New York Times, ce matin

Canadian Number Theorist and IAS Physics Professor understand mysteries of atomic physics

By FANNIE JAWK

PRINCETON, New Jersey --- Members of Princeton's Institute for Advanced Study often look like absorbed by the complicated equations that haunt their minds, but excitement was tangible yesterday, when Canadian Number Theorist Chantal David and IAS Physics Professor and mathematics Fields medalist Edward Witten announced the discovery they made. Nothing more than a theoretical explanation for fluctuations in the mass of the proton, a new theory in particle physics that physicists have already called the Galois Orbit Large Fluctuation theory.

High school students learn that the proton has a definite mass, approximately 1.6 10 -27 kg (one kg - pronounce /ˈkɪləˌgræm/ - the base unit for weights in the international system used by world scientists is about 2 US pounds), a weight that is hard to imagine. However, specialists in particle physics knew for decades that this is just an approximation of physical reality, which is governed by quantum mechanics and the calculus of probabilities. Since the building of the first colliders in the 30s, scientists had indeed observed very tiny fluctuations of the mass of the proton, but a definite theoretical explanation was missing.

This is where Ms. David enters. She is a Number Theorist, a subject from abstract mathematics which looks fare distant from Particle Physics. However, the Institute for Advanced Study has a fairly good experience of those interactions between different fields: its small community of researchers meet everyday at tea time, in the beautiful reception room of Fuld Hall. And readers of the NY Times might remember that in 1997, at the very same place, and at the same moment of the year, a similar conjunction of brains had finally allowed to unveil the remaining secrets of the Riemann hypothesis, a famous problem in pure maths left open by 19th century's genius Bernard Riemann.

Chantal David lectured recently in New York, about ``fluctuations in the number of points of curves over finite fields''. Despite a partial similarity in the name, finite fields have nothing to do with quantum field theory, at least that's what scientists would have said two weeks ago. Finite fields were invented by another 19th century's math genius, Evariste Galois. They are amenable to the usual four operations but possess a distinguished property of discreteness, just like matter does at the tiny scales quantum mechanics studies them. And while Ms. David recalled about the Katz-Sarnak philosophy, it appeared to Professor Sarnak, who by chance was in the audience, that the same theoretical apparatus also applies to this open problem in quantum mechanics that Professor Witten had told him about a few months before. What Professor Witten just needed then was to apply the traditional perturbative approach - with a symplectic twist, in fact - and solve a stochastic partial differential equation, a computation unfortunately too large to fit in this column. This quickly led to the Galois Orbit Large Fluctuation theory. The European LHC collider at CERN is just running his acclaimed experiment (see yesterday's Times) and they could presumably test the new theory within the next few weeks.

As Professor Sarnak explained to our reporter, ``this is a fantastic development and it opens the way to a real understanding of our micro-scale world''. Dr. Peter Goddard, current Director of the Institute for Advanced Study, adds, not without his distinctive British sense of humor, that ``the delicious cookies that we prepare everyday for our members prove once again their efficiency''.

Not published in the New York Times, April 1st, 2010.