Two Famous Brothers-in-law

from AIP Geno Segre Visual Archives

Wigner asked me whether I knew Paul A. M. Dirac passed away. He said he became very sad because he lost his famous brother-in-law. I told him I attended his memorial service held at Florida Sate University in November of 1984. He then told me there is Dirac's bust in the Fine Hall Library (for mathematics and physics), and asked me whether I would be interested going there with him to see the bust. Here is a photo of the bust.

In order to tell the stories Wigner wanted to hear, I had written a book, entitled "Theory and Application of the Poincaré Group with Marilyn Noz who has been my colleague since 1970. It was one year before the book was published in 1986, but I had a typed set of manuscript by 1985. The LaTex was not available at that time.

This book is about Wigner's 1939 paper on his little groups dealing with internal space-time symmetries of particles in the Lorentz-covariant world. I thank Mariano del Olmo for writing a very accurate review of this book. His review contains the following paragraph.

Note that E. P. Wigner's noteworthy paper [Ann. Math. (2)40 (1939), 149-204] was the source of inspiration for the authors when writing this book. There is also a remarkable trace of some of Dirac's papers in this book.

Yes, we wrote this book based on the papers we had written on Wigner's little groups before 1984, and I was ready to talk with Wigner. I was also ready to talk him about some important papers written by Dirac, who was Winger's famous brother-in-law. This is precisely why I was able to tell the stories Wigner wanted to hear. I has no other magic. Wigner was known as one of the most difficult persons to talk to.

Since then, I studied Dirac's papers more systematically. These days, my papers are mostly about Dirac's works. I still work with Marilyn Noz.

When I had a private audience with Dirac in 1962, he told me American physicists should spend more time on understanding Lorentz covariance. At that time, he was working on or had just finished 1963 his paper on A remarkable representation of the O(3,2) deSitter group, which describes the Lorentz group with two coupled harmonic oscillators. Like all other papers by Dirac, it is a beautiful mathematical piece. But can we extract physics from this paper?

The best way to decode this paper is to have a simple graphical desciption. For two coupled ocillators, we are led to use the normal coordinate system where one coordinate expands and the other shrinks, as shown in the figure. The same geometrical interpretation can be given to the Lorentz boosts in the light-cone coordinate system which Dirac presented in his 1949 paper on Forms of relativistic dynamics.

The rectangle given here indeed combines the physics of coupled harmonic oscillators and the physics of Lorentz transformations. Methematicians made the subject difficult for physicists by combinining this rectangular or squeeze transformation with rotations. This then becomes a symplectic (Lorentz group is a cousin of this group), but we should not be afraid of this word. Are you afraid of rectangles? Are you afraid of coupled oscillators?

Mathematically speaking, modern physics is the physics of harmonic oscillators or/and two-by-two matrices, since otherwise problems are not soluble. Dirac was quite fond of harmonic osicllators as we can see from his papers, and Wigner always demanded young people to explain things in terms of two-by-two matrices. Thus, the mathematics of two coupled harmonic oscillator is the closest thing to the "theory of everything."

The Lorentz boost is the basic ingredient of high-energy physics. Dirac's formulation of coupled harmonic oscillators forms the basic language for modern quantum optics, dealing with squeezed states, entangled state, as well as decoherence. Click her for details.

If you think what I said above is too dry for the New Year, you are invited to read the following story about how Dirac and Wigner became brothers-in-law.

Y.S.Kim (2008.1.5)

Wigner's Sisters

Y. S. Kim
Department of Physics, University of Maryland,
College Park, Maryland 20742, U.S.A.
(written in 1995)

Aabstract: Paul A. M. Dirac was a great physicist. Wigner used to call him "my famous brother-in-law." How did they become brothers-in-law? Did these two great physicists have the same view toward physics?

I have been asked by the organizers of this Symposium to write about Eugene Wigner's life. Yes, he was a great physicist and was a great human being. I have been fortunate enough to have been associated with him especially in his late years. However, it will require years of full-time research to write his biography if anyone decides to do so. In the meantime, there is a an excellent book about him entitled "Recollections of Eugene P. Wigner as told by Andrew Szanton" [1].

Eugene Wigner with his parents and two sisters. On his right is Manci Dirac.

At this time, I would like to define the scope of my knowledge about Wigner by quoting a paragraph from what others are saying about me. In his review of the book entitled "Theory and Applications of the Poincar\'e Group" which I wrote with Marilyn Noz [2], Mariano del Omo has the following paragraph [3].

