particle trajectories in topological 3+1 gravity.

The second result concerns GUP, where the situation is quite different. DSR produces an effective attractive force, GUP, on the other hand, results in a repulsive force, which is not a big surprise, as it lays lower bounds to space and time intervals. In contrast to DSR, rather than competing with Newtonian gravity (and thus GR), GUP counteracts it, thus qualifying as a description of pure quantum gravity effects, which has nothing at all to do with classical gravity. In order not to collide with GR, the lowest-order term in GUP must be of a higher power than 2. There is an interesting parallel to loop quantum cosmology [@LQC], where a repulsive behaviour of gravity at short distances, which helps to avoid singularities, is observed.

In the considered example the effects of DSR and those of GUP would be equivalent for some $n>2$, if the roles of $(E,\vec p\,)$ and $(\varepsilon,\vec\pi)$ were interchanged. $\varepsilon$ and $\vec\pi$ would be energy and momentum ascribed to free particles, which can be boosted to arbitrary values with respect to a certain reference frame, as long as no interaction takes place. The physical energy $E$ and momentum $\vec p$, 