You can see Einstein (front row) and Schrödinger (3rd row). You can also see Dirac (2nd row) between Einstein and Schrödinger.

The purpose of this webpage is to provide a caption to this photo.

Schrödinger and Einstein

I was fortunate enough to have an audience with Dirac in 1962. Click here for a story.

• However, Schrödinger's main contribution has been and still is his wave mechanics. He was interested in standing waves when he was 8 years old (1895) as can be seen from his hand-written note. This image was scanned from this photo collection organized by Peter Graf.

• Ten years later, in 1905, Einstein formulated his special theory of relativity based on Lorentz transformations. The question then is how the standing waves look to a moving observer?

  Einstein did not, neither did Schrödinger. They did not have to because they could not imagine a guitar or violin moving with a relativistic speed.

  Let us compare Newton and Einstein. After formulating his law of gravitation between two point particles, he started worrying about what happens between two spherical objects with non-zero radii. It took him 20 years for figure out the gravity law between the sun and the earth.

  Likewise, Einstein could have studied how the electron orbit in the hydrogen atom would appear to a moving observer. Some years later, J. S. Bell came up with this picture for this problem. However, Bell was presenting an outdated picture.

• In 1927, the hydrogen orbit was replaced by a standing wave. Thus, the question became how the standing wave appears to a moving observer.

  Many people attempted to punish me for asking this kind of heretic question. However, I was not the first one to raise this question. Paul A. M. Dirac was the first one to worry about this problem and continued his interest even during his late years. From 1927 to 1949, he published the following three papers.

  1. P. A. M. Dirac, Proc. Roy. Soc. (London) A114, 243 (1927).
  2. P. A. M. Dirac, Proc. Roy. Soc. (London) A183 , 284 (1945).
  3. P. A. M. Dirac, Rev. Mod. Phys. 21 , 392 (1949).

• On the other hand, Dirac made no attempts to combine these three papers into one.

  1. In his 1945 paper on harmonic oscillators, he introduces the time variable, but makes did not give a physical interpretation to this variable in terms of the c-number time-energy uncertainty relation he introduced in his 1927 paper.

  2. In his 1949 paper, he introduced the light-cone coordinate system, but he never mentioned his 1945 paper on the harmonic oscillators.

  3. Also in his 1949 paper, Dirac said the construction of relativistic quantum mechanics is the construction of representations of the Poincaré group. However, for this purpose, he never attempted to use the harmonic oscillator wave functions he introduced in his 1945 paper.

• Dirac's papers are like poems, but Dirac never attempted to use diagrams to illustrate his ideas (physical or mathematical). It is fun to translate those papers into cartoons. Using those cartoons, it is straight-forward to combine them to produce the quantum mechanics of harmonic oscillators consistent with the Lorentz-covariant world.

  Click here for the cartoons.

  The question is whether it is necessary to introduce physical principles not in known in quantum mechanics or special relativity.

• The most pressing question is how to Lorentz-boost boundary conditions. The Bohr radius is the space separation between the proton and electron. If it is Lorentz-boosted, it picks up a time-like component.
  1. The time-like separation does not exist the present form of quantum mechanics. However, according to Einstein, this variable clearly exists. In his article on Einstein, Heisenberg confesses he did not understand the issue of simultaneity. If simultaneous events are space-separated, they do not appear simultaneous for a moving observer.

  2. I was once brutally punished by Phys. Rev. referees and by one of the editors for mentioning this variable, but I am not guilty of introducing this variable. Read the paper Feynman published in 1971 with his students. They said there is a time-like separation between the quark inside a hadron. They also say they will drop this variable because they did not know what to do with it. Indeed, Feynman was my savior in the early stage of my professional life.

     Dirac and Feynman, in Jablonna near Warsaw in July (1962). Photo from the Caltech Photo Library. Personal note. I will be in Warsaw from November 17 to 21, and I hope to go to this place and have a photo of myself. If you wish to go with me for fun, let me know. I will be staying in a hotel close to the UW physics department. My email address is yskim@umd.edu.

