There are many stars in the sky. You like to regard one of them as yours. Likewise, there are many research papers in the journals and books. There must be one paper which played the essential role in shaping up your professional life.

I would like to talk about one paper that built a bridge between me and Albert Einstein.

My Bridge to Einstein

Same photographer. How is it possible to place me next to Einstein? Click here.

• Young Suh Kim
  Professor Emeritus
  Department of Physics
  University of Maryland
  College Park, MD 20742, U.S.A.

• On March 12, 1958, while I was a senior at the Carnegie Institute of Technology in Pittsburgh, I received a letter from Princeton University telling me I ranked very high among the 15 students selected for their graduate program in physics.

  Going to Princeton meant working with Albert Einstein even though he went to Heaven three years earlier in 1955.

  My Carnegie Tech professors congratulated me. They knew Einstein was no longer at Princeton, and they advised me to work with Eugene Wigner there. It was my first time to hear his name. Wigner's name was known to them but not to me.

• When I went to Princeton in July of 1958, Wigner's office was in the mathematics building, and he was totally isolated from the younger physics professors there. I chose a young associate professor named Sam Treiman as my thesis advisor. He was a good teacher, and he taught me how to write articles coherently and stylishly. I am forever grateful to him, even though I had to be completely separated after I left Princeton.

  Click here for his Wikipedia page. I am on the list of the students he advised. The most famous person on the list is Steven Weinberg (Nobel 1979). Since Weinberg was so famous that there is every reason for me to brag about sharing the same thesis advior with Weinherg at Princeton. However, I had to work hard to be known as Wigner's youngest student.

  Why?

  In order to build my bridge to Einstein, Treiman was not enough.
  I had to become Wigner's student:
  Einstein-to-Wigner, and then Wigner-to-Kim.

  Counterclockwise: Princeton's Einstein genealogy.

  While I was a student at Princeton, I became interested in Wigner and his articles, since my professors at Carnegie Tech talked about him. Among his articles, one of them caught my attention. This paper was published in a mathematical journal, and was written in mathematical language. When I mentioned this paper to my physics professors at Princeton, they said the paper is about mathematics and has nothing to do with physics. They told me not to waste time on that useless paper.

  However, I maintained my interest on that paper, and I choose to call it Wigner39 throughout this webpage.

  After finishing my PhD degree in 1961, I was invited to stay there for one additional year as a pot-doc. Princeton University was very nice to me.

  In 1962, I became an assistant professor at the University of Maryland.

  1. Going from Princeton to Maryland was a hopeless demotion from Princeton's point of view. My friends there gave me a farewell party, but it was a funeral party. They thought I would disappear from the physics world.

  Yet, coming to Maryland was the best decision I made in my life. Its College Park campus was created by Abraham Lincoln as an agricultural college, with huge area of farmland. This campus is in the Greater Washington area, 20 kilometers north of the White House.

  In the Washington area, there are many Korean residents, and they say Washington is the capital city of (south) Korea. Kim Dae-Jung was the president of (south) Korea from 1998 to 2003. In 1969, he visited Washington, DC to introduce himself to the American political establishment. He received a Nobel peace prize in 2000. I had a photo with him at a meeting of Koreans welcoming him in 1969. Koreans in Washington say that you need a permission from the United States before running for the president of (south) Korea. We hope very much North Korea's ruling family will make efforts to get supports from the United States. They do not seem to like their big brothers: China and Russia.

  1. We hope very much this city will soon become the capital city of North Korea. Koreans there, including their ruling family, do not seem to like their big brothers: Chinese and Russians.

  2. How about DPRK (north Korea) as a separate country as colony of the United States, competing against the South? Quite possible, but much better than now.

  3. Two competing Koreas are easier for Americans to control the entire peninsula of Korea, according to the traditional British wisdom (divide and conquer). Korea is important for Americans because it keeps China and Japan separate.

• I am not a politician. Let me go back to my profession. The best aspect of my life at this new place was to develop my own research program, separate from those big shots at Princeton.

