The Newton and Coulomb laws as information transfer by virtual particles

In elementary particle physics the philosophy of virtual particles is widely used. We use this philosophy to obtain the famous inverse square law of classical physics. We define a formal model without fields or forces but with a virtual (auxiliary) particle, information carrier. This formal model admits a very simple (school level) interpretation with two classical particles and one virtual. Then we prove (in a mathematically rigorous way) that the trajectories in our model converge to standard Newtonian trajectories of classical physics.