This makes the transition to the limit from fuzzy mechanics to normal variational conservative mechanics correct for It was presumed that the system dynamics for a fuzzy time t follows from the standard variation principle of least action and is the usual Hamilton-Jacobi mechanics. In the limiting case (classical interpretation of time), the measureĬomes in proportion to the delta function. , which is further called macro time, and the difference The operation of defuzzification (weighing) by measure Is the membership function, which is further assumed to be continuously differentiable or finitely continuously differentiable and compact It was proposed to revise the notion of time as a point on the real axis by introducing a fuzzy time as a set of real numbers with a finite membership function but not equal to unity, i.e., the concept of hazy or fuzzy-time. In there another approach was implemented to observed irreversibility. Although, for example, a number of approaches present some features of interest, they do not solve problems for the complete phase space: irreversibility is observed only in Poincare sections at the introduction of the so-termed “K-flows”. So far, it has not been possible to connect the Gibbs and Boltzmann distributions, in other words, to build up a microscopic theory of non-reversible processes, conciliating the contradictions of a number of fundamental physical principles within the standard presentations. The transition to another dimensioned level of description-quantum mechanics-does not save the situation: the Schrödinger equation is reversible in time. Thus, time (chain of events) takes on a definite orientation: the system evolves from the “past” to the “future” from a state with lower entropy to a state with higher entropy. However, concurrently, the Second Law of Thermodynamics is valid here and determines the introduction of entropy: entropy in closed systems increases in an equilibrium state, reaching a maximum. The system’s evolution is represented in the phase space by the Liouville equation, as the motion of an incompressible fluid: the phase space element can be deformed in as complex as it needs to be manner, but the measure, introduced in the phase space, is preserved. The universe based upon such Hamiltonian mechanics is either orbitally stable or is highly sensitive to the initial conditions in the presence of hyperbolic points. Hamiltonian mechanics normally describes the system of particles, but Hamiltonian mechanics (the mechanics of conservative systems) is time-reversible. Īnother problem originates in the field of classical physics of the particle system. It is only in recent times, the theory of non-abelian fields gauge fields has played a significant role in the understanding of weak and strong nuclear forces and raised hope of using similar methods for quantizing gravity fields however, there is no any significant progress observed up-to-date in this direction. However, the gravitational field quantizing leads to some problems: the strong nonlinearity of the gravity field leads to the impossibility of regularizing divergent diagrams, which number rises with increasing the order of the perturbation theory. The general relativity theory describes the gravity field.
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