• In 1965, while I was struggling as an assistant professor, Princeton found the genius of the century named Roger Dashing. He was a fresh PhD from Caltech, and became appointed as a full professor at the Institute for Advanced Study (institute created for Einstein). His appointment was based on his PhD thesis where he calculated the neutron-proton mass difference from a theoretical scheme known as the "bootstrap dynamics," very popular at that time.

• With my Herod complex, I became very unhappy to hear that someone other than myself is a genius. I thus had to find a mistake in his paper, and I did. I then published my result in the journal which carried Dashen's paper.

• However, the reaction from the American physicists became hostile to me.

  Dashen is a genius but you are only a Korean.
  Go back to Korea.

  Thus, my position at my university was in danger. For help, I went to Sam Treiman who was my thesis advisor at Princeton. However, his reaction was much worse. He told me not to come to Princeton again. I am still wondering why he was like a mad man at that time.
  1. It is possible that he had a prejudice against my national origin. He used to call me "Oriental" directly to me and also to others.

  2. He lacked the brain power to understand the technical details about Dashen's paper as I explained.

  3. Perhaps both = idiot + racist.

  This was the end of my connection with Sam Treiman.

I had to develop a new route to Princeton.

How?

• After this catastrophic separation from Treiman, I came to realize why Eugene Paul Wigner (mentioned above) was so isolated from the rest of Princeton.

  The people there did not have enough brain power to resolve the Dashen case, widely known as the Dashen-Frautchi fiasco. Thus, with this limited brain power, they could not understand Wigner's papers. This was the reason why Wigner was so isolated.

  You may not agree with me on my view on "Princeton's brain problems." However, according to the recent ranking of graduate programs in physics, Princeton's ranking was 7th or 9th in the United States. Thanks to Einstein's name, its reputation was No. 1 when I went there in 1958.

  Without their brain problems,
  how could they bring down their reputation that much?

  However, was this blaming enough?

• In 1966, after my separation from Treiman, I restarted studying the above-mentioned paper by Wigner and spent 20 years for publishing my research results based on the Wigner39 until 1986. The purpose was to connect the mathematical formulas (given before 1939) contained in his paper with what we observe in the real world with particle accelerators after 1960.

• After publishing enough papers on the subject matters coming from the Wigner39 with my younger colleagues, I became ready to tell Wigner the stories he wanted to hear. In 1986, 20 years after 1966, I started going to Princeton regularly to tell him the stories.

  Essentially, I was telling Wigner that he deserved one full Nobel prize for his Wigner39 alone, while his 1963 Nobel citation did not mention this paper.

  At that time, Wigner was so isolated that he was known to be the most undo-approachable person in the world. How could I break this barrier? I had to tell him the stories he wanted to hear. Click here for a piece of wisdom I inherited from my Korean root.

• Wigner was so happy to hear my stories that he invited me to publish papers with him. Since I published six papers with him from 1987 to 1990, I became known as Wigner's youngest student in the world of physics.

• So, what was the Wigner39 about? What did I add to the paper?

On a train from Naples to Rome (2013). Wondering how Italian girls would appear when the train moves with a relativistic speed. Italian girls are stylish and open-hearted. I enjoy looking at them and talking with them. Let us change the scale. How would the hydrogen atom appear to me? Nickels Bohr was interested in what happens inside the hydrogen atom. Einstein was interested in how things appear to moving observers. Then how would the hydrogen atom appears to moving observers?

• When Einstein formulated his theory of relativity in 1905, all the particles were point particles. Later, those particles were found to have their own internal space-time structures. For example, the hydrogen atom is small enough to be regarded as a point particle. However, it has a nonzero radius with a very rich internal structure, namely bound state in quantum mechanics.

  During Einstein's time, there were no observable particles on earth moving fast enough to show relativistic effects. Thus, he had to go the universe. Then his theory became "general relativity."

• After 1950, particle accelerators started producing tons of protons moving with speeds very close to that of light.

  Here then comes a new subject. Nickels Bohr was interested in what is going on inside the hydrogen atom, while Einstein was worrying about how things appear to moving observers. Bohr and Einstein were good friends. They met occasionally to talk about things including physics.

