## Space, Time, MatterIn this classic text first published in German in 1918-this is a translation by HENRY L. BROSE (1890-1965) of the 1921 fourth edition-Weyl considers the role of Euclidean space in physics and the mathematics of Einstein's general theory of relativity, exploring: foundations of affine and metrical geometry conception of n-dimensional geometry tensor algebra the stationary electromagnetic field Riemann's geometry affinely connected manifolds space metrics from the point of view of the Theory of Groups relativistic geometry, kinematics, and optics electrodynamics of moving bodies mechanics of the principle of relativity mass and energy gravitational waves concerning the interconnection of the world as a whole and more.HERMANN KLAUS HUGO WEYL (1885-1955)was a German mathematician who spent most of his life working in Zurich, Switzerland. When the Nazi party began to gain power he fled to a job at the Institute of Advanced Study in Princeton, New Jersey where he continued to develop his representation theory. He was one of the most influential mathematicians of the 20th century. He greatly impacted theoretical physics and number theory and was the first to combine general relativity and electromagnetism |

### Contents

1 | |

2 | |

Conception of ndimensional Geometry Linear Algebra Quadratic Forms | 3 |

Foundations of Metrical Geometry | 4 |

Tensors | 5 |

Tensor Algebra Examples | 6 |

7 Symmetrical Properties of Tensors | 7 |

Tensor Analysis Stresses | 8 |

RELATIVITY OF SPACE AND TIME 19 Galileis and Newtons Principle of Relativity | 149 |

Electrodynamics of Varying Fields Lorentzs Theorem of Relativity | 160 |

Einsteins Principle of Relativity | 169 |

Relativistic Geometry Kinematics and Optics | 179 |

Electrodynamics of Moving Bodies | 188 |

Mechanics of the Principle of Relativity | 196 |

Mass and Energy | 200 |

Mies Theory | 206 |

The Stationary Electromagnetic Field | 9 |

Note on NonEuclidean Geometry | 10 |

Riemanns Geometry | 11 |

Riemanns Geometry continued Dynamical View of Metrics | 12 |

Tensors and Tensordensities in an Arbitrary Manifold | 13 |

Affinely Connected Manifolds | 14 |

Curvature | 15 |

Metrical Space | 16 |

Remarks on the Special Case of Riemanns Space | 17 |

Space Metrics from the Point of View of the Theory of Groups CHAPTER III | 18 |

11 | 29 |

27 | 46 |

33 | 51 |

43 | 54 |

Relativity of Motion Metrical Field and Gravitation | 218 |

Einsteins Fundamental Law of Gravitation | 229 |

Stationary Gravitational Field Relationship with Experience | 240 |

Gravitational Waves | 248 |

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

Energy of Gravitation Laws of Conservation | 268 |

World Metrics as the Origin of Electromagnetic Phenomena | 282 |

Application of the Simplest Principle of Action Fundamental | 295 |

BIBLIOGRAPHICAL REFERENCES | 319 |

196 | 321 |

325 | |

328 | |

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### Common terms and phrases

according ćther affine geometry arbitrary assume co-efficients co-ordinate system co-variant condition congruent transference const constant corresponding curvature definite denotes density derived determined differential form direction dx˛ Einstein Einstein's Theory electric electron energy Euclidean geometry Euclidean space expressed force formula four-dimensional function fundamental geodetic gik's gravitational equations gravitational field hence inertial infinitely near points infinitesimal integral invariant light-ray linear form manifold mass mathematical matter Maxwell's Maxwell's equations means measure mechanics metrical field metrical groundform metrical space metrical structure motion parallel displacement particle phase-quantities physical laws plane point-mass positive potential principle of relativity quadratic differential quadratic form quantities radius respect result Riemann rotation scalar second order sphere statical straight line surface symmetrical tensor tensor-density theorem theory of relativity transformation vanish variables variation vector velocity vide note world-line world-point дхі дхк