Introduction

The primary objective of twistor theory originally was—and still is—to find a deeper route to the workings of Nature; so the theory should provide a mathematical framework with sufficient power and scope to help us towards resolving some of the most obstinate problems of current physical theory. Such problems must ultimately include: (1) removing the infinities of quantum field theory, (2) ascertaining the nature and origin of symmetry and asymmetry in the classification of particles and in physical interactions, (3) deriving, from some fundamental principle, the strengths of coupling constants and the masses of particles, (4) finding a quantum gravity theory capable of satisfactorily addressing the issues raised by space-time singularities and the structure of space-time in the small, (5) constructing a picture that makes sense of the puzzling non-locality and conceptual peculiarities inherent in the process of quantum measurement. Does twistor theory have anything of significance to contribute concerning these matters? Might it at least point us in some appropriate directions?

I shall comment on these issues individually in a moment. But as things stand, it must be said that the successes of twistor theory to date have been almost entirely in applications within mathematics, rather than in furthering our understanding of the nature of the physical world. I would think of twistor theory's physical role, so far, as being something perhaps resembling that of the Hamiltonian formalism.