Bryce DeWitt (review date 16 November 1973)
SOURCE: "Much-Esteemed Theory," in Science, Vol. 182, No. 4113, November 16, 1973, pp. 705-06.
[In the following review, DeWitt states that The Large Scale Structure of Space-Time is a masterpiece but laments that it is primarily for mathematicians and not physicists.]
Ask a prospective graduate student in theoretical physics what area he hopes to work in, and the chances today are better than 50-50 that he will reply "gravitation theory." This has caused problems for some physics departments, but it shows where the action is—or at least where many students think the action is. This prejudiced reviewer happens to think the students are right—in that the theory of gravity poses some of the most challenging conceptual problems in physics, problems that touch the foundations of nearly all physical theories. The students are simply expressing a gut awareness of the fact.
The theoretical framework for gravitational research has remained unaltered for nearly 60 years. Although proper attention, both experimental and theoretical, has been given to alternative theories, the theory is still Einstein's general relativity, as it was in 1916. The remarkable stability of this theory may fairly be attributed to the extreme practical difficulties one encounters in attempting to devise crucial experiments to challenge it. The challenges it faces today have mostly been devised from within, slowly and with many false starts, by men and women who were willing to gamble (and in some cases throw away) their professional careers by studying the internal consistency of general relativity and elucidating, with pencil, paper, and computer its many fantastic predictions, most of which Einstein himself never knew.
[The Large Scale Structure of Space-Time] by Hawking and Ellis contains a canonical sampling of these fantastic predictions, as well as a full and rigorous account of the chinks in the armor of the theory, which have been uncovered in the past decade. As a fundamental physical theory general relativity is a failure. It is a failure because it predicts that, under very generalconditions, singularities must occur in space-time, beyond which the theory is incapable of saying anything. That is, the theory predicts that it cannot predict. It is not fundamental enough. It must eventually be superseded by something more universal.
This is an old story in physics: Classical electrodynamics, hydrodynamics, statistical mechanics, and quantum field theory are all examples of theories whose incompleteness can be shown on internal grounds alone. (Think of point charges, shock waves, phase transitions, and quantum field theoretical divergences) But these theories by virtue of their overwhelming utility and beauty are still part of our standard curriculum, and we think none the less of them for their failings. Neither do we demote general relativity in our esteem. On the contrary, we see in the problems it presents to us only wonderful adventures for the future. The student who wishes to share in these adventures must master the material that Hawking and Ellis cover.
Beginning with a 50-page résumé of differential geometry in modern notation and a 20-page statement of general relativity theory as a set of postulates about a mathematical model for space-time, the book proceeds briskly to the construction of the tools needed for proving the main theorems. These tools include the theory of geodesics and conjugate...
(The entire section is 1446 words.)