E. P. Wigner's noteworthy paper [Ann. Math. {\bf 40}, 149-204 (1939)] was the source of inspiration for the authors when writing this book. There is also a remarkable trace of some of Dirac's papers in the book.

According to this review, I am in a position to say something about Wigner and his brother-in-law whose name was Paul Adrien Maurice Dirac. When I was visiting Wigner frequently during the period 1985--90, he had two sisters living in the United States. They were all born in Hungary in a well-to-do family. His elder sister was in Binghamton (New York), and his younger sister was and still is in Tallahassee (Florida). The elder sister's health was deteriorating, and Wigner was always concerned about her and talking about her. The younger sister's name is Margit Dirac or Mrs. Paul A. M. Dirac. She is known as Manci in the physics community. One day when I was in Wigner's office at Princeton, he made a telephone call to Manci in order to say "Happy Birthday" to her. After a brief talk in Hungarian, Wigner laughed and told me Manci was complaining that his call disrupted her shopping trip. He then told me how she became Mrs. Dirac.

Manci was married to a very wealthy man in Hungary. However, at that time in Hungary or perhaps in other parts of the world, it was not uncommon for a wealthy man to have several wives (though not formally allowed).

Princeton's Annex Restaurant on Nassau Street

Manci's first husband was a very handsome person in addition to being rich. He was very popular among women [4]. This was certainly not acceptable to her, and she separated herself from him after having two children. In 1934, Manci visited her brother at Princeton. He took her out for a dinner at a restaurant called "Annex" near the campus [5]. While they were enjoying their dinner, Manci spotted a lonely-looking man sitting at next table, and asked her brother who the man was. Wigner then looked at him, and he happened to be Paul A. M. Dirac. They then invited Dirac to join their table. This is how Dirac became Wigner's brother-in-law.

I met Mrs. Manci Dirac 1978 in Miami (Florida) while attending one of the Coral Gables conferences. I had a burning question to her husband, and I abruptly joined their "husband-wife" conversation in the lobby of the hotel where the conference participants were staying. After I finished the conversation with Paul Dirac, Manci asked me where I came from originally. I told her I came from Korea in 1954 right after high-school graduation. She then told me that I must have been there during the Korean Conflict (1950--53). After I said Yes to her, she asked me how I felt about the result of the inconclusive war which left the country divided. It was quite clear to me that she was extending to a man from Korea her sympathy toward Hungary which is also prone to invasion and dominance by foreign powers, and I gave my appropriate answer to her. While she was talking, I also watched her husband who was a great physicist. He looked amused but did not show any emotion.

Michael's Diner in Trenton (New Jersey) used to be the favorite family restaurant for the Wigners. It has an excellent salad bar for those who believe in healthy food.

I met Mrs. Dirac again in the fall of 1988 while I was visiting Professor Wigner at Princeton. He invited me to join a family dinner consisting of his wife Eileen, his sister Manci, and himself. We all went to one of the Michaels's family restaurants in Trenton. Assuming that Manci knew about England because she lived there, I asked her a few questions about the British prime ministers, particularly about Anthony Eden who succeeded Winston Churchill but had to resign after the Suez crisis in 1956. Not many people talk about him these days. She explained to me the events during the Suez crisis like a history teacher, and she had her own opinion about what happened and what did not happen at that time. I do not know her exact age, but she must have been about eighty years old at that time. She sounded like a professional lady of my age.

Eugene Wigner also used to make his views known, and it is well known that not everybody agreed with him on the issues having to do with the communist world. Yet, I have to point out that he told me many many times Mikhail Gorbachev is a great man. Wigner always wanted to live peacefully with the people on the other side of the Iron Curtain. He had a distaste for the communist regime in Hungary, but his passion for his native country was so strong that I had to contact the science attache of the Hungarian Embassy in Washington.

Ambassador Hazi awarding the academy membership to Wigner

As a result, the Hungarian Ambassador invited Wigner to his residence during the spring meeting of the American Physical Society (April 1988) held in Baltimore. The Ambassador, presumably a member of the Hungarian Communist Party, was kind enough to send his own limousine to Baltimore's convention center where the APS meeting was held. He later arranged Wigner's membership in the Hungarian Academy of Sciences. The Ambassador's name was Vencel Hazi. He did what he had to do, but I am still grateful to him. Indeed, he was a very good communist.

