Introduction to the Theory of Relativity (Dover Books on Physics) by Peter G. Bergmann (PDF)

Description

Comprehensive coverage of special theory (frames of reference, Lorentz transformation, more), general theory (principle of equivalence, more) and unified theory (Weyl’s gauge-invariant geometry, more.) Foreword by Albert Einstein.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐excellent.

⭐I thought it was ok but by far not as great as I had be led (by a friend) to believe. Of course, it’s rather old.

⭐Physicist Steven Weinberg: “For a long time it was the book everyone read when they were studying General Relativity.” (New York Times, 2002) Published in 1942, reprinted in 1976 (Dover). Bergmann is relevant. Why ?Bergmann’s book may have been my first technical exposure to relativity, 1979. My copy was acquired that year. At the time (in high-school) I was incapable of fathoming the subtleties which it has to offer. Happily, with time, my preparation changed. Careful reading of this textbook will be repaid many times over (obviously, part three, Unified Field Theory, is suspect.) Let us read:(1) The initial chapter sets the scene: coordinates, reference frames, rotations (offering a summary ). A rapid-fire survey of classical mechanics, stressing Galilean transformations. The fun begins in chapter three, development utilizing propagation of light. Keep in mind, up to this point, only algebra and simple calculus has been utilized (see page 50 for notation). All remains at introductory vantage.(2) Lorentz transformations given now-standard treatment (twenty pages): “it is impossible to devise an experiment by means of which simultaneity would be defined independently of a frame of reference.” Clarity of exposition kept to the fore. After four chapters, the student is introduced to vectors and tensors. This chapter will be the most challenging. Pay attention, work out each line of each derivation, then the text is within comprehension. Nice that Bergmann retains factors of “c” (speed-of-light) in his Lorentz metric (pages 76 and 77, utilizing signature -2). After this mathematical chapter, Peter Bergmann returns to physics:(3) Mass points, conservation laws, Lagrangians, concluding with “World-Force” defined as “change of momentum with respect to proper time.” Pay particular attention to these sections, page 97 to page 104 ! Then, relativistic electrodynamics providing for a discussion of physical significance of the transformation laws. It also assists one in an explicit mathematical development and serves as preamble to mechanics of continuous media.(4) Chapter nine, applications of special relativity, completes part one. This is a fine chapter which ties together all of the pieces of the puzzle and exposes connections to Bohr-Sommerfeld quantization and De Broglie waves.(5) A thorough discussion of the Principle of Equivalence: “the metric tensor itself becomes part of the field, the metric components are the potentials of the gravitational field” (page 160) following which, mathematics: curvature tensor. Read: “A physical law, such as the equations of the gravitational field, can not be derived by purely logical processes” and “It is important to examine why in one field theory (gravitation) the equations of motion follow from the field equations, and why in another field theory (Maxwell’s theory) they do not” (pages 178 and 240, respectively ). Discussion follows. Nothing will have to be relearned from the standpoint of being modern. One will not meet differential forms or coordinate-free notation, but, the material presented is easily transcribed into modern dress. Finally, one is prepared to tackle the field equations of General Relativity. Bergmann writes with profundity and lucidity. This chapter, written so many years ago, remains fresh and needs little alteration when held up to the light of present day research. With that behind us, we look to:(6) Rigorous solutions (primarily Schwarzschild and Symmetry) following which experimental tests: perihelion advance of Mercury (explicit derivation done almost painlessly), deflection of light and spectral lines. Obviously, this chapter (experimental tests) is the out of date. That can be remedied by perusal of the current literature. Next, equations of motion: first qualitatively (nicely done) then, quantitatively (will need to be supplemented by more modern expositions). The final chapters (gauge invariance, Kaluza-Klein) can be studied at one’s leisure. One loses nothing by ignoring them, although, I would suggest a cursory look, simply for fun !(7) The Dover edition contains supplementary notes: “brief notes that deal with recent progress” (circa 1975).Problems (end-of-chapter) are few in number: some simple, a few are more involved. A tour of this book I have offered. Being one of the older expositions, it will need to be supplemented with a modern textbook. Still, this textbook offers a viewpoint of another time, offered through the lens of an early practitioner.Close attention paid to Bergmann’s words will remain in good stead for the student of Relativity.Recommended to all with an interest in these matters.

⭐good and comprehensive. could have more expanded attention to writing for less mathematically ‘skilled’ audience. ray smith. liked the book.

⭐This book describes the foundations of relativity in a clear and concise way. The development of tensor analysis is especially clear. It is great for anyone who has studied calculus, differential equations, and classical physics. I highly recommend it.

⭐Peter was able to give examples which made the complex easier to understand. The edges of the first sections in a copy in the Caltech library were black from use. I was privileged to be a guinea pig for the first edition.

⭐Although meant to be an introduction to Relativity, this book is hard to read right from the start. The formalism used throughout the entire book makes it hard for you to gain the courage to try to master Relativity in a technical depth.It lacks a light introduction to the basic concepts of Relativity (without math), to use as the foundation from which to build the rest of the book. Not the best way for someone to start on Relativity…

⭐A good book that covers both theories.

⭐If anyone wants to start learning relativity, this book is perfect. It has complex mathematics which really stimulates the mind but isn’t filled full of equations. Very succinct deacriptions and mind blowing! I loved this book being my first introduction to relativity

⭐A nice book. It was written quite some time ago, so student should complement reading this book with some other “modern” book.

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