While Einstein was in Copenhagen
Einstein went to Copenhagen and stayed there at the invitation of Niels Bohr.
- When and how long? I do no know. I hope I can type in exact
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
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).
- Unfortunately, this picture does not take into account the fact
that the electron orbit was replaced by a standing wave in 1927.
- 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.
- 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.
- Unfortunately, this picture does not take into account the fact that the electron orbit was replaced by a standing wave in 1927.
- 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).
- 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.
- 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.
- 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,
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 .
- 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.
- 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
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.
- 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 Energy
E=(m2 + p2)1/2
E = cp Spin, Gauge,
This table is from my PRL paper published in 1989.
Because I made a contribution to the 3rd row of the above table, I am known as Wigner's student in the physics community. Click here for the story.
- E = p2/2m for slow particles, and
You have seen this picture before.
- 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.
- 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
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 and Kirkegaard. Bohr's
- Bohr's grandson talks about
him. Bohr became an oriental philosopher.
- Bohr's hydrogen atom. 100
years from 1913 to 2013.
- Evolution of the hydrogen atom.
- Bohr and Einstein, and
their hidden variable.
- Heisenberg talks about Einstein, including his visit to Einstein's house in 1954.
Bohr's grandson is next to me, and his great grandson (College Park, MD, USA, 2014). 2015 and 1903
The young lady sitting next to me
went to Bohr's high school.
- Bohr and Kirkegaard. Bohr's philosophical background.
- Copenhagen is an interesting city. For high school boys and girls,
their graduation is a big event. They roam around the streets on trucks
- Some of them hijck army trucks.
- I was invited to one of
their trucks to join the celebration in 2015. My own graduation
day was in 1954.
- Even though I am as old as their grandfathers, I always
enjoy mixing up with
them wherever I go.
- How did Bohr look on his graduation day?
- 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.
- 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.