  We demonstrate the emergence of the conformal group SO(4,2) from the Clifford
algebra of spacetime. The latter algebra is a manifold, called Clifford space,
which is assumed to be the arena in which physics takes place. A Clifford space
does not contain only points (events), but also lines, surfaces, volumes,
etc..., and thus provides a framework for description of extended objects. A
subspace of the Clifford space is the space whose metric is invariant with
respect to the conformal group SO(4,2) which can be given either passive or
active interpretation. As advocated long ago by one of us, active conformal
transformations, including dilatations, imply that sizes of physical objects
can change as a result of free motion, without the presence of forces. This
theory is conceptually and technically very different from Weyl's theory and
provides when extended to a curved conformal space a resolution of the long
standing problem of realistic masses in Kaluza-Klein theories.
