- 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
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
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
This table is from one of my papers published in 1986.
Contents of Einstein's E = mc2
Particle Massive/Slow between Massless/Fast Einstein Energy
E = p2/2m E =
(m2 + p2)1/2
E = cp Wigner Helicity
Helicity Gauge Trans.
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
E = p2/2m Einstein's
E=(m2 + p2)1/2
E = cp Helicity
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.
- Click here for his home page.
- His photo-biography.
- His Einstein page.
- His Princeton page.
- His Style page.
I received my PhD degree from Princeton in 1961, seven years after high school graduation in 1954. This means that I did much of the ground work for the degree during my high school years. Click here for my high school diary.