Coulomb's law for Single-Frequency Quaternion Charge

Abstract

Vadim Sovetov*

The law of attraction and repulsion of electric charges was established experimentally by Charles Coulomb in 1785. At that time, the electron was considered as a particle that has a charge and the ability to charge bodies. Bodies with a charge created an electrical tension around themselves, which corresponded to the force of attraction of opposite charges and repulsion of like charges.

In 1925, Erwin Schrödinger formulated a postulate equation that reflected the dual nature of the electron, as a particle and as a wave. In this equation, the interaction of electrons was described by a wave function in 3D space. The physical meaning of the wave function was explained by the probability of finding an electron in the corresponding region of space.

In this article, Coulomb's law is obtained by representing the electron by a quaternion. A quaternion is a hypercomplex number and forms a 4D space in which one coordinate axis is scalar and the other three are imaginary. Using the quaternion representation of the electron in previous works, Maxwell's equation and the wave equation were analytically obtained. It is shown that with this representation of the electron, the Cauchy-Riemann conditions must be satisfied, which correspond to the law of conservation of energy. In this work, Coulomb's law is also obtained analytically, and the appearance of the forces of attraction and repulsion of electrons is explained by the law of conservation of energy. An electron, by virtue of the law of conservation of energy, can occupy in 3D space only certain, and not probabilistic, values corresponding to its total potential and kinetic energy.

According to the law of conservation of energy, when another electron appears, an interaction occurs between them, which restores the electrical neutrality of space. Therefore, the law of conservation of energy also explains the presence of the observer effect in quantum theory.

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