Minimal Length and Small Scale Structure of Spacetime

Abstract

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 $p\to P$. Locality is recovered when $\Omega (p,P)>>L_0^2/2$. I discuss several conceptual implications of the resultant small-scale structure of spacetime for QFT propagators as well as spacetime singularities.

v3: 6 pages; added details and a discussion on the relationship between minimal length and maximal acceleration; final version to appear in Phys. Rev. D

References in corpus (1)

• Vacuum Fluctuations and the Small Scale Structure of Spacetime

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