  The action for a $(3+1)$-dimensional particle in very special relativity is
studied. It is proved that massless particles only travel in effective
$(2+1)$-dimensional space-time. It is remarkable that this action can be
written as an action for a relativistic particle in a background gauge field
and it is shown that this field causes the dimensional reduction. A new
symmetry for this system is found. Furthermore, a general action with restored
Lorentz symmetry is proposed for this system. It is shown that this new action
contains very special relativity and two-time physics.
