Temporal Behavior of Complex Systems: From Microworld to Macroworld

The aim of this work is to discuss concisely the modern paradigm of the concept of time and to analyze its relevance and applicability in the context of classical and relativistic physics. We are touching briefly the different notion of time in classical and quantum mechanics and in special and general relativity to analyze their compatibility or incompatibility. In quantum mechanics we deal with the absolute character of Newtonian (dynamical) time, whereas in quantum field theories we consider the Minkowski metric as the background space-time (at least partially). Classical general relativity is characterized by a dynamical spacetime, but as regards to the quantum gravity the situation is more complicated. We discussed the consequences which these circumstances cause in the quantum gravity theory (“time paradox”) when attempt to operate with both the dynamical spacetime and the so-called “non-dynamical” time. We analyzed critically whether the last notion may be justified with the aid of an analogy with the “coarse grain” averaging procedure in statistical thermodynamics.