Physics – Mathematical Physics
Scientific paper
2009-10-08
P-Adic Numbers, Ultrametric Analysis, and Applications, Vol. 1, No. 4 (2009), 361-367 pp
Physics
Mathematical Physics
8 pages
Scientific paper
10.1134/S2070046609040086
The notion of microscopic state of the system at a given moment of time as a point in the phase space as well as a notion of trajectory is widely used in classical mechanics. However, it does not have an immediate physical meaning, since arbitrary real numbers are unobservable. This notion leads to the known paradoxes, such as the irreversibility problem. A "functional" formulation of classical mechanics is suggested. The physical meaning is attached in this formulation not to an individual trajectory but only to a "beam" of trajectories, or the distribution function on phase space. The fundamental equation of the microscopic dynamics in the functional approach is not the Newton equation but the Liouville equation for the distribution function of the single particle. The Newton equation in this approach appears as an approximate equation describing the dynamics of the average values and there are corrections to the Newton trajectories. We give a construction of probability density function starting from the directly observable quantities, i.e., the results of measurements, which are rational numbers.
Trushechkin A. S.
Volovich Igor V.
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