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The Riddle of Gravitation: Revised and Updated Edition Paperback – January 5, 1993
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" All will be rewarded, the reading is fast, stimulating and entertaining...and, experts will read it, partly out of
personal curiosity and partly in search of pedagogical innovations."
This, a nontechnical survey of Gravitation--that is, General Relativity--is as fresh today as when first published, 1968.
Peter Bergmann, colleague of Albert Einstein (from 1936 to 1941) has a flair for making the abstract more concrete.
Aptly enough, his survey begins with historical antecedents. That is, from Newton to Maxwell on the way to Special Relativity. Obviously, an excursion well worth the effort:
(1) Bergmann enunciates, with clarity, concepts such as position, velocity, acceleration--that is, kinematics.
We read: " The universality of the speed of light in vacuum imposes on the relationship between any two events a characteristic that must be independent of the inertial frame of reference in which the time interval between them, and the distance between them,are measured." Also, "Minkowski's approach is useful because it suggests the need to search for concepts that are natural in four-dimensional space-time and independent of any decomposition into separate space and time." (Page 47).
(2) " Relativity was born of Electromagnetic Theory," that begins the excellent chapter six: elucidation of mass, energy, momentum--that is, dynamics. Following which, Curvature. Then, General Relativity--of course ! We reading:
"Einstein came to recognize that the concept of the infinitely extensible inertial frame of reference might have to be abandoned in favor of the local freely-falling frame of reference; only by taking this step would the principle of equivalence be made part of the foundations of Physics." (Page 88).
(3) Covariance, Curved Space-Time (notice the hyphen !), Schwarzschild, Event Horizons, Collapse and Radiation:
these given due consideration, one after the other. "Gravitational Waves are Polarized." Bergmann subsequently discusses a simple means of estimating power and energy loss in such waves. Cosmology is given qualitative consideration, followed by a thoughtful segue to the quantum entitled: What is an Observable?...." such mathematical expressions will then play the role of observables in the theory of gravitation."
(4) The Appendices are pearls: Kepler's Laws, Derivation of Inverse-Square, Lorentz Transformation derived,
Schwarzschild Radius and Gravitational Radiation touched upon-- in elementary terms.
Nothing in the appendices need be beyond reach given preparation in elementary algebra.
A Glossary of terminology concludes the book. This is an excellent semi-popular book, it can well-serve as preliminary
to Bergmann's (advanced) 1946 textbook of Relativity.
Peter Bergmann's Riddle Of Gravitation predates other excellent semi-technical tomes:
1970, Synge: Talking About Relativity,
1977, Wald: Space, Time And Gravity,
1978, Geroch: General Relativity From A To B,
1988, Ellis: Flat And Curved Space-Times,
All are highly recommended for explication of many a facet of gravitation.