Quantum Coherence between States with Even and Odd Numbers of Electrons

A system with variable number of electrons is described in which the states representing coherent superpositions of states with even and odd numbers of electrons may occur. An experiment is suggested which generalizes the experiment of Nakamura et al. and may provide direct evidence of such coherence and, thereby, justify the reality of a superspace. Quantum coherence between states with even and odd numbers of electrons is of special fundamental interest. In 1952, Wick, Wightman, and Wigner [1] claimed that the coherent linear superpositions of states with even and odd numbers of fermions are incompatible with the Lorentz invariance and introduced the superselection rule, according to which such linear superpositions are physically impossible. In actuality (as was pointed out in [2, 3]), the superselection rule is the alternative to the existence, along with x, y, z, and t, of additional spinor coordinates, which, in fact, are introduced in quantum field theory to account for supersymmetry. In this work, it is proved theoretically that the superselection rule is, generally, not self-consistent. Namely, a simple realistic system with variable number of electrons is considered, which is governed by the Hamiltonian whose eigenvectors are all coherent superpositions of th