Discreteness of Space from GUP in Strong Gravitational Fields

TL;DR

This paper demonstrates that the quantization of length, predicted by the Generalised Uncertainty Principle (GUP), persists even in strong gravitational fields, indicating a fundamental discreteness of space.

Contribution

The study extends the length quantization result from weak to strong gravitational fields, confirming its robustness in various spacetime regimes.

Findings

Length quantization holds in strong gravitational fields.

GUP-induced corrections are robust across different spacetime curvatures.

Supports the idea of fundamental space discreteness.

Abstract

A large class of quantum theories of gravity show that the Heisenberg's uncertainty principle is modified to the "Generalised Uncertainty Principle" (GUP) near the Planckian scale. It has also been shown that the GUP induces perturbative corrections to all quantum mechanical Hamiltonians, even at low energies, and thereby introduces Planck scale corrections to the Schr\"odinger equation and to the relativistic quantum mechanical equations. Some of these corrections give rise to potentially measurable effects in the low-energy laboratory. Another prediction of these corrections is that a measured length must be quantized, as seen by studying the solutions of the GUP modified Schr\"odinger, Klein-Gordon, and Dirac equations in a one, two, and three dimensional box. This result was subsequently extended to spacetimes with weak gravitational fields. In this work, we further extend this length quantization to spacetimes with strong gravitational fields and show that this result continues to hold, thereby showing that it is robust.