Synopses & Reviews
"The standard treatise on the general theory of relativity." —
Nature"Whatever the future may bring, Professor Weyl's book will remain a classic of physics." — British Journal for Philosophy and Science
Reflecting the revolution in scientific and philosophic thought which accompanied the Einstein relativity theories, Dr. Weyl has probed deeply into the notions of space, time, and matter. A rigorous examination of the state of our knowledge of the world following these developments is undertaken with this guiding principle: that although further scientific thought may take us far beyond our present conception of the world, we may never again return to the previous narrow and restricted scheme.
Although a degree of mathematical sophistication is presupposed, Dr. Weyl develops all the tensor calculus necessary to his exposition. He then proceeds to an analysis of the concept of Euclidean space and the spatial conceptions of Riemann. From this the nature of the amalgamation of space and time is derived. This leads to an exposition and examination of Einstein's general theory of relativity and the concomitant theory of gravitation. A detailed investigation follows devoted to gravitational waves, a rigorous solution of the problem of one body, laws of conservation, and the energy of gravitation. Dr. Weyl's introduction of the concept of tensor-density as a magnitude of quantity (contrasted with tensors which are considered to be magnitudes of intensity) is a major step toward a clearer understanding of the relationships among space, time, and matter.
Synopsis
Excellent introduction probes deeply into Euclidean space, Riemann's space, Einstein's general relativity, gravitational waves and energy, and laws of conservation. "A classic of physics." — British Journal for Philosophy and Science.
Synopsis
"The standard treatise on the general theory of relativity." -- Nature
"Whatever the future may bring, Professor Weyl's book will remain a classic of physics." -- British Journal for Philosophy and Science
Reflecting the revolution in scientific and philosophic thought which accompanied the Einstein relativity theories, Dr. Weyl has probed deeply into the notions of space, time, and matter. A rigorous examination of the state of our knowledge of the world following these developments is undertaken with this guiding principle: that although further scientific thought may take us far beyond our present conception of the world, we may never again return to the previous narrow and restricted scheme.
Although a degree of mathematical sophistication is presupposed, Dr. Weyl develops all the tensor calculus necessary to his exposition. He then proceeds to an analysis of the concept of Euclidean space and the spatial conceptions of Riemann. From this the nature of the amalgamation of space and time is derived. This leads to an exposition and examination of Einstein's general theory of relativity and the concomitant theory of gravitation. A detailed investigation follows devoted to gravitational waves, a rigorous solution of the problem of one body, laws of conservation, and the energy of gravitation. Dr. Weyl's introduction of the concept of tensor-density as a magnitude of quantity (contrasted with tensors which are considered to be magnitudes of intensity) is a major step toward a clearer understanding of the relationships among space, time, and matter.
Synopsis
Excellent introduction probes deeply into Euclidean space, Riemann's space, Einstein's general relativity, gravitational waves and energy, and laws of conservation. "A classic of physics." British Journal for Philosophy and Science.
About the Author
Along with his fundamental contributions to most branches of mathematics, Hermann Weyl (1885-1955) took a serious interest in theoretical physics. In addition to teaching in Zürich, Göttingen, and Princeton, Weyl worked with Einstein on relativity theory at the Institute for Advanced Studies.
Hermann Weyl: The Search for Beautiful Truths
One of the most influential mathematicians of the twentieth century, Hermann Weyl (1885-1955) was associated with three major institutions during his working years: the ETH Zurich (Swiss Federal Institute of Technology), the University of Gottingen, and the Institute for Advanced Study in Princeton. In the last decade of Weyl's life (he died in Princeton in 1955), Dover reprinted two of his major works, The Theory of Groups and Quantum Mechanics and Space, Time, Matter. Two others, The Continuum and The Concept of a Riemann Surface were added to the Dover list in recent years.
In the Author's Own Words:
"My work always tried to unite the truth with the beautiful, but when I had to choose one or the other, I usually chose the beautiful."
"We are not very pleased when we are forced to accept mathematical truth by virtue of a complicated chain of formal conclusions and computations, which we traverse blindly, link by link, feeling our way by touch. We want first an overview of the aim and of the road; we want to understand the idea of the proof, the deeper context."
"A modern mathematical proof is not very different from a modern machine, or a modern test setup: the simple fundamental principles are hidden and almost invisible under a mass of technical details." — Hermann Weyl
Critical Acclaim for Space, Time, Matter:
"A classic of physics . . . the first systematic presentation of Einstein's theory of relativity." — British Journal for Philosophy and Science
Table of Contents
INTRODUCTION
CHAPTER I EUCLIDEAN SPACE. ITS MATHEMATICAL FORM AND ITS RÔLE IN PHYSICS.
§ 1. Derivation of the Elementary Conceptions of Space from that of Equality
§ 2. Foundations of Affine Geometry
§ 3. "Conception of n-dimensional Geometry, Linear Algebra, Quadratic Forms"
§ 4. Foundations of Metrical Geometry
§ 5. Tensors
§ 6. Tensor Algebra. Examples
§ 7. Symmetrical Properties of Tensors
§ 8. Tensor Analysis. Stresses
§ 9. The Stationary Electromagnetic Field
CHAPTER II THE METRICAL CONTINUUM
§ 10. Note on Non-Euclidean Geometry
§ 11. Riemann's Geometry
§ 12. Riemann's Geometry (continued). Dynamical View of Metrics
§ 13. Tensors and Tensor-densities in an Arbitrary Manifolds
§ 14. Affinely Connected Manifolds
§ 15. Curvature
§ 16. Metrical Space
§ 17. Remarks on the Special Case of Riemann's Space
§ 18. Space Metrics from the Point of View of the Theory of Groups
CHAPTER III RELATIVITY OF SPACE AND TIME
§ 19. Galilei's and Newton's Principle of Relativity
§ 20. Electrodynamics of Varying Fields. Lorentz's Theorem of Relativity
§ 21. Einstein's Principle of Relativity
§ 22. "Relativistic Geometry, Kinematics, and Optics"
§ 23. Electrodynamics of Moving Bodies
§ 24. Mechanics of the Principle of Relativity
§ 25. Mass and Energy
§ 26. Mie's Theory
Concluding Remarks
§ 27. "Relativity of Motion, Metrical Field, and Gravitation"
§ 28. Einstein's Fundamental Law of Gravitation
§ 29. Stationary Gravitational Field. Relationship with Experience
§ 30. Gravitational Waves
§ 31. Rigorous Solution of the Problem of One Body
§ 32. Further Rigorous Solutions of the Statical Problem of Gravitation
§ 33. Energy of Gravitation. Laws of Conservation
§ 34. Concerning the Inter-connection of the World as a Whole
§ 35. Word Metrics as the Origin of Electromagnetic Phenomena
§ 36. Application of the Simplest Principle of Action
Fundamental Equations of Mechanics
APPENDIX I
APPENDIX II
BIBLIOGRAPHICAL REFERENCES
INDEX