I met Paul A. M. Dirac in 1962.

  • When Paul A. M. Dirac visited the University of Maryland in October of 1962, I was a first-year assistant professor, and I had to provide convenience for him. At that time, I was confused. The Physical Review Letters was constantly sending out new words, such as Regge poles, N/D method, bootstrap dynamics, strip approximation, etc. However, to me, they did not sound like the physics I really wanted to do.

      Dirac and Feynman in Poland while attending a relativity conference hosted by Leopold Infeld in July of 1962.

      I was there in 2013.

    I was fortunate enough to spend 30 minutes alone with Dirac. I asked him what I should do in physics. He said American physicists should spend more time to understand Lorentz covariance. This was a totally unexpected answer to me.

  • It was like the anwer Nicodemus got from Jesus. Nicodemus a Pharisee (upper-class Jewish man) unhppy with what was happening in his environment and went to Jesus for wisdom, but he got the anwer totally strange to him.

  • It took me some time to understand what Dirac was really telling me. First of all, by American physicists, did he meet anyone in particular? It was not until after reading some of Feynman's papers to realize he was talking about Feynman. Dirac was right, Feynman or his students could have studied Lorentz transformations more carefully. For instance, the paper with his students

    contains many new physical ideas, but it is a total mess from the mathematical point of view. They could have done much better job if they had studied Wigner's papers on the Lorentz group.

    Only after I read Feynman's papers, I realized Dirac was talking about Feynman when he said "American physicists." Dirac and Feynman met in July of 1962 (three months before I met Dirac). They met in Poland.

  • How about Dirac's papers? The best way to understand what Dirac told me in 1962 was to read Dirac's own papers. Dirac's papers all sound like poems, but they do not contain figures. The best way to understand his papers is to translate all those poems into cartoons. Here are thus my cartoons to tell you what Dirac told me and what I did.

  • First of all, let us translate what Dirac told me into a cartoon.

In the real world,
this ellipse appears as
  • You do not have to be a genius to combine the above two figures. This figure means many different things in physics. Among them are

    1. Lornerz-covariant picture of bound states.

    2. Quarks and partons as one Lorentz-covariant entity.

    3. Coupled Oscillators as a model for the Lorentz-covariant world.

    4. Squeezed states of light.

    5. Squeeze transformations in physics. Symplectic transformations.

    6. Feynman's rest of the universe.

    7. Role of entropy in the Lorentz-covariant world.

    8. Entropy and Lorentz transformations,
      Physics Letters A 147, 343 (1990).

    9. Entangled space and time variables.

    10. Coupled oscillators, entangled oscillators, and Lorentz-covariant Oscillators
      Journal of Optics B: Qauntum and Semiclassical 7, s 459 - 467 (2005).

      I like this computer. It generates both quantum mechanics and special relativity.

  • Note added in 2018. After realizing that Dirac's life-time interest was in making quantum mechanics consistent with relativity, I became interested what Dirac was really telling me when I met him 1962. In 1962, he submitted his paper to the Journal of Mathematical Physics, in which he constructed, from two harmonic oscillators, the Lie algebra of the Lorentz group applicable to 3-dimensional space with two time variables.

    Click here for Dirac's 1963 paper.

    The harmonic oscillator is the language of quantum mechanics. The Lorentz group is the language of Einstein's special relativity. Does this mean that the special relativity is derivable from quantum mechanics? For many years, this has been my main interest in physics. Click here for my list of publications.

  • Note added in 2019. I became quite excited about contracting Dirac's O(3,2) group into the inhomogeneous Lorentz group, and wrote the following three papers.

    1. Einstein's E = mc^2 derivable from Heisenberg's Uncertainty Relations,
      with Sibel Baskal and Marilyn Noz,
      Quantum Reports [1] (2), 236 - 251 (2019),
      ArXiv. For pdf with sharper images, Click here.

    2. Role of Quantum Optics in Synthesizing Quantum Mechanics and Relativity,
      Invited paper presented at the 26th International Conference on Quantum Optics and Quantum Information (Minsk, Belarus, May 2019).
      ArXiv. For pdf with sharper images, click here.

    3. Poincaré Symmetry from Heisenberg's Uncertainty Relations,
      with S. Baskal and M. E. Noz,
      Symmetry [11](3), 236 - 267 (2019),