A variant of the relativistic continuum mechanics with the measureis presented. The theory satisfies the following principles: the causalityprinciple, the general covariance principle, the correspondence principle,and Einstein's principle of relativity. The group analysis of theresulting equations shows that they admit the Poincarй group of transformations,and appear to be Lorentz-invariant. The measure conservation law isthe basis of the discussed theory, and the observer is its necessarycomponent.
The theory does not imply any speed limitation of an object. Arbitraryvalues of velocity are admissible. However, since the velocity ofan object is being measured using the signal propagating with somefinite speed, this latter speed in fact acts as a limit for the measuredvelocities of objects. This is due to the fact that objects movingfaster than the speed of the signal (information propagation) eitherbecome unobservable, or their measured velocity turns out to be seemingand does not exceed the signal speed.
Various options for synchronization and construction of spaces ofsimultaneous events are considered. Another distinctive feature ofthe constructed environment model is the smaller number of postulatedstatements. For example, the total energy conservation law holds.However, it is not postulated, as in the classical fluid model., butfollows 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 caseswhen the speed of the signal providing the observer with informationabout 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 similarphenomenon 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 ofthe developed theory - hydromechanical and electromagnetic.Both interpretations are discussed and corresponding systems of equationsare presented.
PACS numbers: 40., 47., 47.10.-g, 47.10.A-