modeling it ad hoc as a homogenous sphere of radius $r_0$, $$\label{cale}
\Delta{\cal E}\approx-\frac{3}{5}\frac{G{\cal
E}^2}{r_0}=-\frac{6}{5}\frac{{\cal E}^3}{m_P^2}.$$ One half of $\Delta\cal E$ is associated to each of the scattered particles to give rise to an energy difference $$\Delta
E_2\approx-\frac{24}{5}\frac{\left(\sqrt{p^2+m^2}-m\right)^3}{m_P^2}.$$ Of course, in view of our rough approximations and the homogenous sphere being rather an indication of ignorance than a seriously-meant model, the factors 6/5 and 24/5 appear ridiculous and will be absorbed into order-of-magnitude factors later. For a more exact description of the scattering of high-energy particles, whose masses do not play a role, an Aichelburg-Sexl metric [@Aic] would be convenient, for our considerations the above simple estimate may be sufficient.

The interesting fact is that $\Delta E_1$ goes as $m{\cal E}^2$ and $\Delta E_2$ as ${\cal E}^3$. As we are looking for gravitational effects for realistic particles, we always have ${\cal E}\gg m$, so that $\Delta E_1$, containing the rest mass $m$, will be normally subdominant in comparison with $\Delta E_2$.

While the virtual particle, and in connection with it the gravitational potential, come into being, the collision partners are attracted and come closer to each other than they would in absence of gravity. During this process the total energy 