  We study the action and the dynamics of a relativistic particle, uncharged or
charged, in multiscale spacetimes. Invariance under reparametrizations and
Poincar\'e symmetries uniquely determine the action and the line element to be
the usual ones, without the weight factors typical of particle mechanics in
these geometries. The resulting spacetime is multiscale only along spatial
directions. This version of the system is also dictated by recovery of the
nonrelativistic limit together with compatibility with Maxwell and
electrodynamics field theory. Giving up all these requirements and allowing for
a nontrivial weight factor in the time direction produces a modified line
element and considerably complicates the dynamics in the case of a charged
particle.
