The first clue, in the theory of relativity, the 4-vector force acting on a particle is orthogonal to the 4-vector velocity of the particle, this orthogonality means that there is some difference between the orthogonality and the usual statement: the
Coulombs force (or gravitational force) acts along the line joining a couple of particles (in usual 3D space), so the direction of 4-vector Coulombs force is carefully investigated, it is found that Maxwells equations can be derived from classical Coulombs force and the orthogonality. The second clue, 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 4-vector force reduces to 3, however we prove that 4-vector Coulombs force can merely provide 2 independent components, this situation means that there is an undefined component accompanying the 4-vector Coulombs force, hinting that this missing undefined component is a hidden variable. The third clue, the best way to study the hidden variable is to establish a new concept: Z-space, in which the undefined component of 4-vector Coulombs force can be clearly defined as the hidden variable for the quantum mechanics. At the last, the undefined component is regarded as a fluctuating source that contributes to Lorentz force, so that the quantum wave equation can be derived out in the ensemble space of particle motion from the relativistic Newtons second law.
