Re: Do gravitons emit gravitons?

Dear Eliza,

Virtual particles are theoretical constructs that are useful in a
way of calculating called "perturbation theory".  Since problems
in quantum mechanics and quantum field theory involving interactions
are extremely difficult to solve exactly, one uses easily derived
solutions to the non-interacting theory to build up solutions to the
complicated interacting theory.  In some cases, perturbation theory
works so well that it is tempting to think of the virtual particles
as real.  I advise against this.

No one has yet quantized a theory of gravity, but when they do there
is already a name for the particle that carries the gravitational
force, the graviton.  Even before quantizing the theory of gravity,
we know that the graviton will couple to other gravitons.  As an
aside, the force carrier of the strong nuclear force, the gluon,
also interacts with other gluons.  In contrast, the force carrier of the 
electromagnetic force, the photon, does not couple directly to other 
photons.

In the perturbative method of calculation, the graviton can emit
a virtual graviton, and this virtual graviton can emit yet another
virtual graviton, and so on.  But this does not imply that the
gravitational force will be infinite anywhere because the virtual
particles will still obey Heisenberg's Uncertainty Principle.
Mathematically, the Principle looks like

               dE * dt >= hbar/2

where dE is the uncertainty in the energy, dt is the uncertainty in the
time, and hbar is Planck's constant divided by (2 pi).

The virtual particle can violate conservation of energy by an amount
dE, but only for an amount of time dt given by the Uncertainty
Principle, before it vanishes.  The energy of the virtual particle can
be anything from a minimum energy that depends on the particle type
(zero for the graviton) to infinity.

So gravitons with a lot of energy don't last very long and can't have
much of an effect before they are absorbed.  And gravitons that last a
long time don't have much energy, so they also can't have much of an
effect.  This is the way out of the paradox.

Your statement that the graviton is massless is correct.  Both the 
graviton and the photon are massless particles.  This can be deduced
from the inverse square force laws of Newton (gravity) and Coulomb
(electrostatics).

--Dr. Randall J. Scalise    http://www.phys.psu.edu/~scalise/