Let us go back to Manci. I told her that I was invited to the memorial convocation held at Florida State University (Tallahassee) for Paul A. M. Dirac in November of 1984 and I went there. But I was not able to spot her. I asked her where she was at that time. Her answer was that she was so sad that she did not want to show her depressed face to others. Indeed, she was talking like Queen Elizabeth or Margaret Thatcher. It is quite fortunate for the physics community that Manci took good care of our respected Paul A. M. Dirac. Dirac published eleven papers during the period 1939-46. It is not clear whether he knew Europe went through World War II. In either case, Dirac was able to maintain his normal research productivity only because Manci was in charge of everything else.

On the other hand, we were not fortunate enough to have Manci as a physicist. This is particularly so because there is a gap between Dirac's approach and Wigner's approach to physics even though they had the same ultimate goal in physics. Manci could have filled this gap if she had been born as a physicist. What was then their common goal? Dirac and Wigner both had a distaste for renormalization procedure, and therefore they did not accept the present form of quantum field theory as the ultimate theory. Yet, both of them believed that the uncertainty principle should someday be made consistent with special relativity if not general relativity [6].

During the period 1985--90, Wigner was keenly interested in approaching this problem by constructing representations of the Poincar\'e group using quantum phase-space distribution functions which are widely known as Wigner functions. Dirac, on the other hand, believed that fundamental laws in physics should appear as beautiful mathematics. His publication list indicates clearly that he was quite fond of building relativistic models using harmonic oscillators [7-9]. I was indeed fortunate to be able to explains to Wigner what Dirac did, and he used to enjoy listening to me.

Dirac wrote a number of papers on the Lorentz group. His best known paper on this subject is entitled "Forms of Relativistic Dynamics" and is in the special issue of the "Reviews of Modern Physics" dedicated to Einstein's 70th birthday in 1949 [10]. In this paper, Dirac writes down the commutation relations, which he calls the Poisson brackets, for the generators of the Poincar\'e group, and states that "the problem of finding a new dynamical system reduces to the problem of finding a new solutions of these equations." This is exactly what Wigner proposed in his 1939 paper on the "Inhomogneous Lorentz Group " [11]. Dirac's "instant form" and "front form" can be connected to Wigner's O(3)-like and E(2)-like little groups for massive and massless particles respectively [2]. As I said earlier in this report, I had a "burning question" to Dirac in 1978 simply because I wanted to understand Dirac's 1949 paper [10] in terms of Wigner's representation theory. Dirac of course gave me his clear answers in terms of what he said in his own papers, but he was not familiar with the papers written on the same subject by his "famous brother-in-law."

It is somewhat frustrating to note that these two "great brothers-in-law" did not have much communication with each other in physics. On the other hand, I was able to find many homework problems from this gap, and this is why I was able to write my first book. This will explain why Del Olmo made a remark about Dirac's influence on my book with Noz [2,3]. But this story is not restricted to me or to my book. The communication gap between these two great physicists offers a great challenge to many young physicists. Try to establish a bridge between Dirac and Wigner. It may become a very profitable enterprise.

1. A. Szanton, "The Recollection of Eugene P. Wigner" (Plenum, New York, 1992).
2. Y. S. Kim and M. E. Noz, "Theory and Applications of the Poincar\'e" Group} (Reidel, Dordrecht, 1986).
3. M. A. del Omo, Math. Rev. {88a}, 160 (1988).
4. Hungary is a Christian country which does not allow more than one wife.
5. The Annex restaurant is located on Nassau Street across from the Firestone Library of Princeton University. This restaurant had a different name before 1949.
6. M. E. Noz and Y. S. Kim, "Special Relativity and Quantum Theory," Edited Volume consisting of Wigner's papers, Dirac's papers, and others (Kluwer, Dordrecht, 1988).
7. P. A. M. Dirac, "Quantum Electrodynamics, Comm. Dublin Inst. Adv. Stud." ser. A, No.1 (1943).
8. P. A. M. Dirac, Proc. Roy. Soc. (London) {A183}, 284 (1945).
9. P. A. M. Dirac, J. Math. Phys. {4}, 901 (1963).
10. P. A. M. Dirac, Rev. Mod. Phys. {21}, 392 (1949).
11. E. P. Wigner, Ann. Math. {40}, 149 (1939).