Einstein, Dirac, Wigner, Feynman

One hudred years ago, Einstein was interested in how things look to moving observers, while Bohr was worrying about why the hydogen energy levels are discrete. They are discrete because the electron orits are standing waves. Thus, there is a well-defined problem.

How would the standing waves look to moving observers?

Click here for the definition of the problem.

Many distinguished physicists worried about this problem. Among them were Dirac, Wigner, and Feynman.
Let us review their works and integrate them.

Three Wise Men from the 20th Century ?
Click here for a story

Three papers

Click here
for detailed references.
  1. 1927. c-number time-energy uncertainty relation.
  2. 1945. Harmonic oscillators for the Lorentz group.
  3. 1949. Light-cone coordinate system.
Combine all three.
  1. 1932. Wigner functions.
  2. 1939. Little group for internal space-time symmetries.
  3. 1953. Group contractions.
Combine 1. and 2. Combine 2. and 3.
  1. 1969. Parton model.
  2. 1971. Harmonic oscillators.
  3. 1972. Rest of the universe.
Combine all three.

Major Contributions c-number time-energy uncertainty, harmonic oscillators, light-cone coordinate system. Little groups defining internal space-time symmetries. Parton model, oscillator model for Regge trajectories, in addition to Feynman diagrams.

Favorite language Poems. Dirac's writings are like poems. Two-by-two matrices. Diagrams and pictures.

Soft spots Lack of figures and illustrations. Lack of physical examples. Lack of concrete physical examples. His 1939 paper could not explain Maxwell's equations. Sloppy mathematics.

We all know that Einstein's special relatibity is best decribed by s hyperbola. We also know how to add to this hperbola a circle tangent to this hyperbola. Let us write their equations as
    t2 - z2 = 1 for the hyperbola,

    t2 + z2 = 2 for the circle.

Dirac's idea is to use the Gaussian function (the language of quantum mechanics) for the circle.

  • Click here for a paper on this subject.

  • Click here for applications of the same mathematics to modern optics.

  • If we assemble these nine papers, we end up with

    Further Contents of Einstein's

    E = mc2

    1. Click here for a story. Another story.

    2. Click here for the detailed references for the papers mentioned above.

    Einstein's Lorentz-covariant World

    Massive/Slow between Massless/Fast
    Energy Momentum E=p2/2m Einstein's
    E=(m2 + p2)1/2
    Gauge, Helicity
    S1 S2
    Little Group
    Gauge Trans.
    Gell-Mann, Feynman Quark Model Lorentz-covariant

    copyright@2018 by Y. S. Kim, unless otherwise specified. The Photo of Dirac by Bulent Atalay, and photo of Wigner by Y. S. Kim (1988). Feynman's photo is from the main lobby of the Feynman Computing Center at the Fermi National Accelerator Laboratory, Batavia, Illinois, USA.