Invalidity of the relativity principle and a proposal of the twofold metric principle

TL;DR

This paper challenges the validity of the relativity principle, proposing a twofold metric principle that modifies the understanding of inertial systems, and derives several classical results using this new framework.

Contribution

It introduces the twofold metric principle as an alternative to the relativity principle, providing new derivations of key physical phenomena.

Findings

All inertial systems are not equivalent.

The Lorentz transformation is not the space-time transformation for inertial systems.

Derivation of the twofold Schwarzschild metric and planetary orbits.

Abstract

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 / \beta(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- v^2/c^2}. By depending on the twofold metric principle and the energy-velocity equation, I derive beta(v)mc^2, 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.