Wilson with Poincaré

On May 3 (2003), I was at the Geneva airport. I asked a lady at the information booth what the cheapest way is to go to Geneva. She asked me where my destination in the city was. I said "Hotel President Wilson." She laughed and told me I cannot go there by the cheapest way. Yes, the President Wilson is one of the most expensive hotels in Geneva, and the hotel cashier (money lady) was a Jordanian lady who speaks Arabic, English and French fluently. In Switzerland, Arabic is the language of money.

I stayed there for two nights. In so doing, I had to spend about $600 more than necessary. There are many people who say that I do conferences because I am not bright enough to do physics, but they would agree that I am not stupid enough to waste this much money. Then what was the reason? I did this in order to write an article about Woodrow Wilson and myself. Click here if you like to read the article.

In this photo taken at Versailles (France) in 1919, you will see Woodrow Wilson with Raymond Poincaré. They were the presidents of the United States and the Republic of France respectively. Wilson went to Paris with his peace formula giving independence to all nations. However, Poincaré was not ready to give up French colonies, and he won.

Is he the Poincaré we wish to talk about? Raymond had a cousin named Henri. Indeed, according to Bertrand Russell of England, Henri Poincaré was the most intelligent man France produced. We are indeed fortunate to see him through the sphere named after him.

This sphere was originally constructed to understand polarization of light waves. These days, it serves as the basic instrument for understanding the density matrix and decoherence mechanism mentioned very frequently in the physics literature.

Another physics instrument formulated by Henri is the Poincaré group. Whenever I give talk at optics conferences, they say I am not an optics man. Fine, but I studied Poincaré group thoroughly enough to tell Eugene Wigner the stories he wanted to hear. I wrote a book entitled "Theory an Applications of the Poincaré Group" with Marilyn Noz. Wigner of courses wanted to hear what was going on in the field of the Poincaré group. I used to tell him optics is the new frontier of this subject.

The Poincaré group is the inhomogeneous Lorentz group consisting of Lorentz transformations and translations. Indeed, this group forms the basic space-time symmetry of this world. Because Poincaré so elegantly formulate the basic space-time symmetry, there are people who claim that Poncaré, not Einstein, invented special relativity (I do not agree with them).

Then, why did I tell Wigner optics is the new frontier of the Poincaré group? The answer is very simple. The Poincaré sphere is a representation of the Lorentz group. It is very easy to see. The Poincaré sphere is basically the physics of 2-by-2 matrices, so is the universal covering group of the Lorentz group called SL(2,c). Optics, both classical and quantum, is the physics of 2-by-2 matrices, so is the Poincaré sphere. Thus, what told Wigner is fully justified, and my optics colleagues do not have to tell me I am not an optics man.

With Sibel Baskal and Elena Georgieve, I am preparing a review article entitled "Physics of two-by-two matrices." If you are impatient, you may read my paper with D. Han and M. E. Noz, Phys. Rev. E., Vol. 61, page 5907 (2000).

Y.S.Kim (2 August 2003)

The photo of the Poincaré sphere on this webpage came from Christian Brosseau's book entitled "Fundamentals of Polarized Light, A Statistical Optics Approach" (Wiley, New York, 1998). I am grateful to Professor Brosseau for sending me a copy of this book.