Einstein, Dirac, Wigner, Feynman
In 1905, Einstein formulated special relativity and worked out Lorentz transformations of point particles. Did he ever worry about Lorentz transformation of the hydrogen atom? How would the electron orbit appear to a moving observer? How can we approach this problem? Click here for the definition of the problem.

    Figure out how to Lorentz-transform Localized Waves!

I am not the first one to worry about this problem. Wigner, Dirac, and Feynman did.


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


Three papers

Click here
for detailed references.
Dirac
  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.
Wigner
  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.
Feynman
  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.


One Mathematics The mathematics of two coupled oscillators is well known. All of the above papers can be understood in terms of this mathematical instrument.



If we assemble these nine paper, we then 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.

Lorentz-covariant World
Massive/Slow between Massless/Fast
Energy Momentum E=p2/2m Einstein's
E=(m2 + p2)1/2
E=p
Spin,
Gauge, Helicity
S3
S1 S2
Wigner's
Little Group
S3
Gauge Trans.
Gell-Mann, Feynman Quark Model Lorentz-covariant
Oscillators
Partons


copyright@2012 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.