• After spending four years (1958-62) at Princeton as a graduate student and a post-doctoral fellow, I came to the University of Maryland as an assistant professor in 1962. The Maryland physics department was new, and thus I had to continue my research line I followed while I was writing my PhD thesis.

    However, for me, it was not a good experience to realize that Princeton was doing nonsense physics. It took me 20 years to construct my own way of doing physics by building a bridge to Einstein.

  • My program starts with finding a mistake made by Princeton's new genius named Roger Dashen. However, American physicists would not accept my research result. Their response was

    Dashen is a genius, but you are only a Korean.
    How can you be right? Go back to Korea.

    Yet, I stood firm and developed my own research line. It took me 20 years, but I was able to build a bridge to Einstein based on my own Princeton background. This program started with Princeton's event widely known as

Dashen-Frautschi Fiasco

  • On April 29, at the 1965 spring meeting of the American Physical Society in Washington, Freeman J. Dyson of Princeton's Institute of Advanced Study (institute created for Einstein) presented an invited talk entitled "Old and New Fashions in Field Theory," and the content of his talk was published in the June issue of the Physics Today (pages 21-24). This paper contains the following paragraph.

      Freeman Dyson (1923-2020).
      Photo by Heka Davis, courtesy AIP Emilio Segrč Visual Archives, Physics Today Collection.
  • The first of these two achievements is the explanation of the mass difference between neutron and proton by Roger Dashen, working at the time as a graduate student under the supervision of Steve Frautschi. The neutron-proton mass difference has for thirty years been believed to be electromagnetic in origin, and it offers a splendid experimental test of any theory which tries to cover the borderline between electromagnetic and strong interactions. However, no convincing theory of the mass-difference had appeared before 1964. In this connection I exclude as unconvincing all theories, like the early theory of Feynman and Speisman, which use one arbitrary cut-off parameter to fit one experimental number. Dashen for the first time made an honest calculation without arbitrary parameters and got the right answer. His method is a beautiful marriage between old-fashioned electrodynamics and modern bootstrap techniques. He writes down the equations expressing the fact that the neutron can be considered to be a bound state of a proton with a negative pi meson, and the proton a bound state of a neutron with a positive pi meson, according to the bootstrap method. Then into these equations he puts electromagnetic perturbations, the interaction of a photon with both nucleon and pi meson, according to the Feynman rules. The calculation of the resulting mass difference is neither long nor hard to understand, and in my opinion, it will become a classic in the history of physics.

  • Dyson was talking about the papers by R. F. Dashen and S. C. Frautschi published in Phys. Rev. 135, B1190 and B1196 (1964). They use the S-matrix formalism for bound states.

    Later in the same year, Steve Adler and Roger Dashen became full professors at the Institute for Advanced Study. Naturally, they were admired by their colleagues, and many young physicists studied Dashen's paper on the neutron-proton mass difference.

    I was one of those who studied the paper carefully during the summer of 1965. I then published my paper in the Physical Review [142, 1150 (1966)], telling that Dashen made a mistake.

  • In their paper, Dashen and Frautschi use the S-matrix method to calculate a perturbed energy level. Of course, they use approximations because they are dealing with strong interactions. If we translate what they did into the language of the Schrödinger picture, they are using the following approximation for

      (φ, δV φ),

    for the mass difference.

    There are however "good" and "bad" approximations. I showed in my paper that Dashen and Frautschi use the formula

      good , δV φbad) .

    I then pointed out their infrared divergence comes from this bad approximation.


  • How could those two distinguished physicists make this kind of mistake?

    If you solve the Schrödinger equation for negative energy states, there are two solutions: "good" and "bad." We then impose a localization condition to eliminate bad wave functions. This results in a discrete spectrum of bound-state energy levels. Thus a slight departure from a given energy level will result in a bad wave function. Click here for an article on this subject.

    Dashen and Frautschi use the S-matrix formalism where the bound-states appear as poles in the complex energy plane. A slight mislocation will lead to the inclusion of the bad wave function. This is precisely the course of the so-called "Dashen-Frautschi Fiasco."

  • I am indeed fortunate to have gone through an excellent undergraduate education in physics. I took my first-year quantum mechanics when I was a senior (1957-58) at the Carnegie Institute of Technology (now called Carnegie Mellon University) in Pittsburgh.

    Michel Baranger was the professor, and taught me why bound-state energy levels are discrete. I still remember those good and bad wave functions he drew on the blackboard.

    In 1997, I attended his 70th birthday celebration held at MIT. My wife and I posed with him in this photo. We were very happy!

Toward a New Research Program

Feynman was on my side!

  • After publication of my paper, many voiced objections based on the belief that Princeton could not have made this kind of mistake or misjudgment. There were also many who knew Dashen's calculation was wrong, but they were not sympathetic to me. Their assumption was that I would disappear from the physics world. One prominent Princeton professor told me wave functions have nothing to do with physics and everything should come the S-matrix and the current algebra.

      I am standing in front of Feynman's portrait at the entrance of Fermi Lab's Feynman Computing Center (June 2003).
    Since then, I became devoted to wave functions. In 1970, I was very fortunate to find a very important person who shared the same ideology as mine. His name was Richard P. Feynman. People these days ask me what connection I have with Feynman. This was the very beginning of my Feynman connection. Yet, it takes time to transform ideology to concrete results in physics. For this, I lived in isolation for fifteen or twenty years (depending on how to count). It was like living in prison. The person who pulled me out of prison was Eugene Paul Wigner, and I am forever grateful to him.

    As for the wave functions, I was particularly interested in their localization property, as you can see from the "good" and "bad" wave functions. The burning issue was and still is whether the hydrogen wave function localized in one Lorentz frame appears to be localized to observers in other Lorentz frames. This is a well-defined problem, and I enjoyed working on this problem in the past. I enjoy giving invited talks on this subject under current titles, such as symmetries of extended particles, covariance of Feynman's parton picture, Feynman's rest of the universe, squeezed states, Feynman's decoherence, Wigner's little groups, and other trademarks of current interest.

  • You may visit my Scope of Research page to find out what I am talking about.