  They could have asked how the hydrogen atom appears to moving observers. However, there are no written records to indicate they ever discussed the issue of moving hydrogen atoms or moving bound sates in quantum mechanics.

• I was interested in how to extend Einstein's relativity to the inside of the hydrogen atom or the quantum bound state in Einstein's world.

  Let us hear one of the radio interviews I had on this issue. Click here.

  In order to attack this problem, we need the mathematical framework constructed by Eugene Paul Wigner in his Wigner39 published in the Annals of Mathematics.

  I found out this paper while I was a graduate student at Princeton (1958-61), and it appeared to be impressive to me even though I could not understand its contents at that time.

  While I was a student at Princeton, Wigner was totally isolated from the rest of the physics faculty. His office was in the mathematics building, and younger professors routinely said "Wigner is gone." They told me not to waste my time on that useless paper.

• In his Wigner39, Wigner starts with a particle with Einstein's energy-momentum relation. When the particle moves, it carries its momentum p . Then, according to Einstein, the energy-momentum relation becomes
  E² = (mc²)² + (cp)²,

  leading to E = mc² when the particle is at rest with p = 0, and E = cp when the particle is massless with m = 0.

• Wigner then discussed additional dynamical variables.
  1. When the particle is at rest with p = 0, it can spin and can have its angular momentum. It is like a rotating top.

  2. When the particle is massless with m = 0, Wigner noted that the symmetry was like that of the rotation and translations on the two-dimensional plane.

  His observations created two fundamental problems on massless particles.

  1. The rotational symmetry on the two-dimensional problem can easily be associated with the helically of the massless particle. What about those two translational degrees of freedom on the two-dimensional plane?

  2. The energy-momentum relations for massive and massless variables can be connected as two different limiting cases of one formula given above, namely
     E² = (mc²)² + (cp)².

     Is it possible to derive those two different internal symmetries as two limiting cases of one symmetry formula?

• As for the first question, it took many painful years for the physics world to realize that those two translational degrees of freedom collapse into one unobservable gauge degree of freedom for massless particles. We can list some of the authors and their papers who contributed to this important task:
  1. S. Weinberg, Phys. Rev. 133, B1318 (1964).
     
  2. S. Weinberg, Phys. Rev. 134, B882 (1964).
     
  3. S. Weinberg, Phys. Rev. 135, B1049 (1964).

  4. A. Janner and T. Jenssen, Physica 53, page 1 (1971), and Physica 60, page 292 (1972).

  5. J. Kupersztych, Nuovo Cimento B 31, page 1 (1976).

  Indeed, these authors noted that the two translational degrees of freedom lead to the gauge degrees of freedom.

• However, why does one gauge degree of freedom requires two translational degree of freedom?

  Indeed, I struggled with Wigner on this problem, and had to publish a number of papers on this problem.

  1. The two-dimensional Euclidean group is generated by one rotation and two translations in orthogonal directions on a flat plane.

     Let us consider a cylindrical surface, with a rotational symmetry around the z axis. We can then consider an up-down translation along the z direction. This up-down translation can take place on the xz plane or on the yz plane. In either way, the amount of translation along the z direction can become the same.

     Illustration of the Kim-Wigner collaboration (1987-1980). Without changing the algebra given in the Wigner39, it is possible to change the geometry. The geometry of the symmetry on a plane (one rotation and two orthogonal translations) can be changed to that of a cylinder with one rotation and one up-down translation. The sphere can be pancaked to become a flat plane, but it can also be elongated to become a cylinder.

     In this way, we can replace the two-dimensional Euclidian symmetry in the original paper with cylindrical symmetry as shown in this figure.

     In their joint paper published in 1987, Kim and Wigner provided the answer to this problem by introducing the cylindrical symmetry as described here.

  2. As for the second question, I had to publish papers with Wigner to settle the issue. The rotations can be described by a three-dimensional sphere.

     This sphere can be compressed to a pancake-like two dimensional plane.

