Then, I read the following passage in Lee Smolin book "The trouble with physics" (p. 85): "[...]each gravitational wave could be seen quantum mechanically, as a particle called the graviton - analogous to the photon, which is the quantum of the electromagnetic field."
I thought I had finally understood the concept of force-carrying particle : according to general relativity, the gravitational force is nothing but the deformation of space-time by the presence of mass, which causes objects to move otherwise than in uniform rectilinear motion, hence making us invoke a force, gravity, to explain their motion according to Newton's Second Law. Now, assume that a mass is suddenly placed somewhere in space-time. Its deformation of space-time will propagate at a finite speed, that of light, making its effect felt at greater and greater distances. These are gravitational waves. In analogy with electro-magnetic waves, which are quantized in photons, gravitational waves are quantized in gravitons, which are therefore the particles "carrying" the gravitational force, i.e., making its effects felt at distance.
This at last made sense to me. But then I watched the DVD version of Brian Greene's book "The elegant universe", in which there is an animation showing two persons throwing small balls at each other, and getting attracted toward each other as they throw the balls harder and harder. So we are back to this idea of momentum exchange, and this does not make sense to me for explaining attractive forces such as gravity!
Is there a theoretical physicist around who could help me understand this better?