Time Crystals, Their Networks, and Self-Organized Vacuum

Abstract

The phenomenon of dissipative self-organization is studied on the example of time-crystal networks. Par-ticular attention was given to transient processes, attractor topologies, phase transitions, and asymptotic stability. New concepts were introduced, including topological phases, spinorial states, and bond flavors. Concepts such as ground states, chemical potentials, elastic forces, temperature, and statistical distribu-tions were endowed with a new meaning associated with asymptotic stability. Phenomena usually at-tributed exclusively to quantum physics have been shown to occur in this essentially classical environment. They coexist with, and in some cases, such as charge quantization, are related to the phenomenon of time dilation. The approach was applied to model vacuum self-organization. We have shown that under the ac-tion of competing forces, such as gravity and antigravity, a cascade of phase transitions can transform an unorganized vacuum into phases in which interactions, fields and waves resemble electromagnetic, weak, and strong, and their elements can be used as building blocks for prototype particles. In addition, some interrelation field parameters and probabilities of particle transmutations were calculated, which are not predicted by the standard model. The results are consistent with the experiment. The presented material and methodology may be of interest for studying self-organization in different environments.