2011/01/28 by John F. Barrett, Barrett, John F · 2 citations
Mathematics · Physics and Astronomy · #FOS: Physical sciences #General Physics (physics.gen-ph) #History and Theory of Mathematics #Mathematics and Applications #Relativity and Gravitational Theory
paper · pdf · doi:10.48550/arxiv.1102.0462
openalex publication_date 2011/01/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The book is based largely on the author's researches presented at conferences in the period 1992 onwards. It is a historically based exposition and an extension of the hyperbolic version of special relativity first proposed by Varićak (1910 etc) and others not long after the appearance of the early papers of Einstein and Minkowski. The book's approach puts emphasis on the concept of hyperbolic velocity (scaled rapidity) and in this respect differs markedly from the gyro theory of Ungar. New formulations are given in optics relating hyperbolic velocity with logarithmic redshift and in dynamics including a reformulation of Newton's 2nd law in terms of hyperbolic acceleration so avoiding velocity-dependent mass. The concept of differential Minkowski space is introduced and related to the hyperbolic theory and to Carathéodory's axiomatic approach to the special theory.