Comment on "Fractional quantum mechanics" and "Fractional Schroedinger equation"

TL;DR

This paper critiques previous works on fractional quantum mechanics, highlighting issues like the invalidity of the fractional uncertainty relation and the particle teleportation phenomenon, which has implications for understanding relativistic effects and quantum phenomena.

Contribution

It identifies fundamental shortcomings in earlier fractional quantum mechanics papers and proposes the concept of particle teleportation as an observable relativistic effect.

Findings

Fractional uncertainty relation does not hold generally.

Probability continuity equation has a missing source term.

Particle teleportation can be linked to relativistic quantum effects.

Abstract

In this comment, we point out some shortcomings in two papers "Fractional quantum mechanics" [Phys. Rev. E 62, 3135 (2000)] and "Fractional Schroedinger equation" [Phys. Rev. E 66, 056108 (2002)]. 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 one 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 a destination.