Einstein and Mesons

Let us see how insignificant special relativity was and still is. When we learn special relativity in college, we start with a thunder simultaneously striking both ends of a train, and other illustrations. These are only gedanken experiments. We are not capable of observing those events in the real world.

However, in 1930, Wolfgang Pauli used the conservation of energy to predict the existence of neutrinos in the neutron beta decay. By that time, Einstein's E = mc² was firmly established.

Yukawa with Einstein in Princeton (1953). Photo from Mainichi Shinbun.

In 1935, Hideki Yukawa predicted a particle heavier than electron and lighter than proton. This particle was given a name. This new particle was called the meson.

In 1936, Carl Anderson discovered mesons in cosmic rays bombarding this earth, using the cloud chamber he used in his earlier discovery of positrons in 1932. However, it was decided that Anderson's mesons were different from those predicted by Yukawa. These mesons are now called mu-mesons or muons.

In In 1947, Cecil Powell, César Lattes and Giuseppe Occhialini at the University of Bristol discovered another species of mesons from cosmic rays using emulsions. These mesons indeed turned out to be the particles predicted by Yukawa in 1935. They are now called pi-mesons or pions.

The time dilation and space contraction are observed in this muon decay during the flight (top). Carnegie Tech's 450-MeV FM cyclotron (1957).

In this figure, a muon is created 9000 m above the ground and decays when it comes down after 30 micro-seconds. The speed of the muon is 0.998 m/s. On the other hand, measured from the muon-rest frame, it reaches the ground after 2 micro-seconds. This phenomenon clearly establishes the validity of Einstein's special relativity with its time dilation and space contraction. When the muon decays, it obey's Einstein's E = mc².

Einstein's special theory of relativity is complete enough.

I learned special relativity and this observable muon event from Lincoln Wolfenstein while I was an undergraduate student at Carnegie Tech, now called Carnegie-Mellon University, (1954-58). I was fortunate enough to have a photo with him in 1997 at MIT's faculty dining hall.

During the summer of 1957, I worked at Carnegie Tech's Nuclear Research Center with its 450 Mev cyclotron. It was fascinating to learn that the cyclotron frequency had to be modulated as the proton orbit becomes larger with the increasing proton speed. It was of course due to the mass becoming larger when the proton moves faster. How exciting! Einstein was so close to me.

I learned all these while I was a college student (1954-58), but these items must have been known before 1949, when Einstein became 70 years old. The American Physical Society dedicated to him one of the 1949 issues of the Reviews of Modern Physics. You will be interested in the list of the authors who contributed to this issue. Feynman was too young to be on the list.

You would agree that, also in 1949, the Nobel Committee could have considered a special edition of Nobel prize for Einstein. By 1949, he became the creator of modern particle physics. Indeed, Einstein is very happy to be with Yukawa in this photo.

• As early as 1927, Paul A. M. Dirac worried about whether the c-number time-energy uncertainty and Heisenberg's position-momentum uncertainty can be combined into one Lorentz-covariant form. He invented the Dirac equation in 1928 which led to the concept of positron and anti-particles. The Dirac equation has something to do with special relativity. In addition, Dirac made his life-long efforts to a quantum mechanics consistent with special relativity, as you can see in the following papers.
  1. P. A. M. Dirac, Proc. Roy. Soc. (London) A114, 243 (1927).
  2. P. A. M. Dirac, Proc. Roy. Soc. (London) A183 , 284 (1945).
  3. P. A. M. Dirac, Rev. Mod. Phys. 21 , 392 (1949).
  4. P. A. M. Dirac, J. Math. Phys. 4 , 901 (1963).

• In 1962, I was a first-year assistant professor at the University of Maryland. Paul A. M. Dirac visited the University in October, and I had to provide convenience to him. I was fortunate enough to have an audience with him for 30 minutes. At that time, I was a confused young man. I was led to believe that physics is about the harmony of singularities in complex planes as stars are in the sky (Chew's bootstrap years). I told Dirac I was confused and asked him what I should do.

  I was like Nicodemus asking Jesus for ultimate wisdom.

  Dirac told me American physicists should spend more time on Lorentz covariance. There are many challenging problems. It was three months after Dirac talked with Richard Feynman in Poland. By "American physicists," Dirac could have been talking about Feynman, but he could have said about "physicists of all lands." I know this from the referee reports on my papers on Lorentz covariance, since 1973.

• In 1969, Feynman presented his parton picture of the proton moving with speed close to that of light. If the proton is a bound state of quarks like a hydrogen atom, Feynman's partons have properties quite different from the quarks. It is a very challenging covariance issue. You may click here for my webpages dedicated on this issue.

• We all know Feynman diagrams have something to do with special relativity. We all know that all Feynman diagrams have external legs. This means they are effective in dealing with scattering problems. How about bound-state problems in the Lorentz-covariant regime? In 1970, Feynman gave an invited talk at the spring meeting of the American Physical Society. For bound-state problems, he told us not to use his Feynman diagrams, but to start with harmonic oscillators. Click for a story.

  Among those solutions, there is one set of solutions constituting a representation of Wigner's little group dictating internal space-time symmetries of elementary particles in the Lorentz-covariant regime. What is the little group? It consists of Lorentz transformations for a fixed particle momentum. There are six generators for the Lorentz group. Since the momentum freezes three degrees of freedom, the little group has the remaining three degrees of freedom. I learned this directly from Eugene Wigner while I was a graduate students at Princeton (1958-61). Most of my papers, including my PhD thesis, are based on this secret. My thesis advisor was Sam Treiman.

  The Lorentz covariance of Maxwell's equations played a very important role in Einstein's development of special relativity. You may be interested in the latest story about this issue. Click here the story.

  The story of the Lorentz group in physics is endless. Let me stop here, but I have to mention one more item. The Lorentz group constitutes the basic mathematical language for optical sciences. You may click here to see how this is possible.