Relativity and Geometry (Dover Books on Mathematics) (Paperback)

by Roberto Torretti (Author)

Editorial Reviews

Product Description
High-level study discusses Newtonian principles and 19th-century views on electrodynamics and the aether, covers Einstein’s electrodynamics of moving bodies, Minkowski geometry and other topics. A rich exposition of the elements of the Special and General Theory of Relativity.

Product Details

• Paperback: 416 pages
• Publisher: Dover Publications (April 2, 1996)
• Language: English
• ISBN-10: 0486690466
• ISBN-13: 978-0486690469
• Product Dimensions: 9.1 x 6.1 x 0.9 inches
• Shipping Weight: 1.2 pounds (View shipping rates and policies)
• Average Customer Review: 4.5 out of 5 stars See all reviews (2 customer reviews)
• Amazon.com Sales Rank: #245,703 in Books (See Bestsellers in Books)

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Customer Reviews

Most Helpful Customer Reviews

11 of 11 people found the following review helpful:

5.0 out of 5 stars A Superb Overview Of Relativity, July 21, 2004

By	Mike Birman (Brooklyn, New York USA) - See all my reviews (TOP 500 REVIEWER)

Many years ago I took a course on Kant's Critique of Pure Reason with Robert Paul Woolf, a renowned Kantian. I loved the course. Here was a Philosopher not given to inscrutable mush about nothing (Hegel, for example). Kant's early work was Scientific and he was interested in all things epistemological: what we know, how we know it and is that knowledge valid? The Critique represents the apex of his "Copernican Revolution", in which he was forcibly awakened from "Dogmatic Slumber" by Hume's Treatise of Human Nature. Kant's Critique is a difficult read. He was inventing a new language for describing cognition and the processing of data presented to us by the Space-Time Manifold. His use of the word Manifold in this context is prescient. Kant also asked whether inferences extracted from that Manifold, and the chain of deductions inevitably attached to those inferences, held validity. These are the synthetic a priori judgements : non-tautological (in which the predicate of a sentence is not semantically contained in the subject-term) judgements held independently of sense experience. Since mathematical truths (and the sciences whose truths are written in mathematics) are dependent upon such judgements, Hume's fierce attack on our notion of causality essentially forced Kant to verify the possiblity of Mathematics and Science.

Roberto Torretti's book is a wonderfully deep study of Relativity. He offers what he calls a "historico-critical" exposition in the spirit of Mach. His emphasis is on geometrical ideas but it is emblematic of the richness of this study that it begins with Kant and his analysis of geometry (as part of the structure of our minds) as a paradigm of our a priori knowlege of nature. Torretti returns to Kant throughout the book (as well as Philosophers like Reichenbach and Cassirer) because it is Einstein's dismantling of Kant's notion of geometry as well as the innate Categories of Time and Space that is the true revolution begun in 1905.

But Philosophy is merely the background upon which events play out. For Torretti provides a clear, precise and well-documented analysis of the rise of Newtonian physics, the development of 19th Century electrodynamics and ideas about the aether, growth of non-Euclidean geometry and the experimental crisis at the end of the century. Einstein's electrodynamics, Minkowski spacetime and Einstein's revolutionary gravitational theory ease us into the 20th. All important concepts are discussed: simultaneity, causality, time, space, the nature of mass and motion. The very fabric of reality is what is at stake so the field of discussion is wide.

An Appendix provides a splendid discussion of differentiable manifolds, fiber bundles, linear connections and various other topics. 85 pages of detailed notes at the end of the book are informative. The mathematics in this book are non-trivial. Maturity is assumed. You will not, however, see vast fields of tensor indices. You can refer to older volumes if you miss them. This book was originally published in 1983 and the geometric approach to Relativity holds sway. I found the discussion of various geometries to be endlessly fascinating, and there ARE many geometries mentioned here. For example, the chapter on Minkowski spacetime has an in-depth analysis of the Zeeman topology (1967) proposed by Zeeman as a substitute for the Minkowski geometry. Tensors are handled with relative delicacy (you knew there had to be some). The chapter on gravitational geometry is the densest mathematically, beginning with Ricci tensors, leading to Cartan's geometric reformulation of Newton's theory of gravity using bundles (enabling him to point out to Einstein that spacetime has a flat non-symmetric linear connection when essentially void of matter. This is Einstein's final theory in essence). A. Friedmann's brilliant analysis in 1922 of Einstein's field equations pointing out the possibility of infinite solutions, any of which might entail the expansion or collapse (the solutions are indifferent to time reversal) of the galaxies is discussed here as well as Lie groups. I found this chapter the most difficult and re-read it several times.

This is a book for physicists, mathematicians and philosophers of science with a strong background. It is not beyond the reach of the intelligent, motivated layman. This is a fascinating study even for old hands. I recommend it unreservedly.

5 of 8 people found the following review helpful:

4.0 out of 5 stars Moderate writing with good information., May 1, 2000

By A Customer

Although there were a few bumps in the road, this book tended to convey the main ideas without getting too technical and too pedestrian. In short, it is a good summary of the basic principles of relativity and how they apply to geometrical situations.