Functional mechanics and black holes

Arbitrary real numbers are unobservable, therefore the widely used modeling of physical phenomena by using differential equations, which was introduced by Newton, does not have an immediate physical meaning. It was suggested in [1], [2] that the physical meaning should be attributed not to individual trajectory in the phase space but only to probability distribution function. This approach was motivated by $p$-adic mathematical physics. 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.
Applications of this non-Newtonian functional mechanics to the black hole formation paradox will be discussed. It is believed that many galaxies, including the Milky Way, contain supermassive black holes at their centers. However there is a problem that for the formation of a black hole an infinite time is required as can be seen by an external observer, and that is in contradiction with the finite time of existing of the Universe. In the functional approach to general relaivity one deals with stochastic geometry of spacetime manifolds which is different from quantum gravity. Probability of formation of the event horizon for the external observer in finite time during collapse is estimated.

References

1. I. V. Volovich, Time irreversibility problem and functional formulation of classical mechanics, arXiv: 0907.2445
2. I. V. Volovich, “Randomness in classical mechanics and quantum mechanics”, Found. Phys., 41:3 (2011), 516–528