Classical random geometry and black hole firewall problem

The usual modeling of physical phenomena by using differential equations, which was introduced by Newton, does not have an immediate physical meaning since arbitrary real numbers are unobservable. It was suggested that the physical meaning should be attributed not to individual trajectory in the phase space but only to probability distribution function. Even for the single particle the fundamental dynamical equation in the proposed “functional” approach is not the Newton equation but the Liouville equation or the Fokker–Planck–Kolmogorov equation. The Newton equation in functional mechanics appears as an approximate equation for the expected values of the position and momentum.
In this approach there are classical fluctuations of the space-time geometry. Applications of this stochastic approach to the black hole information paradox and the firewall problem will be discussed.