Minimal Length and Small Scale Structure of Spacetime

Understand

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 bi-scalar $\Omega(p,P)$ which measures squared geodesic interval between spacetime events $p$ and $P$.
• I show that there exists a \emph{non-local} deformation of spacetime geometry given by a \emph{disformal} coupling of metric to the bi-scalar $\Omega(p,P)$, which yields a geodesic interval of $L_0$ in the limit $p \rightarrow P$.
• Locality is recovered when $\Omega(p,P) >> L_0^2/2$.