  Adopting a purely two dimensional relativistic equation for graphene's
carriers contradicts the Heisenberg uncertainty principle since it requires
setting off-the-surface coordinate of a three-dimensional wavefunction to zero.
Here we present a theoretical framework for describing graphene's massless
relativistic carriers in accordance with this most fundamental of all quantum
principles. A gradual confining procedure is used to restrict the dynamics onto
a surface and normal to the surface parts and in the process the embedding of
this surface into the three dimensional world is accounted for. As a result an
invariant geometric potential arises in the surface part which scales linearly
with the Mean curvature and shifts the Fermi energy of the material
proportional to bending. Strain induced modification of the electronic
properties or "straintronics" is clearly an important field of study in
graphene. This opens a venue to producing electronic devices, MEMS and NEMS
where the electronic properties are controlled by geometric means and no
additional alteration of graphene is necessary. The appearance of this
geometric potential also provides us with clues as to how quantum dynamics
looks like in the curved space-time of general relativity. In this context, we
explore a two-dimensional cross-section of the wormhole geometry realized with
graphene as a solid state thought experiment.
