Customer Reviews

Essential Relativity: Special, General, and Cosmological (Theoretical and Mathematical Physics)

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As a modern textbook in the theory of relativity, this book is rare, in that its goal is to give the reader a conceptual introduction to the theory, and not just mathematical formalism. The author also does not hesitate to include some philosophical argumentation wherever needed. It is written for the advanced undergraduate, and will prepare such a reader for more advanced reading in the subject.

The first chapter of the book is the best, for it is a comprehensive discussion of the origins of the theory of relativity as one that rejected the assertion that space and time were absolute. The author also gives an interesting historical discussion of Lorentz's ether theory, wherein Lorentz hypothesized that bodies moving through the ether undergo a contraction, and he discovered a time transformation that implied that clocks moving through the ether run slow. As the author points out, Lorentz thought such considerations were purely mathematical, and not important physically. In addition, in the section on Mach's principle, the author discusses briefly the work of Dennis Sciama who showed that the 1872 gravitational theory of F. Tisserand included Mach's principle. I was not aware of this work, and it motivated me to do further reading on the subject. The author also gives several examples to show that Mach's principle is not physically vacuous, but has observational consequences.

Chapter two overviews the kinematic consequences of the special theory of relativity. The most interesting part of this discussion was the section on the formulation of special relativity without assuming the invariance of the speed of light. The author shows that the principle of relativity implies that either all inertial frames are related by Galilean transformations, or all are related by Lorentz transformations with the same (postive) velocity (squared).

A discussion of optical effects follows in chapter 3. One unexpected and interesting result in this chapter is that a moving sphere has a circular outline to all observers because of length contraction.

Some of the mathematical formalism needed in special relativity is overviewed in chapter four. The class of four-vectors and four-tensors is defined, and the light cone geometry discussed in detail.

The relativistic mechanics of point particles is covered in chapter five. Such a theory is cast in the language of four-vectors, and the author explains nicely the mass-energy equivalence, analyzes scattering from a relativistic standpoint in the center of momentum frame, and shows how Newtonian mechanics is altered in the relativistic realm. He also spends a little time on relativistic continuum mechanics, via the energy tensor of the simplest continua: dust.

The connection between relativity and electrodynamics is outlined in chapter six. The material is standard and found in most books on relativity.

The author begins the study of general relativity in chapter seven with some elementary considerations of the differential geometry of curved surfaces and also Riemannian spaces. The author endeavors, rightfully, to explain the mathematics in a way that is intuitive as possible, rather than hitting the reader with highly abstract formalism.

He then presents the mathematica foundations of general relativity in chapter eight. After a brief review of tensor calculus, the author considers the gravitational field equations in a vacuum, emphasizing their nonlinearity. This is followed by a detailed discussion of the famous Schwarzschild solution. In addition, he considers a particular exact solution of the Einstein field equations in a vacuum, namely a plane-fronted gravitational wave. Although not physical, this solution illustrates some important properties of general gravitational radiation.

The author ends the book with a fairly detailed overview of cosmology. The difficulties in the pre-relativistic cosmology are discussed, one of the more interesting being the consideration of the Newtonian gravitational field inside a cavity resulting from the removal of a finite sphere from a static universe. Recognizing that Poisson's equation does not have a constant solution led to the alteration of the Newtonian potential and thus a modification of the Poisson equation. As the author observes, this move to get a static Newtonian universe is formally the same as what Einstein did via the introduction of the cosmological constant in his field equations (also to get a static universe). The author also considers the Robertson-Walker, Milne, and Friedman universe, and compares these to what is known observationally.

Although not the most comprehesive text on the subject (see Thorne's tome, Gravitation), Essential Relativity is perhaps the most fulfilling book from which to learn both special and general relativity on a graduate school level. Flipping through the pages, one cannot help but notice that it often reads like a novel. For the student or the adventurous, a wide variety of problems are found in an appendix. The author's background in differential geometry is very evident in his excellent explanations of difficult concepts.

This is a wonderful book, very amusing and thought provoking. Without trying to be comprehensive, it sheds much light on the basics of the theory, as well as of the mathematics. His discussion of Mach's principle is brilliant, and ends with a proposal of an experiment to test it with satellites! Very good at computations too, boasting tables for computing the curvature tensor from the metric tensor which are very useful.

This is a good book to learn the basic concepts behind relativity beyond the popular science books. It is a mid-level text aimed at an audience familiar with mathematics/physics but less inclined to go through something more comprehensive like Weinberg. Its value is largely in its discussion rather than rigorous derivations and proofs. In fact, it is quite lacking in the mathematical discussion (results occasionally show up with little introduction or explanation). What popular science tries to convey via hand waving and the advanced texts ignore (due to their "philosophical rather than scientific relevance"), this book attempts to correctly explain. Examples would be discussions regarding inertial frames, Mach's principle, and the general physical/philosophical/practical implications of seemingly "benign" results.

I would not recommend this book to learn general relativity (as opposed to special relativity), however. It glosses over several mathematical preliminaries, especially those of tensor calculus. Once the concepts and strategies are understood, the best way to learn general relativity is directly via tensor calculus. Lawden's concise book in this case (Introduction to Tensor Calculus, Relativity and Cosmology) is undoubtedly one of the best investments to make in this regard. Otherwise, Weinberg is, as mentioned previously, the veritable bible of relativity and related cosmology but is not definitely not something to read sitting in front of the fireplace.

Also be warned, the hardcover copy is of quite poor quality. The pages seem low grade recycled (nothing wrong with that though) and the print is blurry (not crisp).