Abstract

The equations of electrodynamics must, first of all, satisfy the law of conservation of energy. It is shown that Maxwell's equations can be obtained from the Cauchy-Riemann conditions for a quaternion in 4D space. Electrons are written as 4D vectors in energy space, in which the first elements represent the real part of the quaternion (scalar), and the other three represent the imaginary part. From the point of view of conservation of energy, an electron cannot move into an arbitrary state, but only makes quantum jumps to those places in space in which it stores energy. Consequently, the movement of electrons in time occurs along an orbit. Since scalars are formed by the interaction of electromagnetic waves, 4D electrons have a spectrum. The mathematically obtained equations of quaternion electrodynamics have the same form for electric and magnetic intensity, but differ from Maxwell's equations by the presence of a scalar part. A charged electron is considered as the scalar part in the equation of circulation of the electric field strength. The electron spin is considered as the scalar part in the equation of magnetic intensity circulation. The equations of the scalar parts correspond to Gauss's law and form a single connection with the equations of the imaginary parts. Also, unlike Maxwell's equations, instead of currents induced by circulations of intensities, the electromotive forces that form these currents are shown. As is known, in the equation for the circulation of magnetic intensity, Maxwell added a current formed by the change in electric flux over time. In the obtained expressions, this term appeared mathematically and represents the electromotive force generated by the change in the magnetic field over time.