Many generic arguments support the existence of a minimum spacetime interval $L_0$. Such a “zero-point” length can be naturally introduced in a locally Lorentz invariant manner via Synge’s world function biscalar $\Omega (p,P)$ which measures squared geodesic interval between spacetime events $p$ and $P$. I show that there exists a nonlocal deformation of spacetime geometry given by a disformal coupling of metric to the biscalar $\Omega (p,P)$, which yields a geodesic interval of $L_0$ in the limit $p\to P$. Locality is recovered when $\Omega (p,P)\gg L_0^2/2$. I discuss several conceptual implications of the resultant small-scale structure of spacetime for QFT propagators as well as spacetime singularities.

• Received 9 August 2013

DOI:https://doi.org/10.1103/PhysRevD.88.104029