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Space, Time, Matter (Dover Books on Physics)

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This book bewitched several generations of physicists and students. Hermann Weyl was one of the very great mathematicians of this century. He was also a great physicist and an artist with ideas and words. In this book you will find, at a deep level, the philosophy, mathematics and physics of space-time. It appeared soon after Einstein's famous paper on General Relativity, and is, in fact, a magnificent exposition of it, or, rather, of a tentative generalization of it. The mathematical part is of the highest class, striving to put geometry to the forefront. Actually, the book introduced a far-reaching generalization of the theory of connections, with respect to the Levi-Civita theory. It was not a generalization for itself, but motivated by the dream (Einstein's) of including gravitation and electromagnetism in the same (geometrical) theory. The result was gauge theory, which, slightly modified and applied to quantum mechanics resulted in the theory which dominates prese! nt particle physics. Weyl's unified theory was proved wrong by Einstein, and his criticism alone, accepted by Weyl and included in the book, would justify the reading. Though wrong, Weyl's theory is so beautiful that Paul Dirac stated that nature could not afford neglecting such perfection, and that the theory was probably only misplaced. Prophetic words! The philosophic parts are, alas, too much for our present cultural level, but you can ignore them. The mathematical and physical parts are perfectly accessible and, of course, of the highest class. The pity is that the number of misprints is immense, particularly in the formulas, so that the reading is made much more difficult than it should. Also, the English edition is not the latest one. If you read German, choose the original, also available here.

Weyl's book is most famous for introducing gauge theory, which was later reborn in the form of phase transformations in quantum theory. Weyl did not live guite long enough to hear of the latter being applied by Yang and Mills, though he socially interacted with Yang in his last year at Princeton.

Einstein and Pauli both criticized Weyl's original unified theory based on general relativity using a length gauge, both as implying false empirical consequences (Einstein), since it implied tiny changes of length dependent on path and as untestable (Pauli). (Obviously it could not both be empirically false and non-empirical.) Yet Eddington and later Einstein himself revived similar theories. Eddington claimed that the length differences were to tiny as to be undetectable, but also that his own gauge theory could be thought of not as literal space/time structure but as a geometrization of an abstract background theory for specific space/time structures.

Thomas Ryckman's The Reign of Relativity: Philosophy in Physics 1915-1925 (Oxford Studies in the Philosophy of Science)has an excellent eighty page discussion of these ideas of Weyl in relativity, as well as chapters on those of Eddington in the 1920s.

Another novelty is Weyl's suggestion that General Relativity could be tied to observation via the conformal structure as representing light cones and the projective structure as particles in free fall. This alternative to the rods and clocks approach, on the basis of which Weyl was criticized, has been developed by Ehlers (who edited the new German edition of this work Raum, Zeit, Materie: Vorlesungen über allgemeine Relativitätstheorie (German Edition)) Pirani and Schild.

Weyl also introduces what he calls "tensor densities" which Shouten called "Weyl tensors" and Synge and Schild call oriented tensors, often called twisted tensors. These are analogous to and include "axial vectors."

Weyl's introduction of the "affine connection" after criticism of Levi-Civita's notion of parallelism led the way to further notions of connections and generalization of the notion of connection as such by Elie Cartan and others.

These are but a few of the intellectual gems in this work.

The philosophical parts are, unfortunately, almost uniformly mistranslated. The phenomenological introduction is re-translated in Kockelmans and Kisiel, eds. Phenomenology and the Natural Sciences (SPEP). (Courant suggested Weyl as successor to Husserl in the philosophy chair at Goettingen!) This together with the misprints in formulas, makes it desirable that the whole book be retranslated.

In 1918, Hermann Weyl developed a theory of the combined gravitational-electromagnetic field that was based on an early form of today's gauge formalism. This book neatly summarizes Weyl's motivations for what can be considered the first serious attempt at unified field theory. This attempt failed, but the gauge idea did not, and in 1929 Weyl transformed it into the gauge-invariant concept of quantum mechanics. Today, gauge invariance is arguably the most profound concept in modern quantum theory, and our understanding of the strong and weak nuclear interactions would not have been possible without it.

Weyl was first and foremost a mathematician, but he also proved to be a visionary theoretical physicist who was greatly admired by the likes of Einstein, Pauli, Dirac and Heisenberg. He was also a great human being who was involved with humanity. In spite of its great age, Space-Time-Matter has earned a place of distinction in the physics literature, if only because of Weyl's gauge idea. The Dover edition costs next to nothing; get it and enlighten yourself.

Not long after Einstein published his general theory of relativity one of the greatest mathematician of his time trumped it. Space-Time-Matter has been published by Dover press for a very long time. My copy was put out in the 5o's. I bought it used in the late 60's. I have never regretted buying it. It is difficult reading even when you know what he is talking about: when I got it , it read like Greek. It isn't an easy read, but he predicts a tenth planet in it that was never found! And lays the foundation of what later became gauge theory. He introduces group theory at a time when quantum groups were just beginning. His tensor discussion is very basic and he doesn't even introduce the Weyl tensor! But he taught me the basic metrical equations and the applications of non Euclidean geometry to relativity. Together with Weinberg's flawed Cosmology this book has been my teacher. I wish I could say he did a good job, but since it took me years to wade through it without falling asleep, I can't say he did!

This book is esoteric initiation into spacetime physics. Written with intellectual passion, full of powerful insights & alluring legions of equations- you will enjoy even by immersion in its spirit. Read it slowly and in awe: witness great ideas grow & collapse. Not a textbook, proven wrong in not few points, this is a mutable & profound vision of reality by one of the last universal mathematicians. If you want profit- look elsewhere.

To the publisher I would appreciate it if the publisher could produce an audio adaptation of this book. I would love to listen to this while I drive to work and to let my 16 month old son listen to it as a bedtime story. Arnold D Veness