quantum principle of superposition imposed by the superselection rule. This rule was introduced by Wick,
Wightman, and Wigner in order to avoid the violation of Lorentz invariance due to the absence of physical
invariance under rotations by an angle of 2
in states which are a coherent superposition of states with an even and odd number of fermions. We describe a mesoscopic system (a semiconductor double quantum dot at low
temperatures) where such superpositions are realized; this is confirmed by experiments. We suggest a new
experiment which explicitly demonstrates the absence of physical invariance under rotations by an angle of 2
. We note that an alternative to the superselection rule is the existence (along with x, y, z, and t) of additional
spinor (Grassmann) dimensions of spacetime introduced in quantum field theory for realization of supersym-
metry. It is proved that additional dimensions are real; their physical meaning is clarified for nonrelativistic sys-
tems of fermions.