     Yes, this variable exists. Feynman did not know what to with it. This was not the reason for me to look for the physics of this variable. In his 1927 paper, Dirac talked about the c-number time-energy uncertainty relation. There is an uncertainty between the time and energy variables, but there are no excitations.

  3. In his 1927 paper, Dirac said this space-time asymmetry makes it difficult to construct quantum mechanics consistent with relativity. In his 1945 paper, Dirac wrote down a Gaussian distribution for both space and time variables in his attempt to construct harmonic oscillator wave functions in the Lorentz-covariant world.

     However, Dirac did not attempt to specify his time variable as the time-separation variable. Neither did he attempt to associate this Gaussian time distribution with the c-number time-energy uncertainty relation he discussed in his 1927 paper.

  4. Click here for Dirac and Feynman, and for their conflicts and resolutions.

     The question most cruel to theorists is whether the resulting theory can explain what happens in the real world. Click here for a story.

  Wigner's sister became Dirac's wife. I met all three of them.

• As for the lack of time-like excitations, it is totally consistent with Wigner's O(3)-like little group for massive particles. Wigner's little groups dictate the internal space-time symmetries of particles in the Lorentz-covariant world. For a massive particle, such as the proton, it is enough to worry about space-like excitations.
  1. Click here for a 1979 paper on this subject. I am one of the three authors of this paper, and I was not as knowledgeable as I am today. We forgot to mention there Wigner's little group while the entire subject was about this group. It is a pleasure to see I kept growing up since then, and I hope I am still growing up.

  2. Click here to see where Wigner's little group stands in understanding standing waves in Einstein's world.

  3. As for the time-separation variable, it clearly exists. Yet, we do not know how to measure it in quantum mechanics. If we do not measure the existing variable, it causes a rise in entropy. I was very fortunate to be in a position to publish a paper on this subject with Eugene Wigner. Click here for the paper.

  Running waves and standing waves are treated differently. Feynman diagrams take care of running waves. For standing waves, there are boundary conditions. Do you know how to Lorentz-boost them?

  Schrödinger collection at the Austrian Central Library for Physics. It was a real pleasure to have this photo of myself with young physicists in Schrödinger Zimmer of the University of Vienna. I was sitting on the Schrödinger chair with my left elbow on his desk.

• Based on what I said above, I can now construct this historical chart.
  1. In constructing this chart, Dirac was not enough, and the story is the same for Feynman and Wigner. We have to combine all three of them. Like to see how they are combined? Click here.

  2. We know how the hydrogen atom appeared to us 100 years ago. How does it look these days? Click here for the evolution of the hydrogen atom.

  3. Click here for Einstein and Bohr.

  In order to make this page more meaningful, I visited Schrödinger's Vienna while I was in Europe in June (2013). I went to the Institute of Physics of the University of Vienna to see how Schrödinger wrote his papers.

  Here are some of the photos I took there.

  1. Entrance to the Institute at 5 Boltzmanngasse. Here is a close-up view.

  2. Erwin Schrödinger Zimmer. His office is now used as a gathering place for graduate students. It was a great pleasure for me to have a photo with them in this room.

  3. Schrödinger Auditorium was closed when I was there.

  4. Schrödinger's Notes were kept in the library room belonging to the Austrian Central Library of Physics. Dr. Peter Graf was kind enough to show me the Schrödinger collection there. From these pages, you can see how Schrödinger was meticulous in doing physics.

  5. Schrödinger Photo Collection is available for purchase at this library. When I have a clear understanding of the applicable copyright laws, I hope to post many photos to this website.

• You may also be interested in my Vienna page which I constructed in 2008. Vienna is known as as a great music city. I would like to add more photos when I have time. In the meantime, please send me photos you like to show to others. I will be very happy to include them.

Y. S. Kim (September 2013)