Speed of Light in Vacuum in the Case of Various Linear and Nonlinear Systems

Abstract

Further to two previous works by the author which claimed an infinite speed of light in vacuum in a problem of electromagnetics and in the case of a lumped electric circuit, in this paper the same infinite speed of light in vacuum result is proved in the case of various linear and nonlinear systems. Linear and nonlinear systems in state-space formalism and a single-input, single-output (SISO) nonlinear system represented in the form of a differential equation are considered. All of the systems are at rest in the laboratory frame $K$ . The inertial frame $K^{\prime}$ starts its motion abruptly at $t=t^{\prime}=0$ . The time derivative of the state variable vector or the highest order time derivative of the output function of the SISO system in $K$ is Lorentz transformed to frame $K^{\prime}$ and the continuity of the transformed vector or the SISO system function in $K^{\prime}$ is exploited to infer that $c$ , the speed of light in vacuum has to be infinite. The emergence of a Dirac delta function in case this continuity condition is not satisfied, causes a mismatch of delta functions in the system equations which paves the way to the infinite $c$ finding. Because in order to transform the space and time coordinates between inertial frames the Lorentz transformation is used and one postulate that the Lorentz transform is based on is the relativity principle of special relativity theory, it must be watched that the system equations taken up obey the relativity principle.