## Space, Time, Matter"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 ScienceReflecting 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. |

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### Inhalt

INTRODUCTION | 1 |

EUCLIDEAN SPACE ITS MATHEMATICAL FORM AND ITS RÔLE IN PHYSICS | 11 |

Foundations of Affine Geometry | 17 |

Conception of ndimensional Geometry Linear Algebra Quadratic | 23 |

Tensors | 33 |

Tensor Algebra Examples | 43 |

Symmetrical Properties of Tensors | 54 |

9 The Stationary Electromagnetic Field | 64 |

Einsteins Principle of Relativity | 169 |

Relativistic Geometry Kinematics and Optics | 179 |

Electrodynamics of Moving Bodies | 188 |

24 Mechanics of the Principle of Relati | 196 |

26 Mies Theory | 206 |

Relativity of Motion Metrical Field and Gravitation | 218 |

Stationary Gravitational Field Relationship with Experience | 240 |

Gravitational Waves | 248 |

CHAPTER II | 77 |

11 Riemanns Geometry | 91 |

Curvature | 117 |

Remarks on the Special Case of Riemanns Space | 129 |

Space Metrics from the Point of View of the Theory of Groups | 138 |

CHAPTER III | 149 |

Electrodynamics of Varying Fields Lorentzs Theorem of Relativity | 160 |

Energy of Gravitation Laws of Conservation | 268 |

Application of the Simplest Principle of Action Fundamental | 295 |

APPENDIX I | 313 |

BIBLIOGRAPHICAL REFERENCES | 319 |

325 | |

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