  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.
