### Astronomy Bio...Roger Penrose

#### Jay Bitterman

Roger Penrose was born on August 8, 1931, the son of an eminent British human geneticist in Colchester, Essex. He grew up in a family of scholarship and creativity, and completed his education at University College, London.

In 1957, while working for his doctorate at Cambridge, he and his father made drawings of three-dimensional geometrical figures that were impossible to construct. They were published the following year in the British Journal of Psychology. The figures became well known when incorporated into a couple of disturbing lithographs by the Dutch artist H. C. Escher. He lectured and had research posts in both Britain (London and Cambridge) and the United States - Princeton, Syracuse (New York) and Texas. In 1966 Penrose was made Professor of Applied Mathematics at Birkbeck College, London. Since 1973 he has been Rouse Ball Professor of Mathematics at Oxford University, where he is engaged in theoretical work on the nature of space and time.

Some of his early work in mathematics included the formulation of the fundamental theorems that describe black holes. Penrose's explanation for the occurrence of black holes in terms of gravitational collapse is now usually given in a form of space-time geometry. Oppenheimer and Snyder had first proposed a model of the behavior of stars that collapse upon themselves in 1939 and their results have been proved valid to a remarkable degree by later work. Their model of spherical collapse, together with an interest in gravitational collapse stemming from a study of black holes, led to vigorous research on the dynamics and the inevitability of collapse to a singularity. In 1964 the most important result of such research was a set of theorems formulated by Penrose and Stephen Hawking. These theorems extend the dynamics of simple spherical collapse to a much more complex situation of gravitational collapse. Singularities in any physical theory might naturally be taken to indicate the breakdown of the theory. By using techniques developed jointly with Hawking and Geroch, Penrose established that once gravitational collapse has proceeded to a certain degree, assuming the truth of General Relativity Theory that gravitation is always attractive, singularities are inevitable. These techniques are now famous as the "singularity theorems".

The existence of a trapped surface within an event horizon (the interface between the black hole and space time), from which little or no radiation or information can escape, implies that some events remain hidden to observers outside the black hole. It still remains unknown whether all singularities must be hidden in this way. Penrose has offered the hypothesis, which is now widely accepted, of "cosmic censorship".

Since he moved to Oxford University, Penrose has been nurturing an insight that occurred to him in 1964 while he was in Texas. This is a model of the universe whose basic building blocks are what he calls "twistors". This model arises in response to a dichotomy in physics: calculations in the macroscopic world of ordinary objects (including Einstein's theory of gravity and the General Theory of Relativity) use real numbers, whereas the microscopic world of atoms and quantum theory often requires a system using complex numbers, containing imaginary components that are multiples of the square root of 1. Penrose contends that, while everything is made up of atoms, and since energy exists as discrete quanta bundles, all calculations about both the macroscopic and microscopic worlds should use complex numbers. Logically, it occurred to him that such a hypothesis would require reformulation of the major laws of physics and of space-time.

The Twistor Theory tries to account for empty space, as does ordinary atomic physics. It applies around neutrons, electrons and other particles, rather than considering only the "solid" matter with which physics is usually concerned. Space and time are usually assumed to be a homogenous and indivisible matrix in which matter and energy occur. Twistor theory questions this assumption, attempting to replace the Einsteinian view with a description of the universe that uses four __complex__ numbers. (The Einsteinian view describes the universe in terms of four __real__ numbers: three spatial dimensions and a fourth temporal dimension.) Because each complex number (a multiple of the square root of -1) is made up of a real and an imaginary part, a total of eight numbers are needed to describe reality. They are the three dimensions of position in space, two angular directions of motion through space- time, the energy, spin and polarization of that motion. The theory yields a much more complicated, but in many ways a more logical picture of the constitution of the universe. In addition to being able to generate observed time and space, twistor theory also implies a complex gravity theory. Einsteinian theory accounted for "the force of gravity" in terms of a warping of space and time resulting from the presence of matter. Likewise, in twistor theory gravity is caused by mass effecting a curvature in space. Instead of a warping of space-time, however, it is now a warping of twistor space, involving all the more complex ways in which twistor theory views reality. Ultimately, by this theory, different deformations in twistor space will be seen to produce natural physical forces like gravitation, nuclear power, electricity, radio and magnetism.

A great deal of work remains to be done; but, if successful, twistor theory will cause a fundamental shift in the understanding of physical reality and, therefore, in the conception of astrophysics.