Space, Time, Matter

The book teaches a way to study relativity not as an intellectual jump from Newton to Einstein, but by a method of "analytical continuation" after the concept of "measurement" is cleaned up. One needs to be a little careful about some of the words such as Force. The use is correct but over time, the phrases are changed and we would say the same things differently. It can be confusing at times. I needed to re-read a few times to see things clearly enough to go on. I noticed one good omen. I think the book has the author's signature in it (?). If I am right, I never said it and I do not have it. I know nothing!! Even though old, the book became very useful to me in learning the subject. Thanks

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) 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.

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

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.