Copernicus (1473-1543) and Islamic Astronomy

Nicolous Copernicus was born in Torun (Poland 1473) and died in Frombork (Poland 1643). He spent four years (1496-1501) in Bologna, Italy. He studied astronomy there.

His life story is well known, but I would like to report what I learned from a TV program about two months ago.

• Padua is a beautiful Italian city. Have you been there? Click here. This city is close to Venice and Bologna. Padovians are very proud of their city. In addition to many beautiful buildings, they are very proud of Galileo Galilei and his observatory. They tell be his observatory is a must-see spot in their city. Click here for photo of the place.

• However, this observatory was built two hundred years ago, and Galileo did not live long enough to see this structure. This observatory is maintained by
  1. Department of Astronomy of the University of Padova.
  2. The entrance to the Observatory was locked when I went there. I went there on Sunday.

  This Department has many documents of historical significance, including Galileo's research notes. In addition, it has

  1. Some of the research notes by Copernicus. Copernicus studied astronomy while he was in Bologna, not far from Padua.

  2. Research notes by Islamic astronomers. Padua is very close to Venice, and Venice was a developed as a gateway to Islamic world. In 2008, the city of Venice celebrated 1000 years of trades with the Islamic world. It is not difficult to see Islamic influences on Venetian architecture even these days. Click here.

  While there were no scientific activities in the Western world during the medieval ages, Islamic people were very busy in developing science and technology. They developed the mathematics of algebra. They invented eye glasses, various forms of medicines, and they developed their alchemy. Did you know Isaac Newton was an alchemist?

  How about astronomy? Babylonians started looking at the sky. They came up with the number 360 which we still use. The story of three wise men from the East is a product of Persian astrology.

• When that area became Islamic, they had to pray five times a day depending on the exact location of the Sun which was circling around the earth. Indeed, Islamic astronomers carried out rigorous tracing of the Sun's orbit. They also developed mathematics to calculate the orbit.

  During the 13th Century, the Islamic world was invaded by Mongolians. Did those Mongolians kill everybody? This was not always the case, Mongolians were genuinely interested in trading with the Western World. There is even a theory that Marco Polo went to China on a carriage provided by Mongolian troops.

  In either case, Mongolians were in control of a huge amount of money. In addition, they had a Sun-worshipping superstition, and were ready to support those Islamic scholars doing research on the Sun. The Mongolian rulers built a large observatory for the Islamic astronomers to accelerate their research on the Sun.

  Copernicus. Was he the last Islamic astronomer?

  Indeed, those Islamic astronomers carried out enough calculations of the Sun's orbit for Copernicus to look at. He found basic flows in the geocentric system.

• As I said before, I started constructing this web page from what I saw from a TV program. The TV program concluded with a remark that Copernicus was the last Islamic astronomer. This is not necessarily my conclusion, but I can appreciate this remark based on my own experience in physics.

  During the period 1961-65, Geoffrey Chew's "bootstrap" theory was the only valid physical theory. Young physicists had to write the bootstrap papers to get promoted, and I did. I got my promotion to tenure by becoming the last bootsrapper. Being the last man was not easy. Click here for a detailed story.

• Galileo Galilei had something to do with Copernicus and his heliocentric system. Click here for a story.

• I have never been to Bologna. I may go there this summer to take some photos. This city is the birth place of Guglielmo Marconi. I love to talk about him.

Let us now talk about our own problems.

Eugene Wigner and his wife at their home in Princeton (1991).

Among them, one of the most difficult papers is Wigner's 1939 paper dealing with the internal space-time symmetries. He said the internal symmetries are isomorphic to O(3) and E(2) for massive and massless particles respectively. The physics is transparent for O(3)-like symmetry for a massive particle. If it is at rest its spin can rotate in the three-dimensional space.
• For massless particles, Wigner observed the symmetry group is isomorphic to the two-dimensional Euclidean group or E(2), consisting of one rotational and two translational degrees of freedom. It is easy to associate the rotational degree to the helicity. What about the translational degree of freedom? This question was not completely addressed until 1990, 51 years after 1939.

