  We study relativistic particle, string and membrane theories as defining
field theories containing gravity in (0+1), (1+1) and (2+1) spacetime
dimensions respectively. We show how an off shell invariance of the massless
particle action allows the construction of an extension of the conformal
algebra and induces a transition to a non-commutative spacetime geometry. This
non-commutative geometry is found to be preserved in the spacetime
supersymmetric massless particle theory. It is then shown how the basic bosonic
commutators we found for the massless particle may also be encountered in the
tensionless limit of string and membrane theories. Finally we speculate on how
the non-locality introduced by these commutators could be used to construct a
covariant Newtonian gravitational field theory.
