Dirac's Poems and Feynman's Drums
- These days, physicists do physics by writing proposals for funding from their
governments. But, some people did their physics differently. Dirac did his physics
by composing mathematical poems. By definition, poem is an abstract
language. It is thus fun to translate those poems into the language of the real
world, and I do physics for fun.
Dirac's first poem was of course his Dirac equation for spin-1/2 particles. He wrote his last poem in 1962. He published this poem in J. Math. Phys.  901 - 909 (1963). This was about two coupled oscillators. He wrote this poem by writing down ten operators satisfying one closed set of commutation relations (or Lie algebra}.
- I seem to brag about having an audience with Dirac in 1962.
Click here to see how I brag. At that time,
I was on a sinking ship loaded with "dispersion relations, N/D methods,
bootstrap dynamics, Regge poles, etc." If you know at least one of these
words, you are a very old person.
By meeting Dirac, I was "born again." You heard these two words. Do you know where the "born again" came from? Nicodemus was born again after meeting with Jesus according to the Gospel of John. My meeting with Dirac was like Nicodemus meeting Jesus. I was not the first one to identify himself with Nicodemus.
Nicodemus by Michelangelo. It is widely believed that is is a statue of himself. This statue is in Florence's Duomo Museum. I am looking at the coupling carefully. This coupling leads to the mathematics of Einstein's Lorentz boost.
Nicodemus was one of the upper-class men in his Jewish community,
but he did not like the society to which he belong. Thus, he made a
secret visit to Jesus. Jesus told him to be born again.
Michelangelo, like everybody at his time, had to be member of his church. He thought the church system was sinfully corrupt. He expressed his view toward the church by identifying himself with Nicodemus in his sculpture entitled Deposition. In this art work, the statue of Nicodemus is his own sculpture.
I seem to mention Bible stories often in my conference talks and webpages. Yes, I came from Korea with a strong Confucian background. How is it possible to quote Bible stories so often. Click here if interested.
- Let us go back to Dirac's poem on two oscillators. Dirac's
ten operators lead a closed set of commutation relations. It is
possible to construct two sets of matrices.
- Ten five-by-five matrices generating Lorentz transformations
applicable to three space-like and two time-like dimensions.
This group generated by these matrices is the anti-deserter group
- Ten four-by-four matrices applicable to canonical transformations
in the four-dimensional phase space for two oscillators. The group
generated by these ten generators is called the four-dimensional
symplectic group or Sp(4).
- Click here for these stories with mathematical formulas. Click here for a short book on the physics of the Lorentz group.
- Ten five-by-five matrices generating Lorentz transformations applicable to three space-like and two time-like dimensions. This group generated by these matrices is the anti-deserter group or O(3,2).
- With a degree of exaggeration, quantum mechanics is the physics of harmonic
oscillators while relativity is the physics of the Lorentz group. Thus,
Dirac's 1963 paper provides the mathematical base for quantum mechanics
consistent with special relativity.
- You are quite familiar with the Dirac equation for spin-1/2 particles. It is
also a mathematical poem composed by Dirac. He believed in mathematical beauty as
the fundamental principle of physics. Have you ever wondered why the Dirac spinor
contains four components, and the Dirac matrices are four-by-four. Yes, you did.
There are also positrons. However, why are they combined in that way?
We are talking about spin-half particles in the Lorentz-covariant world. The Lorentz group is generated by three rotation generators and three boost generators. See Dirac's 1949 paper on this subject.
The Lie algebra for this group is invariant under Hermitian conjugation. While rotation generators are Hermitian, the boost generators are anti-Hermitian. This means that the Lie algebra (the set of commutation relations) can accommodate both signs of the boost generators. This is the reason why the Dirac spinor has four components and the Dirac matrices are four-by-four. for detailed calculations. Click here for detailed calculations.
- I of course respect and admire Feynman, and I even maintain a
dedicated to him. Yet, I am not able to explain how we could extract
physics from the rhythms. In either case, I like samba music and samba dances.
Let us look at one of the samba videos.
Click here for the dance performed by Silvana Mangano in her
1951 film entitled "Anna.".
The point is that Richard Feynman liked this movie scene. I watched this movie in 1954 one month before coming to the United States to become a freshman at Carnegie Tech (now called CMU). At that time, I did not know who Feynman was. About ten years ago, I found out Feynman used to like this movie scene. What a great feeling! Feynman liked what I like! I should be able to pull out some physics from Silvana's samba.
- While writing articles, I did my own research on the connection between
physics and music. I do not know how to play any musical instruments, but I enjoy
listening music while doing physics. I used to and still like Beethoven's,
string quartets, and you are invited to my
The key issue on those musical instruments is the harmony. The harmony plays as the common denominator between music and physics. I have a webpage dedicated to this issue. Click here.
- Albert Einstein liked music, and he played violin. I do not know how
he extracted physics from music. If you know, please tell me. Send
your email to firstname.lastname@example.org.
My photo with him (middle) and his business manager in Berlin (February 2017). Steigenberger mat is on the floor.
He is a pop violinist and is the leader of the music group named "Johann Strauss Orchestra." This group travels around the world, and they draw a large audience wherever they go, and everybody gets excited.
Again I have to bragg about myself by showing you my photo with a person more famous than I am.
Let us go to some of his videos.
Johann Strauss waltzes
in Paris, starting with the Voices of Spring.
Habanera from Carmen.
100 years of
- Many more videos by Rieu.
- Johann Strauss waltzes in Paris, starting with the Voices of Spring.
- The summer vacation is coming soon. I hope too see you somewhere.
On this issue, let us check what Feynman said.
The artists of the Renaissance said man's main concern should be for men, and yet there are other things of interest in the world.Even the artists appreciate sunsets, and the ocean waves, and the march of the stars across the heavens. There is then some reason to talk of other things sometimes. As we look into these things we get an aesthetic pleasure from them directly on observation. There is also a rhythms and a pattern between the phenomena of nature which is not apparent to the eye, but only to the eye of analysis; and it is these rhythms and patterns which we call Physical Laws.
- copyright@2014 by Y. S. Kim, unless otherwise specified.
The photos of Einstein and Bohr are from the AIP E. Segre Visual Archives. The young boy's father is Carter Hall, on the faculty of the University of Maryland.
Why is he with Einstein?
- Click here for Y. S. Kim's home page.