Wigner Years (1986-90)
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Mr. and Mrs. Toll, Wigner, and myself (1986).
Dr. John S. Toll was the Chancellor of the University of Maryland System.
This photo was produced at his residence.
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- Throughout my research life, I was guided by the paper on the
inhomogeneous Lorentz group published in 1939 by Eugene Wigner (Nobel 1963).
He was a professor at Princeton University when I was a student there.
I used to go to him whenever I had questions other professors could not
explain.
- His 1939 paper deals with the internal space-time symmetries of
particles in Einstein's world. A massive particle can be brought
to the frame where it is at rest. In this frame, the particle
exhibits its internal angular momentum called "spin," and its
spin axis can have three different directions. For massless particles,
like photons, the spin can have one direction parallel to its momentum.
This massless particle has an un-observable gauge degrees of freedom.
Wigner's 1939 did not produce a unified picture of these two different
physical phenomena.
- In 1986, with my younger colleagues, I published a paper containing the following
table. This table tells that Wigner's little group unifies the internal space-time
symmetries for both massive and massless particles, as Einstein's
unifies the energy-momentum relation.
Contents of Einstein's E = mc2
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Particle |
Massive/Slow |
between |
Massless/Fast |
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| Einstein |
Energy Momentum |
E = p2/2m |
E = (m2 + p2)1/2 |
E = cp |
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This table is from
one of my papers published in 1986.
In 1986, I approached Professor Wigner to tell this story to him. He became
very happy and asked me to publish new papers with him. We produced seven papers.
- After publishing my papers with Wigner, I became politically (unfortunate word)
strong enough to publish the following table in
Physical Review Letters.
This table contains my earlier work on the Bohr-Einstein issue
of the Gell-Mann-Feynman issue.
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 |
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Click here for further contents of this table.
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- Let us translate this table into the plain language:
Throughout my academic career, the most important asset has been
my graduate and post-graduate education in Princeton (1958-62). I met
there Professor Eugene Wigner while I was a student. After coming to
Maryland, I continued the research line set up by Wigner. In 1986, I
approached him again after doing enough work to tell him what he really
wanted to hear. In this way, I published seven papers with Wigner.
Thus, it is possible to construct Princeton's Einstein genealogy as
shown in this photo.
- Click here for my Wigner file.
- Click here for his little groups
spelled out in his 1939 paper.
- The most rewarding aspect of my association with Wigner is that I am known
as
- Wigner's youngest student at Princeton.
My dissertation adviser was Sam Treiman at Princeton. However, I am widely
known as Wigner's youngest student. The reason is very simple. I published
a number of papers with Wigner, later years after I left Princeton.
- My scientific association, as described above, allows me to construct
this Einstein Genealogy as shown above.
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