## Axiomatization of the Theory of Relativity |

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### Contents

The logical status of the axioms | 3 |

The logical status of the definitions | 7 |

Provisional remarks concerning the results of the axiomatization | 13 |

Coincidence | 16 |

SPECIAL THEORY OF RELATIVITY | 23 |

The Axioms and the Construction of the Metric 5 The concepts of real point and signal | 25 |

Axioms of time order | 28 |

Axioms of the comparison of time | 31 |

Definition of simultaneity by means of a velocity less than that of light | 128 |

Consistency minimal character and independ ence of the axioms | 129 |

GENERAL THEORY OF RELATIVITY | 131 |

The Axioms and the Construction of the Metric 30 Preliminary mathematical remarks concerning the metric in infinitesimal regions | 133 |

The conservation transformations in infinitesimal regions | 136 |

Content of the general theory | 141 |

The spacetime axioms of the general theory | 142 |

The validity of axiom X1 1 | 144 |

Spatial neighborhood and the comparison of neighboring clocks | 40 |

Fermats axiom | 42 |

Axiom of stationarity | 43 |

The roundtrip axiom | 49 |

The spacemetrical light axiom | 51 |

Proof of the uniqueness of definition 12 of the relative rest of real points | 54 |

Uniformly moving systems | 66 |

The Lorentz transformation | 71 |

The state of motion of inertial systems | 76 |

Summary of the requirements contained in the Lorentz transformation | 83 |

Material metrical objects | 86 |

The matter axioms | 88 |

Critical Considerations 20 The experimental confirmation of the axioms | 92 |

Remark on the principle of the constancy of the velocity of light | 94 |

Absolute time | 96 |

Absolute transport time | 97 |

The transverse Doppler effect | 108 |

Absolute signal time | 113 |

Unreal signals | 117 |

Two more attempts at a definition of absolute time | 123 |

The validity of axiom X1 2 | 145 |

Light geometry in a gravitational field | 151 |

The characteristic length of a unitmeasuring rod | 155 |

The construction of the metric in the general case | 157 |

Integral Properties 39 The problem | 160 |

Static fields | 161 |

A time definition whose unit is transportable | 167 |

Red shift deflection of light perihelion of Mercury | 168 |

Stationary fields | 170 |

The rotating circular disk | 172 |

Stationary fields Continuation | 178 |

Real systems | 179 |

The validity of axioms I and II in real systems | 185 |

The most general admissible systems | 192 |

List of Axioms | 197 |

List of Definitions | 199 |

List of Theorems | 201 |

Reference Notes | 202 |

205 | |

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### Common terms and phrases

absolute signal according to axiom according to definition arbitrary arrival assertion assumption axiom IV axiom VIII axiomatization causal chains circular disk concept constant construction contradiction coordinate system coordinative definition defined definition of simultaneity derived direct signal editor's reference notes Einstein's empirical epistemological equal equations Euclidean exists Fermat's principle finite gravitational field Hans Reichenbach holds inertial system infinitesimal interval length light axioms light geometry light ray light signals linear transformation Lorentz transformation matter axioms means measuring rods metrical determination natural clocks objective coincidences obtained orthogonal system path philosophical Philosophy of Space physical possible PP'P presupposes principle proof properties quadratic form real points real system relations relativistic requirement rest result rigid rod rotating satisfied signal chain singularities space-time special theory static field synchronism temporal theorem theory of relativity tion topological transition transverse Doppler effect uniform unique validity of axioms vanish velocity of light