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Einstein's E = mc2 derivable from the Heisenberg brackets.
Paul A. M. Dirac
Before I received my PhD degree in 1961, I had to study Dirac's bra
and ket vectors, the Dirac equation and Dirac matrices, positrons,
Fermi-Dirac statistics, and Dirac neutrinos.
Good and bad bound-state wave functions. From 1960 to 1967, the main-line
U.S. physics could not tell the difference between
good and bad
- Perhaps not many of you know about Sections on "permutations as
dynamical variables" in his book "Principles of Quantum Mechanics."
I studied these sections very thoroughly in 1958, and was able to
correct an error in
the 1971 paper of Feynman et al.
You may be interested in my
- In 1962, I came to the University of Maryland as an assistant professor.
At that time, the physics world was dominated by a superstition which forced
every young physicist to believe that the origin of physics is in the
complex planes, consisting of complex energy and complex angular momentum.
I had to produce papers along this direction in order to get promoted to
a tenured position.
I did not like this envirionment, and I got my promotion for my 1965 paper showing
how stupid this superstion was. Click here
for a detailed story. Of course, it was difficult to fight against the
established line of research, and I almost got kicked out from the United States.
Indeed, I am grateful to my senior colleagues at the University of Maryland for
making the correct judgment.
- In the fall of 1962, Paul A. M. Dirac visited the University of Maryland,
and I had to provide convenience to him. I had an opportunity to spend about
thirty minutes with him without anyone else. Because I was not happy with the
physics environment at that time, I asked Dirac what he thought about the trend
in American physics. I was like Nicodemus who made a secret visit to Jesus.
Nicodemus made a secret visit to Jesus in order
to find out about himself. He did not like the society to which he
belonged and was seeking a new wisdom. From Jesus, Nicodemus got a
totally un-expected answer. This Nicodemus story is in the Gospel of John
in the New Testanenent.
I was like Nicodemus, and I got an answer having
nothing to do with the prevailing research lines at that time. Dirac told me
American physicists should study more about Lorentz transformations and Lorentz
covariance. I followed Dirac, and this is the reason why I still enjoy having
quarrels with referees more than 50 years after 1962.
- I was able to appreciate what Dirac told me because I had made
several attempts to understand Wigner's
1939 paper on representations
of the inhomogeneity Lorentz group when I was a graduate student.
In 1963-65,Steven Weinberg was publishing his papers on Wigner's
little groups actively, but I could not join his bandwagon because I
was not prepared. Instead I had to continue my research on "bootstrap
dynamics." In in 1965, I found out how
laughable it was.
- In 1970,
Richard Feynman gave a talk at the APS spring meeting held in
Washington, DC. He showed that the so-called Chew-Fratuschi plot
was nothing more than a manifestation of the degeneracy of
three-dimensional harmonic oscillator. The Chew-Frautschi plot was
the basis for the Regge-pole theory.
In 1971, Feynman published his talk in Physical Review D with his
students. They wanted to present their work in a Lorentz-covariant
manner, but there were many soft spots. Indeed, Dirac was right
when he was talking to me in October of 1962. When he talked to
me three months after he had a meeting with Feynman in Poland.
Dirac said "American physicists should -- ," instead "You should..."
Dirac could have talked about Feynman when he was commenting on
Since then I started rewriting Feynman's 1971 paper using a correct
language of the Lorentz group. With Marilyn Noz, I wrote published
my first paper on this subject in 1973.
- Since then, I published many papers, and here is
one of my recent papers.
- Dirac and Feynman. They become
strong when they are put into one box.
- I also wrote many stories about Dirac. Among them are
- Heisenberg and Dirac.
How are they different?
- Lorentz Covariance. Dirac
introduced the light-cone coordinate system. The Lorentz boost
is a squeeze transformation.
- Wigner's brother-in-law.
Dirac married Wigner's younger sister.
- Lorentz and Dirac
on Lorentz transformations.
- Dirac's polarized neutrinos.
- Dirac's Squeezed States.
- Chaucer, Dirac, and Feynman
- Indeed, my consistent interest in Dirac's papers led to my webpage
where I placed my photo of 1961 next to the 1947 photo of Einstein.
Click here for the page.
- copyright@2015 by Y. S. Kim, unless otherwise specified.
- Click here for his home page.
- His photo-bio.
- Princeton page.
- Einstein page.
- The photo of Dirac is from AIP Emilio Segre Visual Archives.
- The photo of Dirac and Feynman is from the Caltech Photo Archive.
This photo was taken by Marek Holzman during the International
Conference on Relativitic Theory of Gravitation in Warsaw (Poland)
on July 25-31 1962, organized by Leopold Infeld.
The image of Jesus and Nicomemus is from "The Picture Bible"
(David C. Cook Publishing Co., Elgin, Illinois, U.S.A., 1978).