Dirac's Poems and Feynman's Drums

This young physicist is trying to extract physics from these two oscillators (2016).
In 1963, Paul A. M. Dirac published this mathematical poem based on two oscillators.

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. [4] 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.
1. 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).
2. 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).
3. Click here for these stories with mathematical formulas. Click here for a short book on the physics of the Lorentz group.

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.

What did they talk about? They must have talked about how the hydrogen atom looks to moving observers. Yet, we do not know anything about their conversation on this subject. It is thus our job to figure quantum bound states in the Lorentz-covariant world.

Thus, we can go back to the Bohr-Einstein issue. Bohr was interested in the quantum mechanics of the hydrogen atom, while Einstein was interested in Lorentz boost. What is then the difference between the hydrogen atom and the harmonic osciilator? Yes, you know the answer, but you also know that they share the same quantum mechanics. On this issue, you may be interested in the following webpages.

Evolution of the hydrogen atom.
What did Bohr and Einstein talk about when they got together?

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.

Feynman's Drums

My grandson wants to become a physicist. He was one year old when this photo was taken.

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.

I of course respect and admire Feynman, and I even maintain a webpage 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.
In 1945, after the war was over, Italians decided to live like Italians and elected the most beautiful girl in Rome. Silvana Mangano was Miss Roma. Since then, she starred in number of classy films. Italians still love her.
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 Beethoven page.
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 yskim@umd.edu.

My photo with him (middle) and his business manager in Berlin (February 2017). Steigenberger mat is on the floor.

In general physicists like music, and most of us can put up good conversations when we meet professional musicians. While I was having a vacation trip to Europe in February of this year, I met a violinist named Adre Rieu in the main lobby of the Hotel Steigenberger near the Hauptbahnhof (main railway station) in Berlin.
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.
1. Johann Strauss waltzes in Paris, starting with the Voices of Spring.
2. Bessame Mucho.
3. Radetzky March.
4. Rosa Munda.
5. Habanera from Carmen.
6. Cieliti Lindo.
7. La Paloma.
8. 100 years of Johann Strauss.
9. Many more videos by Rieu.
The summer vacation is coming soon. I hope too see you somewhere.
Y.S.Kim (2017.4.28)

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.

How did he talk to Einstein?
Click here for Y. S. Kim's home page.