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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Primitive notions and axioms
Temporal order on a path
Collinearity and temporal order
Existence and properties of collinear sets
Paths and optical lines in a collinear set
Theory of parallels
Standard model of Minkowski spacetime
affine applies Axiom axiomatic system belong bijection bounded called Chapter classes of parallels closest collinear set Collinearity Theorem completes concept consequence consider contains Continuity contradiction convergent coordinate system corresponding cross define definition denoted described direction discussed distinct events distinct paths divergent equations establish Euclidean Existence Theorem Figure follows geometry given implies the existence indexed induced inequality integer interval invariant isomorphism isotropy mappings kinematic triangle Lemma linear meets Minkowski space-time obtain optical line order relation orthochronous pair parallels path Q paths which meet plane points positive previous theorem proof properties rapidity record functions reflection Remark respectively result satisfied Second segment set of events set of paths side signal functions similar space specified statement subset symbols Theorem 13 Third translation Uniqueness unreachable set Veblen whence
Non-Euclidean Geometries: János Bolyai Memorial Volume
János Bolyai,András Prékopa,Emil Molnár
No preview available - 2006