Bohr and Einstein on the Hydrogen Atom
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on an Italian train from Naples to Rome (1999), wondering
how the world appears to a moving observer, as Einstein did.
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- 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.
- P. A. M. Dirac,
Proc. Roy. Soc. (London) A114, 243 - 265 (1927).
- P. A. M. Dirac,
Proc. Roy. Soc. (London) A183 , 284 -295 (1945).
- 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.
- There are no trains moving fast enough to show this Einstein effect.
- How about fast-moving hydrogen atoms. The hydrogen atoms are neutral particles.
Particle detectors cannot detect them.
- 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.
- 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.
- 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.
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He appears differently viewed from different angles. How would
he appear to moving observers?
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- 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.
- 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:
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Energy Momentum |
E=p2/2m |
Einstein's
E=(m2 + p2)1/2 |
E = cp |
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Helicity Spin, Gauge |
S3 S1
S2 |
Wigner's 1939 paper |
S3 Gauge Trans. |
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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:
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Energy Momentum |
E=p2/2m |
Einstein's
E=(m2 + p2)1/2 |
E = cp |
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Helicity Spin, Gauge |
S3 S1
S2 |
Wigner's 1939 paper |
S3 Gauge Trans. |
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Hadrons, Bound States |
Gell-Mann's Quark Model |
One Lorentz-Covariant Entity |
Feynman's Parton Picture |
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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.
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- 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.
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Empty Land with two Towering Figures.
Let us build a bridge between them.
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- 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.
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