  In undulatory mechanics the rest mass of a particle is associated to a rest
periodicity known as Compton periodicity. In carbon nanotubes the Compton
periodicity is determined geometrically, through dimensional reduction, by the
circumference of the curled-up dimension, or by similar spatial constraints to
the charge carrier wave function in other condensed matter systems. In this way
the Compton periodicity is effectively reduced by several order of magnitudes
with respect to that of the electron, allowing for the possibility to
experimentally test foundational aspects of quantum mechanics. We present a
novel powerful formalism to derive the electronic properties of carbon
nanotubes, in agreement with the results known in the literature, from simple
geometric and relativistic considerations about the Compton periodicity as well
as a dictionary of analogies between particle and graphene physics.
