M Theory: Uncertainty and Unification

We are in the middle of a series of important centennials: Wolfgang Pauli in 2000, Enrico Fermi and Werner Heisenberg in 2001, and Paul Dirac in 2002. This has presented an excellent opportunity to go back and review the scientific achievements of these men. Of course, the work that they did in the 20’s, in their twenties, was their most important. But what I found more interesting was the work that they did afterwards. After they discovered quantum mechanics and established the basic framework of physics, they went on to try to understand the nuclear interaction, and quantum field theory, and the spectrum of particles and how all these things fit together. Some of these problems have since been solved, and it is interesting to compare their efforts with what we now know. Some of these problems we still struggle with, and it is even more interesting to compare the things that they tried with what we are trying today. In many cases their point of view was surprisingly modern. Many of them tried to find a unified theory. Pauli, for one, was very attracted by Kaluza-Klein theory, the unification of gravity and electromagnetism in higher dimensions. Einstein, who was older of course, is well-known for his attempts at a unified theory, and Heisenberg is remembered for his attempts at a Worldformula. Today many of us believe that there is a Worldformula. That is, there is a physical-mathematical structure that incorporates quantum mechanics, special relativity, general relativity, and the particles and their interactions, and which is beautiful and unique. We do not know the final form of this theory; we are like the quantum mechanicians in the early twenties, discovering the theory a piece at a time. In this talk I would like to present our current understanding of the Worldformula, M theory, and to structure the talk around some of the themes that were important in Heisenberg’s work: a fundamental length, uncertainty, nonlinearity, and observables.