Click here for
moving quantum bound states: Bohr-Einstein issue.

Click here for
Einstein's E = mc2 derivable from the Heisenberg brackets.

While Einstein was in Copenhagen

Einstein went to Copenhagen and stayed there at the invitation of Niels Bohr.

    I had a photo with one of these Nobels in June of 2015. His name is Ben Mottelson.
    Mottelson was born in U.S.A. and he received his PhD degree from Harvard in 1950. His advisor was Julian Schwinger.
  • When and how long? I do no know. I hope I can type in exact numbers later.

    He stayed in this building known as the NBI (Niels Bohr Institute). The third floor of this building was used as hotel rooms for visiting physicists during the period 1920-1940, while Americans were doing Newtonian mechanics in USA. Bohr's residence was next to this building.

    The list of visitors is very long, including Heisenberg, Dirac, Pauli, as well as Einstein. Here are the photos of some of those visitors. One of those photos contains images of Bohr, Dirac, and Heisenberg.

  • Even though Einstein never liked the Copenhagen interpretation of quantum mechanics, it is safe to assume that Bohr and Einstein discussed physics. What did they talk about? It is possible that they talked about their own respective issues.

    Bohr was interested in the electron orbit of the hydrogen atom, while Einstein was interested in how things look to moving observers.

    Then how would the hydrogen atom look to a moving observer?

  • This is a well-defined problem understandable to every undergraduate physics major. Einstein and Bohr could have talked about this subject because they did not have to get into the debate over the Copenhagen interpretation.

  • I am not the first one to worry about the Bohr-Einstein issue of moving hydrogen atoms. Click here for those earlier physicists.

  • John S. Bell was and still is a giant in the Copenhagen debate. For a Lorentz-boosted hydrogen atom, he included a figure like this

    in his book entitled Speakable and Unspeakable in Quantum Mechanics (1988).

    1. Unfortunately, this picture does not take into account the fact that the electron orbit was replaced by a standing wave in 1927.

    2. You may also ask about a Lorentz-covariant picture of the Bohr radius. Its longitudinal component picks up a time-like component according to Einstein. Click here for details.

    3. Bell used Newtonian mechanics to explain the hydrogen atom of 1988. On the other hand, with this picture, he transformed the old problem of Bohr and Einstein into a new research subject. Bell left us in 1990.

    Indeed, the problem of moving hydrogen atoms has been my primary interest in physics since 1956. I was an undergraduate student (1954-58) at the Carnegie Institute of Technology (now called CMU or Carnegie Mellon University). It is still my main business.

  • Inside the NBI building during my visit in June of 2015, I asked young physicists whether Bohr and Einstein ever discussed the moving hydrogen atom. They all said they do not know, even though they clearly understood my question.

    Dirac and Feynman in Poland,
    Poet and Cartoonist (1962).

    However, one of them told me Paul A. M. Dirac worked on this problem, and told me to read his papers. This young man did not want to spend any more seconds to entertain my stupid question. He ran away from me.

  • As far as Dirac is concerned, I made a major investment in decoding what he said in his papers. His papers are like poems, and I translated his poems into cartoons. Here is one of my cartoons.

    1. In 1962, I was fortunate enough to talk with Dirac for 30 minutes. It was like Nicodemus meeting with Jesus. Dirac said American physicists should spend more time for understanding Lorentz covariance.

      Dirac did not talk to too many people, but it was three months after he met Feynman in Poland. Thus, he was talking about Feynman while mentioning American physicists.

    2. I then started studying Dirac's papers on this subject. In 1973, I realized that Dirac's light-cone coordinate system allows us to convert the hyperbolic geometry of Lorentz boosts into an elliptic geometry. With Marilyn Noz, I published a paper on Lorentz-squeezed hadrons.

      In his 1949 paper, Dirac suggested the variables (z + t) and (z - t). In terms of these variables, the transformation matrix is diagonal for Lorentz boosts. Let us write

        z2 - t2 = (z + t)(z - t) = constant,

      which converts

      If (z + t) becomes larger, (z - t) should become smaller. This is a high-school algebra, which I learned in 1949. I learned in 1953 (still in high school) that this can squeeze a circle into an ellipse.

      Click here for a detailed explanation .

    3. If Bohr and Einstein never discussed moving hydrogen atoms, there is a good excuse. The hydrogen atom moving with a relativistic speed was far beyond their imagination. Still there are no hydrogen atoms moving fast enough to show their relativistic effects.

    4. In 1964, Gell-Mann invented the quark model where the proton is a bound state of the quarks. The quarks are not electrons, but the proton and the hydrogen atom share the same quantum mechanics.

      Unlike the hydrogen atom, the proton can be accelerated to the speed very close to that of light. In 1969, Feynman observed that the proton appears like a collection of partons whose properties appear to be quite different from those of the quarks.

    5. Thus, the question is whether the quark model and the parton model are two limiting cases of one Lorentz-covariant entity, just like Einstein's energy-momentum relation giving two different limits:

      • E = p2/2m for slow particles, and

      • E = cp for fast particles.

  • Let us look at the following 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
    Little Group
    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.

    You have seen this picture before.

  • Since I derived this picture from Dirac's papers, many people ask me

      How is the squeezed state these days?

    whenever they see me. From now on, they should ask me

      How is the hydrogen atom these days?

    Click here for the Lorentz-boosted hydrogen atom as a further content of Einstein's E = mc2 .

  • I have made many Bohr pages in the past. You may be interested in some of the following pages.

      Bohr's grandson is next to me, and his great grandson (College Park, MD, USA, 2014).
    1. Bohr and Kirkegaard. Bohr's philosophical background.

    2. Bohr's grandson talks about him. Bohr became an oriental philosopher.

    3. Bohr's hydrogen atom. 100 years from 1913 to 2013.

    4. Evolution of the hydrogen atom.

    5. Bohr and Einstein, and their hidden variable.

    6. Heisenberg talks about Einstein, including his visit to Einstein's house in 1954.

    2015 and 1903

    The young lady sitting next to me
    went to Bohr's high school.

  • Copenhagen is an interesting city. For high school boys and girls, their graduation is a big event. They roam around the streets on trucks making noises.

    1. Some of them hijck army trucks.
    2. I was invited to one of their trucks to join the celebration in 2015. My own graduation day was in 1954.

    3. Even though I am as old as their grandfathers, I always enjoy mixing up with them wherever I go.

    4. How did Bohr look on his graduation day? Click here.

    5. Danish Student in Athens (July 2008). She studies Greek history in Athens. This Danish student is sitting next to me, and the other lady is her Greek friend. This photo was taken at the Agora Market place. I went there to produce this page about Socrates.

      She was very proud to tell me that she is a graduate of the high school where Niels Bohr studied. Bohr spent his elementary and high-school years at the Gammelholm School System, but this system was abolished four years after Bohr's graduation. The campus buildings are still used for schools with different names.

    6. While visiting copenhagen in June 0f 2015, I was told independently by two informed Copenhageners that Bohr spent his final high-school years at the high school now called "Rysenstens Gymunasium." I went there to take this photo of the school building.

Click here for the rest of Copenhagen

    I go to Copenhagen fairly often, because it is one of the major transportation centers in Europe. I take photos there and keep adding them to my Copenhagen page.