Invalidity of the relativity principle and a proposal of the twofold   metric principle
  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. 
Kosaburo Hashiguchi