Solitons in the Skyrme—Faddeev chiral model and quantum mechanics

We consider the essence of the well-known discussion between Bohr and Einstein (1935) which concerned the completeness of quantum mechanics. If one followed Bohr, then the wave function would give the probability description of an individual particle. However, Einstein considered the wave function as an instrument for describing the statistical ensemble of identical particles-solitons. On the other hand, Wiener found the special α-representation of quantum mechanics for which the wave function appeared to be an element of the random Hilbert space with the normal dispersion. This fact proves the equivalence of Bohr and Einstein positions, the central limiting theorem being taken into account. Moreover, we show that within the scope of the Skyrme–Faddeev chiral model particles can be considered as self-gravitating solitons. Therefore, we infer that for island systems with the plane asymptotic space-time quantum mechanics ensues from Einstein gravity equations.