## 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 |

CHAPTER I | 6 |

EccLIDEAN SPACE Its MATHEMATICAL FoRM AND ITs RôLE IN PHYsics 1 Derivation of the Elementary Conceptions of Space from that of E... | 11 |

2 Foundations of Affine Geometry | 16 |

Conception of ndimensional Geometry Linear Algebra Quadratic Forms i | 23 |

4 Foundations of Metrical Geometry | 27 |

5 Tensors | 33 |

6 Tensor Algebra Examples | 43 |

21 Einsteins Principle of Relativity | 169 |

22 Relativistic Geometry Kinematics and Optics | 179 |

23 Electrodynamics of Moving Bodies | 188 |

24 Mechanics of the Principle of Relativity | 196 |

25 Mass and Energy | 200 |

26 Mies Theory | 206 |

Concluding Remarks | 217 |

27 Relativity of Motion Metrical Field and Gravitation | 218 |

7 Symmetrical Properties of Tensors | 55 |

8 Tensor Analysis Stresses | 58 |

THE METRICAL CoNTINUUM 10 Note on NonEuclidean Geometry | 77 |

11 Riemanns Geometry | 91 |

12 Riemanns Geometry continued Dynamical View of Metrics 13 Tensors and Tensordensities in an Arbitrary Manifold 14 Affinely Connected Ma... | 102 |

15 Curvature | 117 |

16 Metrical Space | 121 |

17 Remarks on the Special Case of Riemanns Space | 129 |

18 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 |

28 Einsteins Fundamental Law of Gravitation | 229 |

29 Stationary Gravitational Field Relationship with Experience | 240 |

30 Gravitational Waves | 248 |

32 Further Rigorous Solutions of the Statical Problem of Gravitation | 259 |

33 Energy of Gravitation Laws of Conservation | 268 |

35 World Metrics as the Origin of Electromagnetic Phenomena | 282 |

36 Application of the Simplest Principle of Action Fundamental | 295 |

BIBLIoGRAPHICAL REFERENCEs | 319 |

325 | |

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