Independent Axioms for Minkowski Space-Time
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.
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Existence and properties of collinear sets
Paths and optical lines in a collinear set
Theory of parallels
Standard model of Minkowski spacetime
3-SPRAY absolute geometry affine affine geometry affine space applies Axiom I5 Axiom O4 Axiom of Isotropy Axiom of Uniqueness axiomatic system bijection Causality Theorem classes of parallels closest event col[R Collinear Set Theorem Collinearity Theorem Th.7 compact collinear set completes the proof contains contradiction corresponding csp+(Q,S define definition distinct events distinct paths dyadic numbers equations Euclidean geometry event h Existence Theorem Th.14 Figure implies the existence independence model integer kinematic triangle Lemma Let Q lightlike limiting lines Lorentz boost Lorentz transformation Minkowski space-time Optical Line Theorem ordered geometry ordinary lines orthochronous orthogonal transformation parallel paths partial order partial order relation path Q paths which meet plane Poincare group preceding theorem previous theorem real number Reflection Mapping Second Collinearity Theorem Second Existence Theorem segment set of events set of paths space specified subset Theorem 13 theorem implies Third Collinearity Theorem Triangle Inequality unreachable set Veblen vectors whence
Non-Euclidean Geometries: János Bolyai Memorial Volume
János Bolyai,András Prékopa,Emil Molnár
No preview available - 2006