The action for a relativistic free particle of mass m receives a contribution -mds from a path of infinitesimal length ds. Using this action in a path integral, one can obtain the Feynman propagator for a spinless particle of mass m. Assuming that the path integral amplitude is invariant under the ``duality'' transformation dsL^2/ds, one can calculate the modified Feynman propagator. I show that this propagator is the same as the one obtained by assuming that quantum effects of gravity lead to modification of the spacetime interval (x-y) ^2 to (x-y) ^2+L^2. The implications of this result are discussed.
Τ. Padmanabhan (Mon,) studied this question.