Wiener Interpretation of Quantum Mechanics, the Skyrme–Faddeev Chiral Model, and Neutrino Oscillations

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 $$\alpha$$ -representation of quantum mechanics, for which the wave function appeared to be an element of the random Hilbert space with normal dispersion. This fact proves the equivalence of Bohr’s and Einstein’s positions, the central limiting theorem being taken into account. Also the dark matter hypothesis and new possibilities of the Brioschi 16-spinor realization of the Skyrme–Faddeev chiral model are discussed, including the neutrino oscillation problem.