  Thus, this is an interesting topic in history of physics. In 1939, Wigner stated that the symmetry is isomorphic to E(2) and wrote down the matrix of the form

  

• This is the "ugliest" matrix in physics. Even these days, physicists give up if the matrix is not unitary. I know this from my own experience. Since 1973, my papers were based on non-unitary squeeze matrices. Did you know that Lorentz boosts are squeeze transformations? As soon as I start telling this, my colleagues run away from me.

  Weinberg talking to Wigner (1957) (top), my interpretation of Weinberg's interpretation of the E(2) symmetry.

  It was Steven Weinberg who started tackling the above "ugly" matrix in one of his 1964 papers. In 1979, I studied Weinberg's papers with my younger colleagues, namely D. Han and D. Son, and came up with this figure.

  This two-dimensional figure tells about rotations and translations in the E(2) plane, and the translations as gauge transformations. As for the issue of gauge transformations, there are several other authors who said the translations correspond to gauge transformations, and they were quoted in my papers. Most certainly, I am not the first one to observe this aspect of Wigner's E(2)-like symmetry.

• After seeing this, I thought the person who would appreciate this most was Eugene Wigner who wrote the above "ugly" matrix in his 1939 paper. In 1985, I went to Princeton to tell him about the translation-like variables in his E(2)-like group. He became very happy, but asked why there have to be two gauge components ( x and y coordinates).

  I then had to work hard to make Wigner happy. I pulled out Wigner's 1953 paper with Inonu on group contractions, telling that a spherical surface can become flat if the radius becomes large. Thus, we can consider a tangential plane for the E(2) symmetry.

  The E(2) symmetry comes from the plane tangential at the north pole, while the cylindrical symmetry comes from the cylinder tangential at the equatorial belt (left figure). Click here for the 1987 paper by Kim and Wigner. The four-by-four Lorentz transformation matrix produces a geometry which deforms a sphere into an egg and a pancake, which eventually become a cylinder and a plane respectively. Click here for the 1990 paper by Kim and Wigner.

• Indeed, both translation-like variables correspond to one up-down translation on the cylindrical surface. Thus, Wigner's E(2)-like symmetry has one rotational degree and one translational degree of freedom. This translational degree of freedom corresponds to the gauge degree of freedom.

  During the period of five years (1985-90), I went to Princeton frequently to seek guidance from Eugene Wigner. I was like a graduate student working on his thesis research under Wigner's guidance. When I was a "real graduate student" (1958-61), I was afraid of him.

  These days, I am frequently introduced as Wigner's youngest student, while my thesis advisor was Sam Treiman when I got my degree in 1961. I become angry when this introduction is based on my photos with Wigner. I will be very happy if I am so introduced based on the two papers quoted above.

• The above story is based on the following papers.
  1. E. Wigner, Ann. Math. 40 149 (1939).
  2. E. Inonu and E. P. Wigner, Proc. Natl. Acad. Sci. (U.S.) 39, 510 (1953).
     Click here for further information.

  3. S. Weinberg, Phys. Rev. 133, B1318 (1964).
     
  4. S. Weinberg, Phys. Rev. 134, B882 (1964).
     
  5. S. Weinberg, Phys. Rev. 135, B1049 (1964).

  6. A. Janner and T. Jenssen, Physica 53, 1 (1971); ibid. 60, 292 (1972).
  7. K. Kuperzstych, Nuovo Cimento B 31, 1 (1976).

  8. D. Han, Y. S. Kim, and D. Son, Phys. Rev. D 25, 461 (1982).
  9. D. Han, Y. S. Kim, and D. Son, Phys. Rev. D 31, 328 (1985).
  10. D. Han, Y. S. Kim, and D. Son, J. Math. Phys. 27, 2228 (1986).

  11. Y. S. Kim and E. P. Wigner, J. Math. Phys. 28, 1175 (1987).
  12. Y. S. Kim and E. P. Wigner, J. Math. Phys. 31, 55 (1990).

• This page was constructed by Y.S. Kim (2014.4.3).

Click here for my home page.