2022, no. 1

### CONTINUUM MECHANICS FROM AN OBSERVER’S VIEWPOINT (A VARIANT OF RELATIVISTIC FIELD THEORY FREE FROM SOME KNOWN PARADOXES)

#### Belevich M.

A variant of the relativistic continuum mechanics with the measure is presented. The theory satisfies the following principles: the causality principle, the general covariance principle, the correspondence principle, and Einstein’s principle of relativity. The group analysis of the resulting equations shows that they admit the Poincare group of transformations, and appear to be Lorentz-invariant. The measure conservation law is the basis of the discussed theory, and the observer is its necessary component.
The theory does not imply any speed limitation of an object. Arbitrary values of velocity are admissible. However, since the velocity of an object is being measured using the signal propagating with some finite speed, this speed in fact acts as a limit for the measured velocities of objects. This is due to the fact that objects moving faster than the speed of the signal (information propagation) either become unobservable, or their measured velocity turns out to be seeming and does not exceed the signal speed.
Various options for synchronization and construction of spaces of simultaneous events are considered. Another distinctive feature of the constructed environment model is the smaller number of postulated statements. For example, the total energy conservation law holds. However, it is not postulated, as in the classical fluid model, but follows from the mass conservation law and, therefore, is a theorem. Also, local thermodynamic equilibrium does not require postulation. Finally, the second law of thermodynamics does not hold in the cases when the speed of the signal providing the observer with information about the phenomenon under study is less than the speed of the object. Such behavior is corroborated using the corresponding numerical models, in particular, based on the explicit difference methods. A similar phenomenon is known as the absence of stability of the numerical algorithm.
Two levels of description within the considered model are demonstrated. This reflects the presence of two main physical interpretations of the developed theory — hydromechanical and electromagnetic. Both interpretations are discussed and corresponding systems of equations are presented.

Keywords: fluid mechanics; conservation laws; field theory; theory of relativity; Maxwell’s equations; second law of thermodynamics.

UDC: 530.12, 532.5.013.2, 537.8

PACS: 40., 47., 47.10.– g, 47.10.A

DOI: 10.17238/issn2226-8812.2022.1.20-63