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PREFACE
N ow that this book is done I can look back, and identify two purposes which
led me to begin writing, and which have guided the work to completion.
One good practical purpose was to bring together and assess the wealth of data
provided over the last decade by new techniques in experimental physics and in
optical, radio, radar, X-ray, and infrared astronomy. Of course, new data will
keep coming in even as the book is being printed, and I cannot hope that this work
will remain up to date forever. I do hope, however, that by giving a comprehensive
picture of the experimental tests of general relativity and observational cosmology,
I will help to prepare the reader (and myself) to understand the nm\' data as they
emerge. I have also tried to look a little way into the future, and to discuss what
may be the next generation of experiments, especially those based on artificial
satellites of the earth and sun.
There was another, more personal reason for my writing this book. In learning
general relativity, and then in teaching it to classes at Berkeley and M.LT., I
became dissatisfied with what seemed to be the usual approach to the subject.
I found that in most textbooks geometric ideas were given a starring role, so that a
student who asked why the gravitational field is represented by a metric tensor, or
why freely falling particles move on geodesics, or why the field equations are
generally covariant would come away with an impression that this had something
to do with the fact that space-time is a Riemannian manifold.
Of course, this was Einstein's point of view, and his preeminent genius
necessarily shapes our understanding of the theory he created. However, I believe
that the geometrical approach has driven a wedge between general relativity
and the theory of elementary particles. As long as it could be hoped, as Einstein
did hope, that matter would eventually be understood in geometrical terms, it
made sense to give Riemannian geometry a primary role in describing the theory
of gravitation. But now the passage of time has taught us not to expect that the
strong, weak, and electromagnf3tic interactions can be understood in geometrical
terms, and too great an emphasis on geometry can only obscure the deep con-
nections between gravitation and the rest of physics. In place of Riemannian geometry, I have based the discussion of general
relativity on a principle derived from experiment: the Principle of the Equivalence
of Gravitation and Inertia. It will be seen that geometric objects, such as the
metric. the affine connection, and the curvature tensor, naturally find their way
into a theory of gravitation based on the Principle of Equivalence and, of course,
one winds up in the end with Einstein's general theory of relativity. However, I
have tried here to put off the introduction of geometric concepts until they are
needed, so that Riemannian geometry appears only as a mathematical tool for
the exploitation of the Principle of Equivalence, and not as a fundamental basis
for the theory of gravitation.
This approach naturally leads us to ask why gravitation should obey the
Principle of Equivalence. In my opinion the answer is not to be found in the realm
of classical physics, and certainly not in Riemannian geometry, but in the con-
straints imposed by the quantum theory of gravitation. It seems to be impossible
to construct any Lorentz-invariant quantum theory of particles of mass zero and
spin two, unless the corresponding classical field theory obeys the Principle of
Equivalence. Thus the Principle of Equivalence appears as the best bridge
between the theories of gravitation and of elementary particles. The quantum
basis for the Principle of Equivalence is briefly touched upon here in a section on
the quantum theory of gravitation, but it was not possible to go far into the
quantum theory in this book.
The nongeometrical approach taken in this book has, to some extent, affected
the choice of the topics to be covered. In particular, I have not discussed in detail
the derivation and classification of complicated exact solutions of the Einstein
field equations, because I did not feel that most of this material was needed for a
fundamental understanding of the theory of gravitation, and hardly any of it
seemed to be relevant to experiments that might be carried out in the foreseeable
future. By this omission, I have left out much of the work done by professional
geI).eral relativists over the past decade, but I have tried to provide an entree
to this work through references and bibliographies. I regret the omission here of a
detailed discussion of the beautiful theorems of Penrose and Hawking on gravi-
tational collapse; these theorems are briefly discussed in Sections 11.9 and 15.11,
but an adequate discussion would have taken up too much time and space.
I have tried to give a comprehensive set of references to the experimental
literature on general relativity and cosmology. I have also given references to
detailed theoretical calculations whenever I have quoted their results. However, I
have not tried to give complete references to all the theoretical material discussed
in the book. Much of this material is now classical, and to search out the original
references would be an exercise in the history of science for which I did not feel
equipped. The mere absence of literature citations should not be interpreted as a
claim that the work presented is original, but some of it is.
It is a pleasure to acknowledge the inestimable help I have received in writing
this book. Students in my classes over the past seven years have, by their questions
and comments, helped to free the calculations of errors and obscurities. I especially thank Jill Punsky for carefully checking many of the derivations. I have drawn
very heavily on the knowledge of many colleagues, including Stanley Deser,
Robert Dicke, George Field, Icko Iben, Jr., Arthur Miller, Philip Morrison, Martin
Rees, Leonard Schiff, Maarten Schmidt, Joseph Weber, Rainier Weiss, and espe-
cially Irwin Shapiro. Finally, I am greatly indebted to Connie Friedman and Lillian
Horton for typing and retyping the manuscript with inexhaustible skill and patience.
