Natural Science Forum / Physics / Research / September 2007

Good question, but without a specific theory of quantum gravity and
the very small scale structure of spacetime, I don't see how to answer
this other than "On the order of the Planck time" from dimensional
considerations.

On Sep 4, 11:33 pm, "cpoll...@gmail.com" <cpoll...@gmail.com> wrote:

Not a time, but an angular momentum. If you work out some trivial
special relativity for circular orbits around a point source, you will
notice that there is a limit angular momentum which depends only of
the coupling constant. Ie, set a formula for the angular momentum as a
function of the radius of the orbit (very much as in non relativistic
mechanics you get the third law of Kepler) and then take the radius to
zero. Intuitively, it happens because the speed of the orbiting
particle can not be greater than c, but it is not so intuitive to
notice that the limit of zero radious is actually finite.

The adimensional coupling constant of a theory is defined to be the
quotient between this angular momentum and the Planck Constant (as
Planck constant marks the mimimum angular momentum allowed in a
quantum theory).

Of course the mechanism fails for gravity, where the charge is
proportional to the mass, but then funnier things happen. Check for
"quantum haiku" and "kepler length" threads here and in physicsforums,
there some games related to your question are worked out.

Alejandro