A defect of the electromagnetism and it serves as a hidden variable for quantum mechanics

Abstract

According to the theory of relativity, the 4-vector force acting on a particle is orthogonal to the 4-vector velocity of the particle, but we found that the electromagnetic force of the Maxwell's theory can not completely satisfy this orthogonality, this incompletion leads us to find that the electromagnetic force has two independent components in the 4 dimensional space time. A 4-vector force has 4 components, because of the orthogonality of 4-vector force and 4-vector velocity, the number of independent components of the force reduces to 3, while the electromagnetic force can merely provide 2 independent components, this situation means that there is an undefined component accompanying the electromagnetic force. This missing undefined component may serve as a hidden variable which quantum mechanics is eager to find for a long time. The primary purpose of this paper is to strictly proof that the electromagnetic force has two independent components in the 4 dimensional space time. We also briefly discuss the possibility that the undefined component of the electromagnetic force serves as a hidden variable for quantum mechanics.