this is a—they have these publications.
Here’s her name.
Yes. Nio was my last student at Cornell. And she worked for thesis on muonic hydrogen, radiative corrections. And I asked her to work on this, because this is a bound state, not a free particle state like the muon g-2 problem. The bound state has to be handled with more care. And the old-fashioned relativistic treatment of the bound state is based on Bethe-Salpeter formalism. But it is difficult to make it a systematic development of the higher order. So, an alternative method is proposed by Lepage—I don’t remember—L-E-P-A-G-E—it’s integration—of formalism based on consistent talent of the low energy bond state in high-energy effect are correctly treated into account. It was—Lepage was a student of Brodsky, and he wrote a very nice paper for random number integration called Vegas. And at the time when we start using Vegas, we didn’t realize that it is just a convenient way to integrate, using the random sampling of the integral. But it turns out that as we work from sixth-order to eighth-order and tenth-order, Vegas doesn’t really suffer from exponential growth of the integral and so on. In fact, it grows as if it were linear, which is far better than anything else. So, that’s why we can keep going on from sixth-order to eighth-order and tenth-order. And Lepage is still trying to improve his method, but as far as we can tell, his initial one is good enough.
[laugh] This paper. “Everyone Makes Mistakes—Including Feynman.”
That was about that earlier—that we talked about.
That’s right. This paper—
I wrote down—this is a talk I gave at Sirlin’s retirement celebration, since Sirlin was involved in the mistake, too. [laugh]
And also, there was a famous mistake that crept into your calculations in 2001, when you took over a computer program that involved a mistake in it?
What was the mistake?
It’s not in these publications here. But a mistake crept into your calculations, but it was because of the computer program.
Ah. One of the most [inaudible] paper of eighth-order, probably, that’s it. It was corrected in the later publications. But that was an oversight of some contribution in the diagram containing [inaudible]—no, light-by-light scattering sub-diagrams. I don’t remember exactly where. But later on, it was corrected.
But what was it due to?
You see, in choosing the integration path, you go from one end of the muon to the other end, through whatever route you can choose. The result should be independent of the choice of that route. Except in the case of the diagrams involving light-by-light scattering, this choice we made in the first paper didn’t cover all the routes possible. So, we forgot to include one route, and that caused the error. I think that was it. Once you see what the error is, it’s easy to correct. I think that we found our error by ourselves, not by other people. That particular error. Unlike this one.
The Feynman one, yeah. Did you ever consider going back to Japan?
Did you ever consider changing your field of research?
No. As I said, I would be happy to work on dark matter if it were slightly more believable. But now I think g-2 is still my main field. In particular, it’s not finished, as I said. Nio is working, still, in that sense. But I could do something else if—but the problem is I thought dark matter would be an interesting subject because in particular muon g-2 theory and experiment disagrees by more than standard deviations. So, you have to explain—understand why it is. But I started trying to understand that and then I stuck with the program that—for instance, Big Bang Theory, so development of the world, how much you can believe. I’m not sure whether I can believe it as it is.
Oh, I wanted to ask you about the J PSI discovery. What was the impact of the J PSI discovery?
It’s written somewhere.
Because after it, you started working with—oh, the J PSI discovery, that was partly involved with charmonium.
We did talk about this yesterday.
Yeah. Well, this is ‘75. Discovery was—
‘74. And so, now what’s the question?
Oh, just about the impact of the J PSI discovery on your research.
Well, this paper—
But you talked about that yesterday. Getting you to work on charmonium.
Yeah. So, certainly, it had an impact. Personally, I didn’t quite believe the validity of the quark model of hadrons, which was discussed by Gell-Mann and so on. Because there was no concrete evidence. But the charmonium, you can build a model based on the quark, anti-quark bond state, which reproduce—we could reproduce the spectrum of the charmonium in a very simple nonrelativistic Schrodinger equation. So, that made me into a believer in charmonium. [laugh] My point is that theory is fine to propose as whatever theory, but how can wemtell whether the theory is right or wrong experimentally? If that information is lacking, it’s very hard to believe. So, about the cosmology, which I started looking into, it’s mostly speculation. Hard evidence is coming along, but not all of it is available right now. And any additional information may change whatever is the story right now. [laugh] So, I decided not to worry too much about it. [laugh]
Ok, Tom, I’m about tired now.
