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Space, Time, Matter
ISBN-13:
9780486318424
Veröffentl:
2013
Einband:
EPUB
Seiten:
368
Autor:
Hermann Weyl
Serie:
Dover Books on Physics
eBook Typ:
EPUB
eBook Format:
Reflowable EPUB
Kopierschutz:
Adobe DRM [Hard-DRM]
Sprache:
Englisch
Beschreibung:
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.
"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.
"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.
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
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