A Brief History of Time From the Big Bang to Black Holes By Stephen W. Hawking Illustrated. 198 pages. Bantam Books. $18.95.
In 1981, the British theoretical physicist Stephen W. Hawking attended a conference on cosmology organized by the Jesuits in the Vatican. The Pope, he recalls in his new book, told the participants that ''it was all right to study the evolution of the universe after the big bang, but we should not inquire into the big bang itself because that was the moment of Creation and therefore the work of God.'' ''I was glad then,'' Mr. Hawking adds, ''that he did not know the subject of the talk I had just given at the conference - the possibility that space-time was finite but had no boundary, which means that it had no beginning, no moment of Creation.''
Now 46 years old, Mr. Hawking has gained international recognition as one of the most wide-ranging thinkers doing work on the origins of the universe. His pioneering work on black holes and the early history of time and his continuing efforts to find a unified theory of physics (that would combine general relativity, which deals with gravity and the large-scale physical phenomena of the universe, and quantum mechanics, which describe the behavior of elementary particles) have earned him the respect of his colleagues, and they have also begun to alter the way we all think about the universe. Now, in his first book for the layman, Mr. Hawking proposes to explain to the general reader just how recent developments in physics affect our notions of time and space and to put his own and other contemporary theories in perspective with earlier assumptions about the cosmos - from Aristotle through Galileo, Newton and Einstein.
Though it contains several dense passages dealing with ''imaginary time,'' ''string theories'' and ''inflationary'' models of the universe, which this reader (who never got beyond trigonometry in school) found impossible to follow, ''A Brief History of Time'' is, on the whole, a lively and provocative book. Though Lou Gehrig's disease, which has left him almost completely paralyzed, limits his professorial responsiblities, Mr. Hawking clearly possesses a natural teacher's gifts - easy, good-natured humor and an ability to illustrate highly complex propositions with analogies plucked from daily life. He is able to give us an understanding of the process by which theoretical physicists build imaginary models of the universe, and he demonstrates how new information leads to the constant modification (or abandonment) of previous theories. He bluntly examines the practical consequences of various hypotheses (for instance, that human life would be impossible in a contracting, as opposed to an expanding, universe) and he also looks at the religious implications of new scientific findings.
As Mr. Hawking points out, the 20th century has already witnessed breakthroughs that forever destroyed our notions of an unchanging cosmos. The theory of relativity put an end to the idea of absolute time, while quantum mechanics (and the uncertainty principle, which says it is impossible to predict precisely both the location and the momentum of a particle at a given moment) introduced a new element of randomness into the dream of perfect science. What's more, observations made by the astronomer Edwin Hubble in the 1920's showed that our own Milky Way is not the only galaxy, and they further suggested that the universe itself is not static or eternal but dynamic and expanding. Yet if such developments have resulted in a more precarious sense of man's condition, it is also important to remember, Mr. Hawking notes, that ''the whole history of science has been the gradual realization that events do not happen in an arbitrary manner,'' that they instead ''reflect a certain underlying order.''
A single consistent theory that would describe this underlying order and unify the partial theories that already exist is what physicists, since Einstein, have been searching for, and Mr. Hawking believes ''there is a good chance that the study of the early universe and the requirements of mathematical consistency will lead us to a complete unified theory within the lifetime of some of us who are around today.'' To give the reader a cursory understanding of what such a unified theory would involve, he takes us through a brief lesson in the basic principles of general relativity and quantum mechanics and looks at the difficulties of ''quantizing'' gravity - that is, of bringing the anomalous force of gravity under the umbrella of quantum theory.
From there, Mr. Hawking moves on to a succinct discussion of the expanding-universe theory, briefly sketching in his own work, most notably a paper he and Roger Penrose, the British physicist, published in 1970, which argued that the big bang began with what is known as a singularity, an infinitely dense, infinitely small point, a theoretical edge of space and time. ''In the end,'' Mr. Hawking writes, ''our work became generally accepted and nowadays nearly everyone assumes that the universe started with a big bang singularity.''
Ironically enough, it's a position that Mr. Hawking's own subsequent research has led him to reassess. Arguing that there ''must have been a time in the very early universe when the universe was so small'' that quantum mechanics also came into play, he has tried to formulate a quantum theory of gravity to examine its origins. He now speculates that ''there was in fact no singularity at the beginning of the universe,'' ''no edge of space-time at which one would have to appeal to God or some new law to set the boundary conditions for space-time.''
It is hard for the lay reader to grasp all of Mr. Hawking's arguments involving this new vision of the universe, but the implications of his proposal are clear: ''The universe would be completely self-contained and not affected by anything outside itself. It would neither be created nor destroyed. It would just BE.''
photo of Stephen W. Hawking (Miriam Berkley)