Ok, I’m tired too! [End Session 5] [Begin Session 6]
This is Robert Crease and I’m talking with Toichiro Kinoshita. It is January 18th, 2016. First of all, Tom, I wanted to go back to the C-meson theory. What was C-meson theory?
I think I said somewhere, but—C-meson was—the theory of C-meson was invented by Professor Sakata of Nagoya University. The purpose of the invention was to cancel the electron self-energy due to the electromagnetic field. It’s a neutral meson theory. And it turns out that coupling of that C-meson to the electron in a coupling, the coupling constant, if you choose coupling constant squared—let’s say f is a coupling constant, it’s squared, equal to twice of e square, then the self-mass of the electron due to the C-meson and the electromagnetic field cancel, so that you can remove these infinities from the theory. That was the idea. It’s not a complete theory, because there are other infinities coming from electromagnetic fields, like vacuum polarization and, say, charge, also, is modified and so on. So, it’s clearly not a complete theory, but at least the mass can be canceled. So, anyway, that was the idea. And at the time that renormalization was introduced by Koba and Tomonaga, Sakata also introduced this C-meson theory. So, for a while, there were two different ways to deal with the infinities.
And you were hoping that you could detect a measurable difference between the two, an experimental difference?
Yeah, that was the first thing which Koba—I worked with Koba on that subject.
And how would you tell the difference between the two? Was it an experimental test?
What would you test?
Elastic scattering is the process we had in mind.
So, it’s elastic scattering and electron angle it goes out.
So, it’s the scattering of the electron off of—
Off of some potential. To simplify the matter.
And were these experiments actually done in Japan at the time?
No. Actually, experiments of this type had been going on for many years, even before that. Because scattering is the simplest experiment you can do. Let me see. The idea is that can you tell the difference by making a more precise scattering, just not a bulk, but maybe angular dependence or something might be different for such theories. This was a possibility to explore. And Koba was working on it, and I joined his effort. It was theoretical, of course. And the point is when you do just an ordinary Tomonaga-Koba-type scattering cross-section and a C-meson-only scattering cross-section, they differ at low energies, or at a few hundred MeV. However, we noticed that if you have a C-meson theory, why don’t you have also mass renormalization for C-meson. You need a correction. If you include the correction, the low-energy cross-section can’t be distinguished between ordinary theory and the C-meson theory. The difference disappears. That’s what we found. Of course, if you go to much higher energy, you still can see the difference. But at the time of the meson theory, a few hundred MeV was considered the highest energy available. And in that range, it’s not possible to—
Not possible, yeah. Had you meet Sakata at the time?
Probably—afterwards. But certainly, I know—he’s a famous guy. He was a collaborator with Yukawa and people like that, say one generation earlier.
And on the helium measurement, how was the helium—you were calculating the helium atom from the beginning on first principles. How was that measured? Again, you were hoping it would be compared with experiment.
What was being measured?
In this case, there was a very good experiment. I forgot—you see, the experiment is to measure helium ground state to excited—I mean, electron get free, one electron gets free. That is the ionization energy. And that was measured very precisely like to six digits or something of that type. I have to check for exactness but—and the theory of Hylleraas and experiment disagreed maybe point—by the time it goes down to 10-4, four-digits, they disagreed. And the theory, experiment should go to six-digit. So, there are big differences between theory and experiment. And that’s why I looked at Hylleraas’s original calculation, to see what could be wrong with it.
And who had done the experimental measurement?
I think it’s a Canadian experimentalist called Hertzberg or something. I’d have to check.
Hertzberg, ok. It’ll be in your paper, right?
And last time, we talked about your sixth-order calculation and the unexpected problems that you ran into, specifically the light-by-light scattering problem. And what about the eighth-order? Can you talk about how you did the eighth-order?
That’s today’s topic, I suppose.
Yes, yes. Well, actually, before we talk about today’s topic, are there any other things that we talked about last time that you want to say more about?
You see, I think last time I said I was visiting the experimental group at CERN, and they showed this experiment of muon g-2, right?
On the wall, yes.
That inspired me to think about the g-2 problem. That night, I found how to do the leading order term, which turned out to be kind of an applied renormalization group method.
