Hello everyone, I'm currently occupying myself with Loop Quantum Gravity and wonder about some question. In LQG, space is built up from a spin network. However, how is movement of material particles realized in this network? One could tend to the idea, particles are simply hopping from one network node to the next one, like IP packets transmitted from router to router in Internet communication. Assuming this, one could think that a particle's word-line length - which is in theory of relativity identical to the time passing for the particle - is determined by the relation between the number of Planck time intervals where the particle stays on a node and the number of intervals where it hops to next node: every interval without hopping contributes one Planck time for the passing time, every interval with hopping delivers a zero time contribution. So, for a static particle without any movement, that always stays at same network node, passing time is maximal, a particle with sub-light speed, that sometimes hops and sometimes rests, feels some time dilation because of a finite portion of zero time intervals, and finally a photon, travelling with light speed, always hops in every time interval, has no time passing and therefore wold-line length of zero. In other words: Minkowsky length of world-line element ds^2 = (cdt)^2 - dl^2 becomes S = N_rest/N_total * t_Planck where N_rest is the count of intervals where the particles remains at a node and N_total the total count of time intervals. However, I do not really believe that LQG really delivers such an easy picture. Googling for "particles movement in loop quantum gravity", I found some hints that particles movement is closely related to fluctuations of space geometry, where nodes unify, split up, or reconfigure connections to neighbour nodes. And I guess, it might be incompatible with LQG's philosophy, to differ between particles movement and changes in geometry that strict. So, particles movement rather should be realized by changes in network configuration than by hopping through a static network. Therefore I assume a particle's world-line length - or its passing time - is not calculated in that easy scheme I mentioned above. That's why I ask if there's someone here who can tell me how to calculate those things?