Theorists believe that if crystals exist in three-dimensional space, then the same crystals can exist in time.
Symmetry is one of the fundamental concepts in modern physics. It goes far beyond the usual spatial symmetry and, in simple terms, consists in the preservation of the action of certain properties of the system under certain transformations.
For example, no matter how the system is oriented in space, the law of conservation of momentum continues to operate for it - this is how the symmetry of space manifests itself. In a similar way, when transforming (broadcasting) time for the system, the law of conservation of energy manifests itself. In general, in accordance with Noether's theorem, a certain conservation law corresponds to each type of symmetry. It can be formulated and vice versa, symmetrically: conservation laws are a consequence of fundamental symmetry.
However, a number of cases are known and that the Universe does not exhibit symmetry, which, it would seem, follows from some physical laws and principles. This phenomenon is known as spontaneous symmetry breaking: asymmetric final states appear in a system described by symmetric laws and satisfying symmetric initial conditions.
The most striking example of symmetry is the familiar crystals with their highly ordered arrangement of particles. Moreover, the process of crystallization of the solution itself can be called a very striking example of spontaneous symmetry breaking. In a solution, the particles are arranged chaotically, and the entire system is at a minimum energy level. The interactions between particles are symmetrical with respect to rotations and shears. However, after the liquid has crystallized, a state appears in which both of these symmetries are broken: the interaction between particles in the crystal is not symmetric.
Crystals and their spatial symmetry are well studied - but only recently working in the USA researchers Al Shapere and Nobel laureate Frank Wilczek pondered whether the formation of such periodic ordered structures is possible not in space, but in time, structures, during the formation of which the same spontaneous breaking of symmetry occurs. Scientists have come to a positive answer to this question - and it is not at all surprising that they called such structures "time crystals."
With the help of complex mathematical calculations, the authors showed the possibility of the existence of a system at a minimum energy level, which, due to the formation of certain periodic structures not in space, but in time, would come to an asymmetric final state - the very "crystal of time". At a level closer to us, this can manifest itself in the form of periodic changes in certain thermodynamic properties of the system.