1996/06/19 by Kosaburo Hashiguchi, Hashiguchi, Kosaburo
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematics and Applications #Relativity and Gravitational Theory #gr-qc
paper · pdf · doi:10.48550/arxiv.gr-qc/9606053
53 pages
arxiv created 1996/06/19 · openalex publication_date 1996/06/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
I show that all inertial systems are not equivalent, and the Lorentz transformation is not the space-time transformation over two inertial systems moving with relative constant velocity. To do this, I consider imaginary signals travelling over any inertial system K with arbitrarily large velocities. The travelling of an imaginary signal over K is just a time lapse over K. Then I present an example to show that all coordinate systems are not equivalent when the related theory is restricted over tensor-based coordinate transformations, i.e., the genereal relativity principle is not valid. Instead of the relativity principle, I propose the twofold metric principle which may be roughly stated to assert that the set of equations H(v) describing the motion of a material body with velocity v> 0 can be obtained from the corresponding set of equations H(0) for velocity v=0 by replacing, in each differential equation in H(0), each infinitesimal time variable dt with dt / β(v) , each maximal velocity-critical infinitesimal length variable dr with beta(v) dr, and each zero velocity-critical infinitesimal length variable dx with dx, where beta(v) = 1/ sqrt 1- v2/c2. By depending on the twofold metric principle and the energy-velocity equation, I derive beta(v)mc2, the twofold Schwarzshild metric, the centennial procession of planatery orbits and deflection of light. We also present a reason why the Michelson-Morley experiment is observed. Several other topics are also studied.