Minimal Length and Small Scale Structure of Spacetime

الأصل · EN

Many generic arguments support the existence of a minimum spacetime interval L₀. Such a "zero-point" length can be naturally introduced in a locally Lorentz invariant manner via Synge's world function bi-scalar Ω(p,P) which measures squared geodesic interval between spacetime events p and P. I show that there exists a non-local deformation of spacetime geometry given by a disformal coupling of metric to the bi-scalar Ω(p,P), which yields a geodesic interval of L₀ in the limit p → P. Locality is recovered when Ω(p,P) >> L₀²/2. I discuss several conceptual implications of the resultant small-scale structure of spacetime for QFT propagators as well as spacetime singularities.