Space, Time, Matter (Dover Books on Physics)
by Hermann Weyl, Physics
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Book Summary Information
Author: Hermann Weyl, PhysicsEdition: Paperback
Audio: English (Unknown); English (Original Language); English (Published)
Published: 1952-06-01
ISBN: 0486602672
Number of pages: 368
Publisher: Dover Publications
Book Reviews of Space, Time, Matter (Dover Books on Physics)
Book Review: MASTERPIECE OF BEAUTY AND TRUTH
Summary: 5 Stars
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.
Summary of Space, Time, Matter (Dover Books on Physics)
"A classic of physics ... the first systematic presentation of Einstein's theory of relativity." ? British Journal for Philosophy and Science. Long one of the standard texts in the field, this excellent introduction probes deeply into Euclidean space, Riemann's space, Einstein's general relativity, gravitational waves and energy, and laws of conservation.
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