  The geometric calculus based on Clifford algebra is a very useful tool for
geometry and physics. It describes a geometric structure which is much richer
than the ordinary geometry of spacetime. A Clifford manifold (C-space) consists
not only of points, but also of 1-loops, 2-loops, etc.. They are associated
with multivectors which are the wedge product of the basis vectors, the
generators of Clifford algebra. Within C-space we can perform the so called
polydimensional rotations which reshuffle the multivectors, e.g., a bivector
into a vector, etc.. A consequence of such a polydimensional rotation is that
the signature can change: it is relative to a chosen set of basis vectors.
Another important consequence is that the well known unconstrained Stueckelberg
theory is embedded within the constrained theory based on C-space. The essence
of the Stueckelberg theory is the existence of an evolution parameter which is
invariant under the Lorentz transformations. The latter parameter is
interpreted as being the true time - associated with our perception of the
passage of time.