Applied renormalization group method, yeah.
Which I didn’t realize that way, but anyway, it turned out to be that way. And the next day, I went to the experimentalists and told them, “I have found the sixth-order term.” And then I find later the only thing missing is a light-by-light diagram of a muon g-2, which appears in the sixth-order for the first time. And I tried to prove that contribution is very small. It turns out that that is not true. And that’s where I had to do some numerical work. That far, I just had formulas, not numerical work. But this one, you cannot obtain [laugh] by formulas, so you had to either analytically integrate it or do some numerical integration. And it turned out that Brodsky at Stanford was working on the same problem, so we joined forces, and Brodsky essentially told me how to do the numerical work, by random-number generator type sampling of [inaudible]. So, he was using, I forgot the name, but some program using Monte Carlo method, which chooses a random number point in the integration. And he was using that, so he told me how to use that, too. So, we joined forces and found that in fact light-by-light is very huge, ten times bigger than other radiative correction at sixth-order terms. So, this was a big surprise and anyway, we got sort of—muon g-2 maybe 10% in this way. But experiment is better than 10%. And so, you have to do eventually the exact calculation to all the sixth-order terms. That’s what I did. By that time, I said—I did a few more diagrams with Brodsky, but he had something else to do, so I took care of all the remainder. In particular, I had a very good student, and he was responsible for filling out how to do the sixth-order in a numerical way.
Who was that student?
I just [laugh] need to remember. Cvitanovi?.
Cvitanovi?, oh yes.
And then after—many years after, we solved numerically the sixth-order problem, not only the light-by-light, but all the terms, with the help of Cvitanovi?. Then Remiddi in Italy solved light-by-light sixth-order term analytically. Apparently, he was not quite sure whether he got the analytic result right. But when he saw our numerical result, then he was sure that it’s ok. [laugh]
And what is his name?
I’ll write it down somewhere. So, another thing—some Russian much later found why the light-by-light contribution in sixth-order is so large. This is a very nice piece of work. Actually, what happened is that when light-by-light exchange photon with a muon, there are three photons connecting electron and muon. And one of them can be the main term transmitting momentum from bottom to up, or [inaudible]. The other two actually carry very small momentum, and it looks very much like a [inaudible] force for bound state. In fact, the two photons essentially serve as a maker of bound state of muon and electron. And then you [inaudible] pi in such a configuration. And that’s why two photons are acting on that. That means factor pi square is contributing to this [inaudible]. And that’s why this light-by-light amplitude gives you an order of magnitude bigger contribution to g-2 of the muon. But it doesn’t contribute much to the electron g-2.
Ah, so that’s why you thought it might not be a large factor?
Yeah, in the electron case, you have to actually do numerical work for a completely different configuration—or do it analytically like Remiddi did much later.
And who was the Russian?
I have to check. I forgot the name. It’s written up in one of my more recent papers.
I also had a question about your trip in 1953. You say Masa came to the United States by boat…
—after she graduated in April or May of ‘53?
March of ‘53.
The Japanese school system started in April and ended in March.
So, she came—how did she get to meet you?
She graduated—she was in school when I went to the Princeton Institute, so she was behind in Japan, and she wanted to finish school. So, the next March, she finished school, and then took a boat across the Pacific, because we were not rich enough to fly. [laugh] At that point. But from San Francisco—this is in 1953—she flew from San Francisco to LaGuardia, I think. That was the schedule. But then the plane had to stop in Nebraska or someplace, so her arrival at LaGuardia was delayed maybe half a day or something. But we went from Princeton to LaGuardia and picked her up.
That’s right. You did tell me last time. And then a month or so later, you drove across the United States back to L.A.?
This was April or something. And yeah, I think it was probably June, because this was after the Institute session is over—which is actually end of April—I think, is when the Institute shut down. And so, we can—we were free to go anyplace. So, Nambu and I wanted to go to the West Coast. Nambu was to pick up his wife and boy in Los Angeles. And we just wanted to visit Caltech. So, we had separate cars, and Nambu went this way, and I went that way.
And then you came back, and in 1953 to ‘54, you were at the Institute again.
No, two years—second year of the Institute.
