Noncommuting position variables due to quantum gravity

 P: 20 I've read that if one wants to quantize gravity , there must be a smallest length scale " The planck length " . If I want to measure the position of a point particle then in conventional Quantum mechanics I'll find it at the point $(x,y,z)$ at some-time $t$ with an arbitrary momentum but this can't be though in quantum gravity since the smallest length scale that can exist is the planck scale so the particle must be at a neighbourhood of (x,y,z) of area that's equal to planck length . So if we measured the X operator to find the eigenvalue x the particle must be spread in the eigenspace of the Y and Z operators that's X,Y,Z are not commuting operators So we must have [X,Y] not equal to zero . Is this line of reasoning correct ? Have something of this sort been worked out ? It seems that many things in Quantum mechanics should be modified if we want to incorporate gravitational effects