One hundred years ago, Niels Bohr was wondering about the electron orbit of the hydrogen atom (leading to quantum mechanics), while Albert Einstein was interested in how things appear to moving observers (theory of relativity).

How would the hydrogen atom appear to a moving observer?

Bohr and Einstein on the Hydrogen Atom

    on an Italian train from Naples to Rome (1999), wondering how the world appears to a moving observer, as Einstein did.

  • Young Suh Kim
    Professor of Physics Emeritus
    University of Maryland
    College Park, Maryland, USA

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  • Let us go back to the question of how the hydrogen atom appears to a moving observer? I am not the first one to ask this question. Bohr and Einstein met occasionally to discuss physics. It is possible that they discussed this issue, but there are no written records to indicate they ever talked about moving bound quantum states in Einstein's relativistic world (Lorentz-covariant world).

  • Am I the first one? No! There were many distinguished physicists who made essential contributions on this issue. Click here for their contributions made along this direction.

  • Among those distinguished physicists, Paul A, M Dirac (Nobel 1933) published four important papers on this issue. Furthermore, I was fortunate enough to have an audience with him in 1962.

      I was a first-year assistant professor at the University of Maryland in 1962, and John S. Toll was the ambitious chairman of the physics department. Toll invited Dirac to the department for one week and assigned me as a personal assistant (baby sitter) for Dirac. This was a great opportunity to learn things directly from this great physicist.

  • I then studied Dirac's papers carefully. I knew Dirac was great physicist, but he was also a great poet. I read the following three papers written by him.

    1. P. A. M. Dirac, Proc. Roy. Soc. (London) A114, 243 - 265 (1927).
    2. P. A. M. Dirac, Proc. Roy. Soc. (London) A183 , 284 -295 (1945).
    3. P. A. M. Dirac, Rev. Mod. Phys. 21, 392 - 399 (1949).

  • His papers are like poems. Indeed, I really enjoyed reading his papers. On the other hand, he never used figures express his ideas. Thus, it was fun for me to translate his poems into cartoons. Then it is very easy to integrate his ideas, as illustrated in this figure:

Here comes the most cruel question in physics.

Does this figure have anything to with what we see in the real world?

  • We have the following problems.

    1. There are no trains moving fast enough to show this Einstein effect.

    2. How about fast-moving hydrogen atoms. The hydrogen atoms are neutral particles. Particle detectors cannot detect them.

    3. What should we do about this problem?

  • After 1950 (after the era of Bohr and Einstein), particle accelerators routinely produced protons moving with speeds comparable with that of light. However, the proton is not hydrogen atom.

    1. In 1964, Murray Gell-Mann invented the quark model. According to this model, the proton is a quantum bound state of more fundamental particles called the quarks. This proton shares the same quantum mechanics of bound state with that of the hydrogen atom.

    2. In 1969, Richard Feynman observed that Gell-Mann's proton, when it moves with a velocity close to that of light, appears like a collection of the partons whose properties are quite different from those of the quarks.

  • Thus, the quark-parton puzzle becomes the question of moving quantum bound states in Einstein's Lorentz-covariant world, as in the case of moving hydrogen atoms. In other words, we can resolve the issue of moving hydrogen atom by providing a solution to the quark-parton puzzle.

  • Click here for a more extensive discussion on this issue.

  • Let us go back to Einstein. While he was a high school student, he became interested in the philosophy of Immanuel Kant, saying that a given object could appear differently depending on the observer's environment or status of mind.

        He appears differently viewed from different angles. How would he appear to moving observers?
    1. The best way to illustrate the Kantian view of the world is to look at a statue of Japan's Toyotomi Hideyosi. Toyotomi is a very important person in Japanese history. In 1600 AD, he unified Japan by brutally eliminating the rival war lords.

      He is a monkey (O-Saru San in Japanese) to human eyes, while he is a human when monkeys look at him.

    2. If your name is Einstein, you could ask how he appears to a moving observer?

      If the monkey is too complicated, let us choose the simplest object: the hydrogen atom. How would the hydrogen atom appear to a moving observer? We thus return to the original Einsteinian question.

  • Let us come back to the hydrogens and protons. The elementary particles are known to have internal space-time structures. What does the "internal" mean? Click here.

    The electron at rest spins around, and its direction is anywhere in the three dimensional space. The photon with its zero mass is moving with the velocity of light, but its spin direction is either parallel or anti-parallel to the momentum.

    Eugene Paul Wigner (1902-1995) of Princeton University wrote his paper in 1939 showing why they are so.

    This leads to the question of energy-momentum relation between momentum and energy. For the massive particle, it is E = P2/2m, while it is E = cp. Einstein's special relativity gives one formula for both, as is well known.

    Therefore, the internal space-time symmetries should be so unified. Indeed, I worked hard with my younger colleges on this issue, and published our papers in 1983 and 1986, containing this table:

    Einstein's World

    Massive/Slow between Massless/Fast
    E=p2/2m Einstein's
    E=(m2 + p2)1/2
    E = cp
    Spin, Gauge
    S1 S2
    1939 paper
    Gauge Trans.

    In 1986, I went to Princeton and showed this table to Professor Wigner. He became so happy to see this result, and asked me to write papers with him. Click here for detailed stories.

  • Let us come back to the moving hydrogen issue. In earlier years, with Marilyn Noz starting from 1973, I published many papers on wave functions for the harmonic oscillator in Einstein's Lorentz-covariant world.

  • We used this covariant harmonic oscillator wave functions to answer the quark-parton puzzle and published the paper in 1977. We can summarize our result as

  • This result can be added to the above Einstein-Wigner table. I published a paper in Physical Review Letters containing this table:

    Einstein's World

    Massive/Slow between Massless/Fast
    E=p2/2m Einstein's
    E=(m2 + p2)1/2
    E = cp
    Spin, Gauge
    S1 S2
    1939 paper
    Gauge Trans.
    Bound States
    Quark Model
    Parton Picture

    This table is from my PRL paper published in 1989.
    Since I made a contribution to the 3rd row (purple) of this table,
    I am known as Wigner's student in the physics community.
    Click here for the story.

  • This table can be translated into

  • God built mountains and rivers. Humans can build bridges. This bridge in France was built by Romans during the reign of Julius Caesar. I was there in 2017 to inspire myself. Click here for a photo of myself on this bridge.

  • Bohr and Einstein were God-like figures in physics. All I could do was to build a bridge between them.

    Empty Land with two
    Towering Figures.

    Let us build a bridge between them.

  • One hundred years ago, Niels Bohr was studying the electron orbit of the hydrogen atom. He found that its energy levels are discrete and not continuous. This research led to the present form of quantum mechanics.

    Albert Einstein was worrying about how things look to moving observers. This led to his special theory of relativity with his celebrated formula E = mc2.

  • The question then is how Bohr's hydrogen atom appears to moving observers. Bohr and Einstein met occasionally to discuss physics, but there are no written records indicating that they ever discussed this issue. Perhaps, they never did because there are no hydrogen atoms moving fast enough to exhibit this Bohr-Einstein puzzle. This was the Empty Land for us.

  • I like to be remembered as the person who settled this Bohr-Einstein issue.