Independent Axioms for Minkowski Space-TimeCRC Press, 8 окт. 1997 г. - Всего страниц: 256 The primary aim of this monograph is to clarify the undefined primitive concepts and the axioms which form the basis of Einstein's theory of special relativity. Minkowski space-time is developed from a set of independent axioms, stated in terms of a single relation of betweenness. It is shown that all models are isomorphic to the usual coordinate model, and the axioms are consistent relative to the reals. |
Содержание
| 9 | |
| 9 | |
| 17 | |
| 30 | |
| 53 | |
| 78 | |
| 80 | |
Theory of parallels | 113 |
21 | 174 |
Standard model of Minkowski spacetime | 179 |
Independence models | 194 |
Veblens axioms for an ordered geometry | 212 |
Alternative axiom systems | 215 |
Open questions | 222 |
Notes to the chapters | 225 |
12225 | 231 |
20 | 135 |
Onedimensional kinematics | 144 |
Threedimensional theorems | 154 |
References | 233 |
Index | 240 |
Часто встречающиеся слова и выражения
3-SPRAY absolute geometry affine affine space applies Axiom 06 Axiom 15 Axiom of Isotropy axiomatic system bijection classes of parallels closest event col[Q col[R Collinear Set Theorem collinear sub-SPRAY compact collinear set contains contradiction coordinate system corresponding define definition distinct events distinct paths dyadic numbers equations Euclidean geometry Existence Theorem Figure implies the existence independence model integer isomorphism kinematic triangle Lemma Let Q lightlike limiting lines Lorentz boost Lorentz transformation Minkowski space-time Optical Line Theorem ordered geometry ordinary lines orthochronous parallel paths path Q paths which meet plane Poincaré group Poincaré transformation preceding theorem previous theorem properties real number record functions Reflection Mapping satisfied Second Collinearity Theorem Second Existence Theorem set of events set of paths space specified subset Theorem 13 theorem implies Third Collinearity Theorem Triangle Inequality unreachable set Veblen vectors whence
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Стр. 9 - I think that wherever, from the side of the theory of knowledge or in geometry, or from the theories of natural or physical science, mathematical ideas come up, the problem arises for mathematical science to investigate the principles underlying these ideas and so to establish them upon a simple and complete system of axioms, that the exactness of the new ideas and their applicability to deduction shall be in no respect inferior to those of the old arithmetical concepts.
Стр. 9 - Mathematical Treatment of the Axioms of Physics The investigations on the foundations of geometry suggest the problem: To treat in the same manner. by means of axioms. those physical sciences in which mathematics plays an important part; in the first rank are the theory of probabilities and mechanics.
Стр. 212 - A,B,C are in the order | ABC \ they are distinct. II. If points A, B, C are in the order \ABC\ they are not in the order \BCA\. Definition. If A and B are distinct points the. segment AB consists of all points, X, in the order \AXB...
Стр. 212 - AB (A±B) consists of A and B, and of all points X in one of the possible orders ABX, AXB, XAB. The points X in the order AXB constitute the 'segment
Стр. 212 - If the points A, B, C are in the order ABC, they are not in the order BCA. IV. If the points A, B, C are in the order ABC, then A is distinct from C. V.
Стр. 235 - On the Structure of Causal Spaces', Proceedings of the Cambridge Philosophical Society 63 (1967), 481-501.
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