The second year, yes. Now, that was also the time of the Oppenheimer hearings. Did you—
Yes. In my second year, Oppenheimer was in trouble and the hearing was going on. I think it probably was spring of ‘54.
Yeah, it’s April. What did you hear of that? How did you hear of that?
Oh, everybody knew about it. I don’t know how I heard about it. [laugh]
What did you think?
[laugh] My goodness. I think he was clearly sort of a scapegoat, anyway.
And when were you and Masa married, again?
‘51. October ‘51.
And where were you married?
Was it a wonderful occasion?
Yeah. [laugh] Well, anyway, as I said, she was still a student, and so we married in October of ‘51, and then I came to the Institute in the summer of next year, ‘52. And she had to be in school for another year to graduate.
Were there any physicist friends of yours at the wedding? Did Nambu come or—?
Of course, I had some of my physicist friends, and Masa’s friends from Masa’s school. And also, it’s sort of—the master of ceremony was Professor Tomonaga.
Oh, oh! Huh.
So, it was a happy occasion.
Good. Are there any other topics that we didn’t talk about that we should have last—during that time?
I told you last time my father was supposed to inherit from my uncle a sizeable amount of property, mostly rice paddies accumulated by my grandfather or maybe even earlier. I don’t know. But the program didn’t proceed as my grandfather planned because of the war. Right after the war, the American occupation ordered that the holdings of the paddy and field should be distributed to the current workers working on that field, at a very low price. So, suddenly, my family, and my uncle’s family lost most of their property and lost a lot of money together with that. And so, my uncle and father become just ordinary—just a small-patch-of-land type owner, which was not good enough to sustain them [laugh]. And they become very antagonistic.
Your father and your uncle?
Yeah. And they split up.
So, the arrangement made my grandparents essentially disappear. I didn’t have anything to succeed. It was all gone.
So, the occupation army came in, and they insisted that the—and they took the land, redistributed it to the workers—
—so your father and your uncle didn’t have enough even themselves to survive.
And where did that leave you?
Well, yes, so you didn’t get any—you weren’t expected to take over this land, then.
I knew that I had nothing to do with that anymore. Anyway, by that time, I was able to sustain myself with the stipend at the university and so on, so I was not particularly worried. In fact, I was happy that I didn’t have to inherit.
With the rice paddies?
Yeah. If I inherited, I would have been a landowner of some [laugh] small patch. I wouldn’t have become a physicist.
[laugh] By the way, how many workers worked on that land?
You see, the system is that—I think that my grandparents accumulated maybe more than ten, maybe 20 different patches, and they all were distributed to the people who were actually working in the fields. So, it affected probably ten to 20 families. Beyond that, I have no idea.
So, ten to 20 families worked those rice paddies that had been in your family?
Yeah. The arrangement was after they harvested the rice, depending on the size of the field, they paid back to my family a proportion of the rice. So—well, anyway. And typical people probably paid back in terms of rice quite a bit of rice. I don’t know. It was a big type of a straw container. The rice was so much that I couldn’t [laugh] lift it.
What was the container called?
How do you spell it?
T-A-W-A-R-A. Kome Tawara. That’s probably more precise. Kome Tawara.
Kome means rice.
Tawara. So, that was a unit of rice.
Heavier than you could carry?
[laugh] I couldn’t carry.
Who carried them?
How were they carried?
Oh, the famers were strong enough, usually. They could put it on their backs or their shoulders. Or if they had more than one, they used a wheelbarrow or something of that sort.
Ok, onto the eighth-order! [laugh]
So, you finished the sixth-order when? About 1980, did we figure?
You have the—[pause]—I think it started around 1960—
Yeah, the Karchez. This, I think, is where you outline—you talk about the problem of the light-by-light. Paper nine, yeah.
I think this is the one I talked about light-by-light scattering contribution.
Oh, wait a minute. No, that’s the wrong—I’m not looking in the right place.
These are papers, yes. Charmonium. We talked about charmonium. We talked about this last time.
This is a paper—
Sixth-order magnetic moment of the electron. Yes, 1974. Cvitanovi?.
Cvitanovi?. Ok. And for a while, then, you’re working on charmonium.
So, then you start the eighth-order here. Your eighth-order papers start with paper number 68, which is 1983.
