From plank length to compton length

[alejandro.rivero]

>From QG we expect a quantum of area, PA=(Plank length)^2, and
a related quantum of time, PT=(Plank length)/c.

For long distances, the area defined -swept- directly by a test probe
orbiting around a massive particle in a quantum of time is a lot
greater that the plank area. But as the orbit radius is slower, the
area swept in a PT will be smaller than PA. The breaking scale is,
simply, the Compton Length of the particle. In this way one recovers
the quantum mechanics scale from the quantum gravity scale.

Another way to ask the same thing is to invoque Kepler second law,
and ask for which radius a circular, gravitational, orbit around a
particle of mass m will sweep one Plank Area in one Plank Time.

These are trivial comments, but still I would like to know of
didactical (or not so) papers using them. Note I am *not* referring to
the usual definition of plank length as the compton length of plank
mass... that is just a play of words. Here the compton length is the
one of the particle involved; say an electron or a neutrino; but
looking only at gravitational interaction.

Alejandro Rivero