## 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

Conception of wdimensional Geometry Linear Algebra Quadratic Forms 4 Foundations of Metrical Geometry | |

Tensors | |

Tensor Algebra Examples | |

Symmetrical Properties of Tensors | |

Tensor Analysis Stresses | |

CHAPTER II | |

Relativistic Geometry Kinematics and Optics | |

Electrodynamics of Moving Bodies | |

Mies Theory | |

CHAPTER IV | |

Relativity of Motion Metrical Field and Gravitation | |

Stationary Gravitational Field Relationship with Experience | |

Rigorous Solution of the Problem of One Body | |

Further Rigorous Solutions of the Statical Problem of Gravitation | |

Note on NonEuclidean Geometry 11 Riemanns Geometry | |

Riemanns Geometry continued Dynamical View of Metrics 13 Tensors and Tensordensities in an Arbitrary Manifold 14 Affinely Connected Manifo... | |

Curvature 16 Metrical Space 17 Remarks on the Special Case of Riemanns Space 18 Space Metrics from the Point of View of the Theory of Groups | |

RELATIVITY OF SPACE AND TIME | |

Galileis and Newtons Principle of Relativity | |

Energy of Gravitation Laws of Conservation | |

World Metrics as the Origin of Electromagnetic Phenomena | |

APPENDIX I | |

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according æther affine geometry affine relationship arbitrary assume bilinear body calibration co-efficients co-ordinate system conception condition congruent transformation constant contra-gredient contra-variant components corresponding curvature curve definite denote density derived determined differential form dimensional direction distance Einstein electric electron energy Euclidean geometry Euclidean space expressed force formula four-dimensional function fundamental geodetic gik’s given gravitational equations gravitational field hence independent inertia infinitely infinitely near points infinitesimal integral invariant linear form linear transformations manifold mass mathematical matter means measure mechanics metrical field metrical groundform metrical space metrical structure motion non-Euclidean geometry ordinate system parallel displacement plane point-mass positive potential principle of relativity quadratic differential quadratic form quantities respect result Riemann rotation scalar second order skew-symmetrical sphere statical straight line surface symmetrical symmetrical bilinear form tensor-density theorem theory of relativity translation vanish variables velocity vide note world-line world-points