OK, so I wanted to ask about this—your progress here. Can you talk about your eighth-order calculation?
You see, when we did the sixth-order with Cvitanovi?, algebra formulation was general enough you can apply to any order. So, the [inaudible] was already sort of set up. So, going from sixth-to eighth-order theoretically there was no roadblock to worry about except that it was a much bigger problem [laugh] and you needed much bigger computers. And so that’s another problem. But anyway, theoretically, going to eighth-order was not a real problem. And Lindquist, you know him, worked with me on that project around this time. So, the program was written at that time. Around ‘83. The motivation? I wouldn’t do any calculation unless some experiment has come out with a challenge, a new measurement and so on. At this time, when I finished the sixth-order, I thought that was the end of my calculation of g-2 because it was better than the experimental result coming out of Michigan. You see, the Michigan people invented—so to use the precession of election in a magnetic field, it goes around like that, and then the spin direction goes a little bit faster than the momentum—magnetic moment direction goes ahead of the spin vector, a little bit. That’s a precession. And it’s a tiny effect, but if you let it go around a few thousand times, it becomes a sizable effect. And that’s the way the Michigan people measured the electron g-2 three orders magnitude more precisely than the atomic physics measurement. The original measurement was atomic physics. Ok. And so, I thought our sixth-order would beat this precession measurement. And then at the conference, which I am not sure I—I think this is still Lindquist—yeah, photon photon scattering is this—that was ‘89. The last paper of eighth-order—
But this is of the electron.
Yeah. Because electron, there is no enhancement due to renormalization group effect, so you have to compute directly. No trick is available in that case. And this diagram containing no vacuum polarization—that means you cannot use the [inaudible] group technique of the vacuum polarization. And then—let’s see. There is a paper with Ukawa but I can’t find it. It’s a conference paper. [pause] I can’t find it, but there was a conference report, I think. This is—
This was with Ukawa?
1976, this one?
Which? Ah, this one.
Ok. This was a conference—
There’s also a Phys Rev paper.
Yeah. But anyway, this was at the international conference at Tbilisi in 1976.
I was attending the conference, and then a guy named Lowell Brown at the University of Washington told me that I had to get busy again [laugh] because Dehmelt was doing a new experiment using a Penning trap which was three orders of magnitude more accurate than the [inaudible] precession experiment at Michigan. And Dehmelt, a few years later won the Nobel Prize for that work. So, that’s why I started the eighth-order. Or no, let’s see is that eighth-order or tenth-order? I’m not quite sure. Tenth-order essentially I start around year 2000, so later than that. So, must be eighth-order.
But this is for the electron.
What about the eighth-order for the muon?
You see, electron and muon are actually the same program. The difference is the mass of the insertion loops. So, you just change the parameter.
Except for the hadronic contribution for the muon, which is quite sizeable. But for the electron, it’s quite small, like 10-4 times smaller than for the muon. So, qualitatively, they are different problem, but the algebra is exactly identical. So, once you do one of them, the other one is ready to be evaluated.
I see. So, you got started on the eighth after this comment by Brown.
Time to start doing it again. And so, in effect, you worked on the framework by which you could address both the electron and the muon simultaneously?
Always that was what we had done. Because this gives you a chance to check the calculation at least by two experiments, which is quite useful.
The two experiments being the electron experiment that Dehmelt was doing, and the muon experiments—
—at CERN, which is just coming out a little bit after this time, too. ‘79, I think, was the paper.
No, CERN experiment actually came out earlier. Let’s see, it’s hard to tell. You see, the CERN experiment had some good results already in 1966, and that’s why I started working on the g-2 of muon. And then of course the muon measurement also improved a little bit, bit by bit. And then eventually it went to Brookhaven and that was probably an order of magnitude better than CERN experiment. Still much worse than electron g-2 at that time though. So, what was the question?
The question was—so you are set on the track of the eighth-order by this remark in ‘76 at Tbilisi, by Brown.
And you start doing—
That’s Lowell Brown.
Lowell [sic] Brown?
Oh, Lowell Brown.
And you started with Lindquist, who is your grad student at Cornell?