STEVEN WEINBERG
Cambridge, Massachusetts
April 1971
N ow that this book is done I can look back, and identify two purposes which
led me to begin writing, and which have guided the work to completion.
One good practical purpose was to bring together and assess the wealth of data
provided over the last decade by new techniques in experimental physics and in
optical, radio, radar, X-ray, and infrared astronomy. Of course, new data will
keep coming in even as the book is being printed, and I cannot hope that this work
will remain up to date forever. I do hope, however, that by giving a comprehensive
picture of the experimental tests of general relativity and observational cosmology,
I will help to prepare the reader (and myself) to understand the nm\' data as they
emerge. I have also tried to look a little way into the future, and to discuss what
may be the next generation of experiments, especially those based on artificial
satellites of the earth and sun.
There was another, more personal reason for my writing this book. In learning
general relativity, and then in teaching it to classes at Berkeley and M.LT., I
became dissatisfied with what seemed to be the usual approach to the subject.
I found that in most textbooks geometric ideas were given a starring role, so that a
student who asked why the gravitational field is represented by a metric tensor, or
why freely falling particles move on geodesics, or why the field equations are
generally covariant would come away with an impression that this had something
to do with the fact that space-time is a Riemannian manifold.
Of course, this was Einstein's point of view, and his preeminent genius
necessarily shapes our understanding of the theory he created. However, I believe
that the geometrical approach has driven a wedge between general relativity
and the theory of elementary particles. As long as it could be hoped, as Einstein
did hope, that matter would eventually be understood in geometrical terms, it
made sense to give Riemannian geometry a primary role in describing the theory
of gravitation. But now the passage of time has taught us not to expect that the
strong, weak, and electromagnf3tic interactions can be understood in geometrical
terms, and too great an emphasis on geometry can only obscure the deep con-
nections between gravitation and the rest of physics. In place of Riemannian geometry, I have based the discussion of general
relativity on a principle derived from experiment: the Principle of the Equivalence
of Gravitation and Inertia. It will be seen that geometric objects, such as the
metric. the affine connection, and the curvature tensor, naturally find their way
into a theory of gravitation based on the Principle of Equivalence and, of course,
one winds up in the end with Einstein's general theory of relativity. However, I
have tried here to put off the introduction of geometric concepts until they are
needed, so that Riemannian geometry appears only as a mathematical tool for
the exploitation of the Principle of Equivalence, and not as a fundamental basis
for the theory of gravitation.
This approach naturally leads us to ask why gravitation should obey the
Principle of Equivalence. In my opinion the answer is not to be found in the realm
of classical physics, and certainly not in Riemannian geometry, but in the con-
straints imposed by the quantum theory of gravitation. It seems to be impossible
to construct any Lorentz-invariant quantum theory of particles of mass zero and
spin two, unless the corresponding classical field theory obeys the Principle of
Equivalence. Thus the Principle of Equivalence appears as the best bridge
between the theories of gravitation and of elementary particles. The quantum
basis for the Principle of Equivalence is briefly touched upon here in a section on
the quantum theory of gravitation, but it was not possible to go far into the
quantum theory in this book.
The nongeometrical approach taken in this book has, to some extent, affected
the choice of the topics to be covered. In particular, I have not discussed in detail
the derivation and classification of complicated exact solutions of the Einstein
field equations, because I did not feel that most of this material was needed for a
fundamental understanding of the theory of gravitation, and hardly any of it
seemed to be relevant to experiments that might be carried out in the foreseeable
future. By this omission, I have left out much of the work done by professional
geI).eral relativists over the past decade, but I have tried to provide an entree
to this work through references and bibliographies. I regret the omission here of a
detailed discussion of the beautiful theorems of Penrose and Hawking on gravi-
tational collapse; these theorems are briefly discussed in Sections 11.9 and 15.11,
but an adequate discussion would have taken up too much time and space.
I have tried to give a comprehensive set of references to the experimental
literature on general relativity and cosmology. I have also given references to
detailed theoretical calculations whenever I have quoted their results. However, I
have not tried to give complete references to all the theoretical material discussed
in the book. Much of this material is now classical, and to search out the original
references would be an exercise in the history of science for which I did not feel
equipped. The mere absence of literature citations should not be interpreted as a
claim that the work presented is original, but some of it is.
It is a pleasure to acknowledge the inestimable help I have received in writing
this book. Students in my classes over the past seven years have, by their questions
and comments, helped to free the calculations of errors and obscurities. I especially thank Jill Punsky for carefully checking many of the derivations. I have drawn
very heavily on the knowledge of many colleagues, including Stanley Deser,
Robert Dicke, George Field, Icko Iben, Jr., Arthur Miller, Philip Morrison, Martin
Rees, Leonard Schiff, Maarten Schmidt, Joseph Weber, Rainier Weiss, and espe-
cially Irwin Shapiro. Finally, I am greatly indebted to Connie Friedman and Lillian
Horton for typing and retyping the manuscript with inexhaustible skill and patience.
STEVEN WEINBERG
Cambridge, Massachusetts
April 1971
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