     On the other hand, it can be elongated to a cylinder.

     This cylinder can be rotated, and there is also an up-down translational degree of freedom. Then the rotation around the momentum remains as the helicity, and the rotations perpendicular to the momentum become up-down translations on the surface of the cylinder as shown in this figure.

  3. In 1986, I showed Wigner the following table. He became very happy, but not completely happy until the cylindrical issue was completely settled (one to one, but not two to one).

     Contents of Einstein's E = mc2 Massive/Slow between Massless/Fast

     Energy Momentum E = p2/2m Einstein's E2 = (mc2)2 + (cp)2 E = cp

     Helicity Spin, Gauge S3 S1 S2 Wigner's Little Group Helicity Gauge Trans.

     While the black row is for Einstein's energy-momentum formula, the blue row belongs to Eugene Paul Wigner. Wigner liked this table.

  4. This table does not tell anything about the hydrogen atom or the bound state in Einstein's world. The Bohr-Einstein question of how the hydrogen atom appears to a moving observer.

• Yet, the problem is that there are no observable hydrogen atoms moving with relativistic speed. On the other hand, there are protons moving with speed very close to that of light. Protons are not hydrogen atoms.

  According to Gell-Mann's quark model, the proton shares the same bound-state quantum mechanics as the hydrogen atom as illustrated in this figure:

  Fast-moving protons can be observed in laboratories. In 1969, Feynman gave the exact description of those fast-moving protons. It is known as Feynman's parton picture:

  The question is whether the quark model for the proton at rest is consistent with its parton picture when it moves fast. I worked on this problem for many years, and the result was tabulated in the following table.

  Further Contents of Einstein's E = mc2 Massive/Slow between Massless/Fast

  Energy Momentum E = p2/2m Einstein's E2 = (mc2)2 + (cp)2 E = cp

  Helicity Spin, Gauge S3 S1 S2 Wigner's Little Group Helicity Gauge Trans.

  Hadrons, Bound States Gell-Mann's Quark Model One Lorentz-Covariant Entity Feynman's Parton Picture

  This table was published in my paper: Phys. Rev. Lett. [63], 348 - 351 (1989). pdf.

  The green row is added to the table given before. While we cannot detect the hydrogen atom moving fast enough to show the effect of relativity, with particle accelerators, it is possible to produce many protons moving with speeds very close to the light speed.

• The point is that the proton is also a bound state sharing the same quantum mechanics as the hydrogen atom.

I use one of Wigner's papers as my bridge to Einstein. Not Wigner, only one of his papers. Wigner is too big to be a bridge to anyone. In 1963, Wigner received his Nobel prize in physics. The prize however was not for this paper. Wigner was happy with his prize, but not 100% happy because the prize was not for this paper. How do I know this? Wigner told me.

• When Einstein formulated his theory of relativity in 1905, all the particles were point particles. Later, it was found that those particles have very rich internal structures, with internal variables. Eugene Wigner noted that there are internal variables in his 1939 paper. I studied Wigner's paper for many years to construct Princeton's genealogy described above.

• Am I saying my brain is superior to those of the Princeton people during the period (1965-66)? Perhaps Yes or No. In either way,

  I can brag about my persistence to continue my research efforts for 20 years while being isolated and humiliated by my colleagues and friends.

  I am not Jesus, I do not have kind words for those who were unkind to me in the past. On the other hand, I do not have to mention them, since you cannot recognize their names these days. Perhaps, I can mention two names still recognizable in the physics world. Click here.

• While I keep saying the United States has been very nice to me, one prominent American broadcaster says the United States is very grateful to me. Like to hear what he says? Click here for my interview with Doug Llewelyn. In his interview, he asks me
  1. Why is my high school class in Korea was the No.1 class in world.

  2. Where was the blank spot in Einstein's theory of relativity? How did I fill in?

  3. What was the cause of my 20 years of delay in promotions in academic ranks. Did I have enough perseverance to sustain this delay?

• I am scheduled to have a TV interview on September 9 of this year. My hair is not long enough yet, but I am considering a haircut before that date.