That was earlier. He was a graduate student—oh yeah, that probably is the case. Where is Lindquist’s name first showing up? [pause]
Actually, I think it’s—oh, right. No, it’s just here, before this. It’s—I think it’s the next—
No, it’s after charmonium. I believe it’s here, number 66. So, ‘81.
Oh, yeah. Around that—let’s see. Tbilisi conference was when?
‘76, I think. Here.
‘76. And ‘81 means after a few years’ work, we got some result. That’s why it was published. So, Lindquist must have started right after the Tbilisi conference. That’s the late ‘70s. I don’t remember exactly when. But this must be after a few years of hard work. [inaudible] maybe mentioned. [pause] This is all charmonium stuff. ‘74. Ok, anyway, so Lindquist started on the eighth-order and because of Lowell Brown’s information that Dehmelt was now setting up a new experiment or he was getting new results which were three orders magnitude better. So, the eighth-order has to be done. That’s why [laugh] I did it. And as I said, the machinery for eighth-order was already available due to the work of Cvitanovi? in the sixth-order. So, that was not a big problem. The computer at Cornell was never as good as I wished, so I used some national computers at San Diego or someplace. But anyway, the requirement for the computer at that stage was not really big, and so we could get some preliminary results fairly quickly. But then when Dehmelt’s result came out, certainly I wanted to do the next order, the tenth-order, because the tenth-order can be as big as the contribution of the eighth-order. And to test experiment or QED theory, you have to be able to do better than statistical uncertainty of the measurement.
So, when I decided to look into tenth-order, it was around the year 2000, maybe 2001. The tenth-order has altogether 12,672 Feynman diagrams. Actually, many of them—half of them—are not too difficult to evaluate, because the basic structure of that half is essentially eighth-order with an insertion of vacuum polarization or light-by-light scattering and so on. So, the first thing to do was to get rid of those. And at that point, maybe a bit earlier, while I was still working on the eighth-order, I asked my Ph.D. student who worked on muonium hyperfine structure which is a completely different problem—it’s a bound-state problem, but he did the bound-state problem in a completely covariant way, which had not been done before. So, the method I used was by Caswell and Lepage, which was a very nice paper dealing with [inaudible] without sacrificing radiative correction and the renormalization. So, I wanted to understand that paper better and asked my student—she was a Ph.D. student at Cornell at that time—I asked her to look into the Lepage-Caswell paper and do some problems in muon hyperfine structure or something like that. So, I knew she was a very good student, and she went on as a postdoc at Kentucky, and then went back to Japan at the Nara Women’s University. And at some point, around 2000, maybe 2001, I asked her whether she’s interested in the tenth-order g-2. She said yes and started working on that.
What’s her name?
Oh, that’s Nio. Ok.
And then we worked on this easy part of the tenth-order diagrams, and I think published the result around 2002 or something. Nio’s work started on—yeah.
1997. Paper 91.
So, even before. This is part of the thesis work, I think.
Oh, that’s part of her thesis work. Ok.
This is muonic hydrogen. This one, Nio was involved in. And then this is still working on eighth-order.
That’s paper 100.
This is 2006, improving eighth-order.
102, yeah. What is A [α ?] to the fourth? OK, here’s tenth-order, QED.
And this is where I started.
2006. So, when Nio started working with me, actually she was working on eighth-order to improve the eighth-order result, which was Lindquist and company. So, tenth- order started around this time. And let’s see. Yeah. This paper—I think the same year, but—this is a technical problem of any order of QED g-2, with Aoyama, Hayakawa, and Kinoshita and Nio. So, this is—
Some tenth-order results are included. I think this is conference proceedings. And then there are two papers. One is in the other page, and this one is second page, both published in Nuclear Physics B, showing how to put—yeah. It’s a program given the Feynman diagram. Give it as an input to the program. And the outcomes are completely amplitude automatically. But the algebra scheme is based on the original paper of Cvitanovi?. But this now becomes a working computer program.
Which one? 106? Automated calculation scheme, ok.
So, again, this automatically renormalizes—gives you a renormalized result.
Everything is done automatically in this single problem. Renormalization up to tenth order. [laugh] Nobody has done that before. So, this is essentially the beginning of the serious calculation.
Of the tenth-order?
