Currently, with the development of public relations and production systems, there is a need to increase the capacity of communication systems and information transmission. It has been shown theoretically that it is possible to increase throughput by using multidimensional signals in space instead of real signals on a plane. It is now accepted that a multidimensional space, Multiple-Input Multiple-Output (MIMO), can be formed using multiple antennas to transmit and receive in physical space. However, as physicists point out, such space is three-dimensional, and with the addition of time it is four-dimensional. It is clear that in such a physical space, when using more than 2 antennas for transmission and 2 for reception, it is impossible to obtain a gain in throughput of more than 4 times, since according to the laws of cybernetics, the diversity at the channel input will not be transmitted to the exit. It follows that it is necessary to reconsider existing views on the dimension of physical space. Previously, in the work the MIMO data transfer line with three-frequency quaternion carrier, it was shown that it is possible to use a hypercomplex quaternion number as a model of physical space. In this case, the dimension of space will be equal to 4 with 3 imaginary (spatial) axes and one scalar axis. In addition, combinations of three quaternion angular frequencies on the imaginary axes formed 4 single-frequency channels. Accordingly, the gain in throughput compared to real signals reached 4 in orthogonal axes and 4 in frequencies. In this work, an octonion with 7 imaginary (spatial) axes and one scalar is used as a mathematical model of physical space. It is shown that the dimension of physical space will be 8 with 64 single-frequency channels in the form of combinations of 7 angular frequencies. Hence, the gain in throughput will be 8 in orthogonal axes and 64 in frequencies.

With the development of communication systems and the Internet, as well as with the growth of services created on the basis of communication networks, the need to increase the capacity of communication channels is increasing. Theoretically, it is shown that it is possible to increase the capacity of communication channels and exceed the “Shannon limit” by moving from the real space of signals on a plane to a multidimensional one with dimension M. In a multidimensional space, each signal is a multidimensional vector, and when such a signal passes through a channel, a MIMO (Many-Input – Many-Output) scheme is formed. As an alternative to existing methods for implementing a MIMO scheme in a physical space with multiple antennas at the input and output of a communication channel, a method for transmitting information using a MIMO scheme in a hypercomplex vector space with one antenna for transmission and one for reception is proposed for wireless communication systems and communication cables.

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.

A document by Vadim Sovetov. Click on the document to view its contents.