Foundations of Physics, Vol. 16, No. 8, 1986
Book Review General Relativity and Gravitation. Edited by B. Bertotti, F. de Felice, and A. Pascolini. D. Reidel Publishing Company, Dordrecht, The Netherlands, 1984, xvi + 517 pp., $69.00 (cloth). It is now a tradition that every third year the International Society on General Relativity and Gravitation calls an international conference to review the most important advances and developments. The Tenth International Conference on General Relativity and Gravitation was held in July 1983, in Italy. The conference was attended by about 750 scientist, who submitted more than 450 communications. To cope with this flood of information, the conference was divided into plenary sessions and many workshops. All the plenary contributions and reports on the workshops prepared by their chairmen are included in the Proceedings of the conference entitled General Relativity and Gravitation. This book is an invaluable collection of information on the most important and most active areas of research in general relativity. The book is divided into four sections devoted to classical relativity, relativistic astrophysics (including cosmology), experimental gravitation, and quantum gravity. The section on classical relativity includes, among others, a review article by S. Chandrasekhar on the mathematical theory of black holes, an article by A. Ashtekar on asymptotic properties of isolated systems, two articles by T. Damour and M. Walker discussing the quadrupole formula, and a report by E. Witten on his proof of positivity of energy and Kaluza-Klein theory. The section on relativistic astrophysics is mostly devoted to cosmology. G. F. R. Ellis presents his interesting program of observational cosmology. H. Sato discusses evolution of voids in an expanding universe. A. Anile reviews the nonlinear wave propagation in relativistic hydrodynamics and cosmology, and I. M. Khalatnikov et al. discuss the stochastic properties of relativistic cosmological models near the singularity. In the section on experimental gravitation, R. W. Hellings presents for 839 0015-9018/86/0800-0839505.00/0 © 1986 Plenum PubLishing Corporation
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the first time results of the Viking gravitational experiments. R. W. P. Drever reviews prospects and the present state of art of the laser interferometer detectors of gravitational waves. The section on quantum gravity contains three articles. T. Regge discusses free differential algebras, which provide a new framework for local Lagrangian field theories, B. S. DeWitt concentrates on three topics in quantum gravity: the dynamical equations generated by, as proposed by him, approximate effective action, new developments in the theory of effective action, and his attempts to understand the dynamical role of topology of space-time. S. Hawking describes quantum boundary conditions for the universe which, at least in a simple model, lead to a universe remarkably similar to the one we observe. Each section contains reports on workshops devoted to more specific or more popular topics, such as exact solutions, initial value problems, numerical relativity, the early universe, physics and astrophysics of black holes, space experiments, laboratory experiments, and supergravity. Finally J. A. Wheeler summarizes the conference, suggesting deep and important research topics. For years to come General Relativity and Gravitation will be an important source of information, serving not only active researchers in this field but also students who want to join their ranks. Marek Demianski Center for Theoretical Physics University of Texas at Austin Austin, Texas 78712
Foundations of Physics, Vol. 16, No. 8, 1986
Book Review Elements of Mechanics. By Giovanni Gallavotti. Springer-Verlag, New York, 1983, xiv + 575 pp., $48.00 (cloth). Professor Gallavotti has indeed written a book that, as stated in the preface, is "devoted to the foundations." However, such devotion to the foundations in this case does not necessarily serve the student well. As a reference work, however, I believe that the book has significant merit. I will consider Elements of Mechanics from these two points of view. The stated audience to which the book is addressed is (physics?) students of mechanics covering the entire range from undergraduate to graduate. In my opinion, however, none of these groups would be particulary well served by this book as a text. My basic criticism of the book as an undergraduate text is what ! consider to be an overly pedantic and mathematical style. It does not seem good pedagogy to me to present all results in the form of numbered propositions. Little attention is given to helping the reader distinguish what the really important results are and remember them. The primary style of presentation--consisting of definitions, propositions, and proofs--although efficient and predictable, becomes tiring. A great deal of detail is offered in the proofs of the propositions and the examples considered. The author almost completely ignores the great benefit which accrues to the reader from having some phase space pictures of motions. Excessive detail is a weakness as a teaching tool and is an impediment to a qualitative understanding of motion. Despite the author's title to the second chapter, "Qualitative Aspects of One-Dimensional Motion," I find the treatment there, as elsewhere, short on qualitative explanation and discussion and long on quantitative detail. Despite this mathematical detail, the book does very little in preparing the student to understand the language of current research in dynamics. Nowhere is there any introduction to, application of, or mention of differential geometry. Despite these criticisms of the book as a textbook for students, there are many fine things in this book which make it a valuable reference work 841 0015-9018/86/0800-0841505.00/0 © 1986 Plenum Publishing Corporation
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for teacher and researcher. I found a discussion of unusual problems and systems that I have not seen in any other text book. Elements of Mechanics also has an extensive set of problems to enhance and test the understanding of the reader in the spirit of the mathematical presentation. Furthermore, the book contains 14 appendices mostly containing a summary of mathematical results used by the author in the text. The book is more than an explanation of the physics of mechanics; it is also a textbook on elementary analysis in mathematics. With regard to the presentation, I found it somewhat anoying, particularly in the first chapters, when the author would refer ahead to a result which had not yet been discussed. I found the language somewhat pedantic in places, which may be more the fault of the translation than anything. Often the choice of words seemed to be intended to impress rather than enlighten. As one example I offer "elucubrations," which required the services of an unabridged dictionary to "translate." In summary, I believe that as a text Elements of Mechanics has significant shortcomings but would be a valuable reference work for every teacher of mechanics. S. Neil Rasband
