Edward Witten

Reflections on the Fate of Spacetime

Our basic ideas about physics went through several upheavals early this century. Quantum mechanics taught us that the classical notions of the position and velocity of a particle were only approximations of the truth. With general relativity, spacetime became a dynamical variable, curving in response to mass and energy. Contemporary developments in theoretical physics suggest that another revolution may be in progress, through which a new source of “fuzziness” may enter physics, and spacetime itself may be reinterpreted as an approximate, derived concept. (See figure 1.) In this article I survey some of these developments.

Duality, Spacetime and Quantum Mechanics

The purpose of this article is to describe some themes in theoretical physics that developed independently for many years, in some cases for decades, and then converged rather suddenly beginning around 1994–95. The convergence produced an upheaval sometimes called “the second superstring revolution.” It is as significant in its own way as “the first superstring revolution,” the period around 1984–85 when the potential of string theory to give a unified description of natural law was first widely appreciated.

The mass question.

Do the elementary particles known as neutrinos have mass? Yes, according to recent experiments. But how much? A surprising — and controversial — result suggests that the answer is not what we thought.

Quantum Mechanics of Black Holes

The popular conception of black holes reflects the behavior of the massive black holes found by astronomers and described by classical general relativity. These objects swallow up whatever comes near and emit nothing. Physicists who have tried to understand the behavior of black holes from a quantum mechanical point of view, however, have arrived at quite a different picture. The difference is analogous to the difference between thermodynamics and statistical mechanics. The thermodynamic description is a good approximation for a macroscopic system, but statistical mechanics describes what one will see if one looks more closely.

When symmetry breaks down.

Electroweak-symmetry breaking: solving the riddle of how symmetry is broken may determine the future direction of particle physics.