More in the spirit of curiosity, my spouse Gloria and I decided to attend the 80th anniversary of the founding of the Institute for Advanced Study at Princeton; I spent one year there in 1995 as a member. This time, I had another chance to exchange brief words with Freeman Dyson, who may have forgotten that he approved of my membership there, one year of intellectual nirvana where I wrote my paper “An Integral Formulation of Hydrodynamics,” then adjudged beautiful but useless. Little did I realize that what was beautiful for others became a roadmap for my solution of the Navier-Stokes Equation which I just completed and submitted to the Clay Institute of Mathematics in Cambridge. Those of you who are curious should look at their website and refer to Millennium Problems.
I did not regret our attendance. Gloria hit it off with Mrs. Freeman Dyson, who drove her around the Princeton campus to get her back to our hotel. In 1995, Gloria loved to gossip with the wives of very well-known physicists and mathematicians at the Institute. This time, Dyson himself told me that we need not define turbulence the way lawyers do. I could not finish the discussion with him because there were others vying for his attention.
But my encounter with Cecille Morette de Witt was the high point of my visit. We reviewed our days at the Ecoled’Ete de Physique Theoriquein Les Houches, near Chamonix in the French Alps. She was in fact happy that I called here the marm of young theorists in attendance at the Alpine school. She proudly mentioned that 27 of her students there won Nobel prizes. I apologized for not winning any prize, then she asked me what I do. When I told her of my work on turbulence, she exclaimed, “How beautiful!” and asked me to repeat the following several times: “Turbulence is a manifestation of the quantum nature of matter.” Then I taught her how to call her grandson on a cell phone.
I also met Hong-Yee Chiu, my co-editor of several books in astrophysics, who it turned out was also a member. I now remember that he was a pet of Bengt Stromgen, who discovered Stromgen spheres in astrophysics. Hong-Yee was his usual ebullient self, drinking a lot at dinner. It seems that I am still a favorite of his.
But then I asked myself, what did I really do at the Institute? So I looked back at my “beautiful but useless paper” and realized that I could extend it to solve the Navier-Stokes Equation, a problem almost 200 years old, that no one has solved. I invented a new operator identity on re-reading my paper, and produced an exact solution to the Navier-Stokes Equation. Returning to Harvard in Cambridge, and surviving on fare from Dunkin Donut and Au Bon Pain, I crossed Massachusetts Avenue from Harvard Square and the Science Center innumerable times for four weeks to complete my paper, “Time Evolution Equations and a Solution of the Navier-Stokes Equation.” I am glad I did; I was getting tired of doughnuts and Au Bon Pain sandwiches.
The initial version of the paper was presented to Harvard graduate students and post-docs, the smartest audience that I ever had. No offense to Franck Wilcek, who had to listen to me once in a seminar at the Institute, before he won his Nobel Prize. I was so nervous about giving that talk that I asked for three months to prepare my talk.
The end result now is a submission to the Clay Institute of Mathematics in Cambridge from where I await the evaluation of a jury of mathematicians. If lucky, I will have solved a 200-year-old problem, with a very important result, that there is no turbulence from the Navier-Stokes Equation, a negative proof. This equation, which has spawned hundreds of millions of dollars in research grants, cannot be the explanation for turbulence. Instead, one must use quantum mechanics, as described with euphoria by Madame Cecille Morette de Witt, my school marm at the Les Houches Summer School of Theoretical Physics. I would like to visit her in Chapell Hill, North Carolina to show her my solution, which if correct, is worth a tidy sum. I could then ask her, “Now, will you be proud of me, too?”
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Amador Muriel, a Corresponding Member of the National Academy of Science and Technology, is a Fellow in Philosophy at Harvard University, where he is completing his second book on turbulence, “Quantum Theory of Turbulence,” a sequel to “Quantum Nature of Turbulence,” to be released in late 2010. His present position is recognition of his work on turbulence, a new paradigm in the manner of Thomas Kuhn, the physicist-philosopher. He may be contacted at amadormuriel@fas.harvard.edu. He will present his solution to the Navier-Stokes Equation in a seminar at the College of Engineering, UP Diliman, on Jan. 25, 2011.