Is the sign change of spinors under 2π rotations observable?

Hegerfeldt and Kraus's criticisms (see abstr. A42300 of 1968) of Aharonov and Susskind's discussion (see abstr. A27919 of 1967) of the above question are investigated. It is shown that the rotation operator applied to a wave function can be equivalent to solving Schrodinger's equation if gravitational fields are present. The specific example of quantum mechanics on a cone is considered in detail.