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Alex,
Let's have a look at your marble/ball example and why gravitons fail miserably to explain the gravitational interaction between the two.
In this case the marble and ball are treated as point masses.
Since gravitons involve a quantum field theory of gravity one needs to look at the initial and final quantum states.
In this case the initial quantum state could simply be the marble and ball before interaction, the final quantum state is the gravitational interaction between the two.
In between the initial and final states are the intermediate quantum states involving the creation of the graviton and it's momentum, plus the momentum of the marble and ball etc.
The exercise is to sum over the various momenta in each state that produces an answer that not only makes sense but agrees with experiment and observation.
Let's keep this idea to the side for the time being.
In the same way we can examine the electromagnetic interaction between two charged particles involving the creation of virtual photons.
Recall in a PM I introduced you to the concept of Compton wavelength as a way to explain the BB singularity.
When two charged particles interact and a photon is emitted, the particles undergo a resonance which smears the particles over space time.
The particles are no longer considered point sizes of zero dimension but are at dimensions comparable to their Compton wavelength.
This is important has it allows energy limits to be imposed much like the case of String Theory using renormalization. By utilizing renormalization and summing over the momenta for all the initial, intermediate and final states a finite value is obtained.
Unfortunately when it comes to a Quantum field of gravity there is no way we can treat a particle as anything but a point source. Since a point source has a zero radius we find by summing over the momenta we obtain infinite values.
If the particle is treated as a string or a loop which has an infinitesimally small but non zero dimension we have what is known as a renormalizable theory.
Unfortunately a quantum field theory for gravity is non renormalizable.
Until physicists can produce a renormalizable theory one can argue that gravitons don't even exist from a theoretical viewpoint unless one assumes that String or Loop quantum gravity theory is correct which also predicts gravitons.
Steven
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