Comment on "Fractional quantum mechanics" and "Fractional Schrödinger equation".

Abstract

In this Comment we point out some shortcomings in two papers [N. Laskin, Phys. Rev. E 62, 3135 (2000)10.1103/PhysRevE.62.3135; N. Laskin, Phys. Rev. E 66, 056108 (2002)10.1103/PhysRevE.66.056108]. We prove that the fractional uncertainty relation does not hold generally. The probability continuity equation in fractional quantum mechanics has a missing source term, which leads to particle teleportation, i.e., a particle can teleport from a place to another. Since the relativistic kinetic energy can be viewed as an approximate realization of the fractional kinetic energy, the particle teleportation should be an observable relativistic effect in quantum mechanics. With the help of this concept, superconductivity could be viewed as the teleportation of electrons from one side of a superconductor to another and superfluidity could be viewed as the teleportation of helium atoms from one end of a capillary tube to the other. We also point out how to teleport a particle to an arbitrary destination.