And at about that time, Gabrielse and company are getting an experimental result. And from this paper, putting together our result and Gabrielse’s result, you can compute a fine structure constant, and that is this paper. This is a conference report, I think.
And see, at this point we are still working on improving the eighth-order, and that is this paper. But from this point on, all of them are tenth-order.
And why do you call the orders alpha to the n?
Alpha to the n.
N is five.
N is five, but alpha—
Alpha to the n. Alpha to the fifth.
But why is the order expressed in terms of alpha?
You can count in—different people count differently. And we say tenth-order because photons attach to the electron ten times.
Ok. So, an order refers to the attachment of the photon to the electron.
Yeah, that is we call second order. And it’s alpha to the first power.
Can you draw the second order?
This is the second—see, e, comes in here and here. And e square is proportional to alpha. So, this is second—[pause]—alpha, first power.
So, for instance, this diagram, e to the fourth, so we call it a fourth-order diagram. And so on. This is alpha square.
And why does it go up by two each time?
Because photon—well, another photon has to be attached to the electron twice.
So, we started out—up to this point, I think, maybe 2007, Aoyama and Hayakawa, all of us were working at RIKEN in Japan.
I was visiting for a few months. But Nio was permanent staff at RIKEN. But Aoyama and Hayakawa moved to Nagoya University soon after this. So, Nio was in charge of running the calculations. RIKEN has a nice computer. So, that’s why it was now taken care of by Nio, mostly. Although Hayakawa and Aoyam appeared as an author, because they were involved in the early stage.
This is the latest paper.
Yeah. And is this the one that you gave basically at UMass in April?
Yeah. Oh, actually, the talk I gave at UMass is of course a survey of everything, before, including this. So, this is not the only one.
Oh, ok. And how did that talk go in April?
Very well. Some people gave me some compliments after my talk. [laugh] Although unfortunately, there are people, new people to me, and if they say their name, it doesn’t register in my head. [laugh] So, I don’t know who actually was there except I know that the chairman of the department was, [laugh] I remember. So, he was certainly one of them.
And what was the motive for going to the tenth-order?
Oh, as I said already, I think, experimental information from Dehmelt’s company.
Oh, but I thought that was the eighth-order?
No, that was where eighth-order is needed.
But uncertainty in measurement and calculation of nth-order would be—become insufficient if the experiment improves the order of magnitude. In fact, Gabrielse at Harvard improved Dehmelt’s result by more than a factor of ten, and he’s still working to get another few factors. So, the tenth-order must be there before they do the experiment.
I see. So, starting on the eighth, you already knew that the tenth was going to be required eventually.
Now were there any new issues—qualitatively different issues like the hadronic contribution?
For electron, the precision is not good enough to say anything more definite at the moment. That theory and experiment are in agreement. Something like that. [laugh] But if they shrink by another order, it may become like that. Then this has to be explained. That is the current situation. We don’t know what the difference is. However, muon g-2 theory and experiment from Brookhaven have three standard deviation, which has to be explained. And people are talking about the dark matter. Whether it’s true or false, I don’t know. The dark-matter problem is so confusing. So, I don’t know if that gives a precise information anytime soon.
So, what did you start to tell me you were working on now?
As I said, when I came here, and this one is finished—
—at the beginning of last year, and actually Nio was still working to improve the precision. So, in a way, it’s going on. It never stopped, probably. But I am not directly involved with it anymore. So, when I came here, I wanted to understand what is the cause of the discrepancy between muon g-2 theory and experiment, and so I started looking into dark matter. To understand dark matter actually, you have to understand the cosmology. And looking at the cosmology, in particular the Big Bang and so on, there are several assumptions made by people working at that area, and I’m trying to understand the assumptions, and I’m stuck. [laugh] I don’t understand them. It’s assumption—some are too arbitrary.
So, you’re not at the stage of calculating anything. You’re just trying to understand the assumptions.
