Justified?

• One hundred years ago, Albert Einstein was interested in how things appear to moving observers. Niels Bohr was interested in the the hydrogen atom. Bohr and Einstein met occasionally to discuss physics. Did they talk about moving hydrogen atoms?

  If they did, there are no written records on this issue. If they did not, this question was only a metaphysical question to them, because there are no observable hydrogen atoms moving with with speeds comparble with the speed of light.

• My program was to answer this question using the mathematical formalism Eugene Wigner developed in 1939. In his 1939 paper, he formulated the mathematical device known as Wigner's little group, dealing with internal space-time symmetries in Einstein's Lorentz-covariant world.

  In quantum mechanics, particles are known to have intrisic angular momenta. It is called the spin. This spin structure for the particle at rest or with slow speeds is different from that of the massless particle moving with the speed of light, as the energy-momentum relationa different. In his 1939 paper, Wigner showed that the internal space-time symmetry for the particle at rest is like the three-dimensional rotation group with three rotational degrees of freedom, while that for the massliess particle is like that of the two-dimensional Euclidean group with one rotational degree of freedom and two translational degrees of freedom.

• In 1986, with my younger colleagues, I published a paper containing the following table.

  Contents of Einstein's E = mc2 Particle Massive/Slow between Massless/Fast

  Einstein Energy Momentum E = p2/2m E = (m2 + p2)1/2 E = cp

  Wigner Helicity spin, Gauge S3 S1 S2 Winner's Little Groups Helicity Gauge Trans.

  This table is from one of my papers published in 1986.

  This table tells that Winger's little group unifies the internal space-time symmetries for both massive and massless particles, as Einstein's

• I then approached Professor Wigner and showed this table. He became very happy and asked me to write papers with him, and we published a number of papers together. By 1989, I became politically (unfortunate word) strong enough to publish in Physical Review Letters (the most prestigious journal) a paper containing the following table.

  Further Contents of Einstein's E = mc2 Massive/Slow between Massless/Fast

  Energy Momentum E = p2/2m Einstein's E=(m2 + p2)1/2 E = cp

  Helicity Spin, Gauge S3 S1 S2 Wigner's Little Group Helicity Gauge Trans.

  Hadrons, Bound States Gell-Mann's Quark Model One Lorentz-Covariant Entity Feynman's Parton Picture

  Click here for further contents of this table.

  This table contains my earlier work, mostly with Marilyn Noz on how the proton (quantum bound state like the hydrogen atom) appears when it moves with a speed close to that of light. This is known as the quark-parton puzzle in high-energy physics.

• Here is the scientific interpretation of this genealogy.

• Click here for a detailed story.

What do they say about me? Video from the Marquis Who's Who. Video from the IAOTP (International Association of Top Professionals).