Department of Physics and Astronomy Brigham Young University Provo, Utah 84602
Foundations of Physics, Vol. 16, No. 8, 1986
Book Review Theoretical Mechanics. By E. Neal Moore. John Wiley and Sons, New York, 1983, xv + 456 pp., $36.45 (cloth). It is stated on the jacket cover of this text that "the emphasis here is squarely on the solutions of physical problems," and indeed it is. Nonconservative forces, time-dependent constraint forces, the many-body problem, Lagrange points, the tippie top, the pitch, roll, and yaw of a satellite, limit cycles, precession of the equinoxes, nonlinear equations, and orbit s t a b i l i t ~ a l l are discussed clearly at the level appropriate for a senior or graduate course. This emphasis on problems does not displace the development of basic theory. In addition to the material that appears in every book on the subject, there are excellent presentations of Noether's theorem, of Gauss's principle of least constraint, of the Routh-Hurwitz stability criterion, together with a brief mention of the Gibbs-Appell function for the treatment of anholonomic constraints. Nonlinear equations are analyzed by the methods of Poincar6, and the discussion of Hamiltonian mechanics includes nonconservative forces. Linear collision theory assumes an interesting matrix formulation, which is applied to two gliders on an air track, repeatedly colliding elastically with each other and with the ends. It is shown how, for this problem, the collision matrices lead to Chebyshev polynomials of the second kind. The Appendices and parts of the main text form a short course in mathematical physics. Vector analysis in rectangular and curvilinear coordinates, Dirac delta functions (including three dimensions), determinants, matrices, complex variables, contour integration, tensor (including metric tensors and Christoffel symbols) groups, Lie algebras, and their application to mechanics are all clearly described in the last ninety pages. Actually, a Dirac delta function is introduced as early as page 9 of the text in order to determine the center of mass of three point masses, and to determine the moment of inertia about a symmetry axis of a wire bent into the form of a rectangle--an unusual approach, but one which takes some of the mystery out of 6(x-a). Similarly, complex variables and contour integration are 843
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used effectively in the text to apply the Fourier transform to an oscillating system that is driven by a nonperiodic force. The transition from the problem of coupled springs (using matrix theory) to the one-dimensional crystal (based on the theory of complex variables and dispersion relations) and on to continuous media (with Lagrangian density functions and partial differential equations) illustrates the use of a variety of the mathematical techniques that are described in the Appendix and applied to some related and progressively more complex physical situations. Professor Moore intentionally included much more material than could be covered in a one-term course, and if thc teaching schedule would allow it, this would be a good guide in some institutions for a whole year of instruction, although for that type of course other texts are available. As he notes in the preface, the book offers a choice--"there are those who prefer peach to chocolate or vanilla." The instructor can choose the areas that he/she wants to emphasize, according to personal taste and the nature of the class. Taste also plays an important role in discussing the merits of a book. There are few negatives about this particular one and we shall return to them, but there are also some presentations that make me feel uncomfortable, while possibly affecting others differently--a matter, perhaps, of "peach or chocolate." For example, I do not find dyadics a very useful type of analysis, and the description of rotations in terms of dyadics as presented is unnecessarily complicated--no mention of quaternions (so closely related to the Pauli matrices) but with detailed calculations in terms of the dyadic cumbersome notation (pages 151-156, 189-193). The chapter on relativity theory is fairly standard, with some fine examples, but (taste again!) I do not find the Brehme diagram very useful, although it is used extensively in this chapter, and I know that some of my students have found it to be confusing. However, the contracted description of the basic ideas of general relativity, including the Schwarzschild solution, is presented very clearly and the problems that follow the chapter are challenging for the student and are contemporary. For good reasons, the notation x 4 = i c t has been abandoned for a number of years, and most physicists prefer to avoid it by introducing the distinction between covariant and contravariant indices at the level of special relativity theory. The older notation is found only in older books (including two of mine), and the students will eventually have to "unlearn" it if they pursue the subject further. A few minor points: The analysis presented in every chapter is given in detail, including some simple algebra, even to the point of noting in one place that the relation sin20 + cos20 = 1 has been used in the preceding trigonometic algebra. That seems unnecessary for a text at the graduate or
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senior level. Also, I like to see "nonphysical" solutions explained--they often refer to another problem, and the study of them is usually valuable. On page 118 it is noted that the three masses of the restricted three-body problem "might be located in a plane, for example," and in one place a dependent variable is called "independent." Sometimes a substitution is pulled out of the blue (e.g., p. 246), whereas the student should be encouraged to find that substitution by making a general linear transformation and adjusting the parameters to reach the required goal of eliminating linear terms from the Lagrangian. To continue the minor negatives, there are too many "it is easily seen's, "not unexpected's, "wellknown's, etc. Finally, the only real negative criticism I have of this book is the notation. The printers at John Wiley and Sons are to be complimented on not being confused by the carets and primes and arrows and dots that appear over so many symbols--but some students will be. Why print arrows over vectors when boldface would suffice? I find symbols like tJ]c, )÷i, ~', kx = / ~ . . . unnecessarily clumsy. In summary, this is a fine book, clearly written, although it does not pursue all the details given, for example, in Goldstein's Classical Mechanics. It is hard to judge a text until one has taught from it, but for a one-term course this book contains an abundance of material, described, for the most part, very clearly. Herbert C. Corben Harvey Mudd College Claremon t, California 91711