I’m not calculating anything. I want to understand what the physics behind it is. Which as I said is pretty confusing, and in particular whatever data used to do some approximation to form the evolution of the universe and so on. But every new experiment uncovers a new source of matter. I mean, stars and neutron stars and galaxies. Some of them are quite sizable, which could affect the previous assumptions. And in particular, what’s interesting is if some people see nothing in one direction of the space, that’s because they couldn’t see what light is coming out of that stuff. But some people prepared a new operator sensitive to hot X-rays. Then they start seeing big galaxies. So, now the question—how many of such unseen but present galaxies will be there over all of the sky? And it may affect this assumption of, say, standard theory of cosmology says ordinary matter is only 11 or 15%, and dark matter is 30%, and dark energy is 70%. But all these estimates could be upset by discovery of whatever is not seen so far. So, I wait until experimentalists find more of them. [laugh]
Now, what was attractive about g-2 to you was that there was always the possibility of a direct comparison with experiment.
The attraction of the g-2 calculation is that there was always the possibility of a comparison with experiment, and the experiments were getting more and more refined even as your calculation was.
Yeah. The point is, in the realm of, say, quantum field theory, in particular QED, most other things measured in QED, involves some ambiguities because of the measuring apparatus and so on.
Uncertainty principle, yeah.
Yeah, g-2 is the only quantity which is pretty much free from experimental bias.
On the other hand, the electron mass or charge are quantities which should be known but are not known. There’s no theory to compute e or m. So, in the renormalization theory, they are given the value of the observed charge and mass. That’s logically OK, but it is not—the theory is not satisfactory in the sense that it cannot be calculated, at least it has not been calculated based on the principle of the theory. They are simply external inputs to the theory. But given that external input, g-2 is the only thing which you can calculate within the theory.
So, g-2 is a unique number, because A, you can calculate it, and B, you can measure it.
Yeah. That’s right.
But most of the theoretical physics now seems to be interested in super-symmetry and things that you can’t calculate.
So, are you a loner in the field?
In a way, yes, I suppose. [laugh] But I would be interested in super-symmetry if there was evidence, experimental evidence for it. There is none. It’s all speculations.
Why then aren’t more people interested in g-2 calculations?
Well, because to do the amount of work I did and my group did independent of the different methods, would be very difficult, because we essentially swept everything in that field.
You swept everything in that field, you say.
And what computers did you use?
We used many different computers, but right now, we’re using the computer at RIKEN where Nio is. It’s one of the largest computers in Japan, but not the largest in the world. But it’s big enough, good enough for our use. Because we have so many pieces. A few hundred. And each one must be adjusted, computed carefully, to make sure that you didn’t make any mistake. And so, you see, if you had a big enough computer to do the computation once and for all, that would be nice, but only theoretically. Because you cannot do all these things at the same time. In fact, you have to do each small piece separately and very carefully, reducing the error. So, it is actually useful to have a reasonable sized computer, but at your own disposal. Like if you put some input into the theory, you can calculate for a day. The next day you want to change it, and this you cannot do with a huge computer.
Ah. So, it works to have the calculations distributed.
And is there any point in doing the twelfth-order at this point?
Actually, for muon g-2, it may be necessary to estimate the twelfth-order. Actually, a very rough estimate is already written in some paper.
Which paper, I don’t remember. Not the last one. Not the last one, but this may have that.
It’s a complete tenth-order QED contribution. And there is one section—
Phys Rev Let—
—in which I speculated on twelfth-order.
You see, the point is the mechanism of the leading term for the muon comes from the diagram with the insertion of vacuum polarization, light-by-light, and so on. So, you know where the leading term comes from. In the sixth-order, I told you, two of the exchanged photons serve as a bound-state photon. Coulomb photon. In the tenth-order, there are five of these, and four of them serve as a bound-state photon. And so, this must be at least I think a two pi to the fourth contribution, bigger than other normal diagrams. So, you can estimate how big at least the leading term is. Of course, you have to do more calculation to pin down the next leading terms, which may still be fairly large. But the order of magnitude is already given by this leading term. So, I know what the twelfth-order might be. And at the moment, the experimental precision is not good enough to require the twelfth-order. Although it could be as big as [inaudible]. So—well, anyway, I’m not sure whether I can keep going on another ten years. [laugh]
[laugh] Well, Maurice Goldhaber published a paper on his 100th birthday.
Actually, written with his son. So, you have plenty of time.
[laugh] Good. Well, thank you. And as I transcribe these, I will send them to you.
Anyway, all the information’s in here. And this is just a one—not a complete, but just once—went…