Discreteness of Space from the Generalized Uncertainty Principle

TL;DR

This paper introduces a Generalized Uncertainty Principle consistent with String Theory and black hole physics, suggesting that space is fundamentally discrete and that measurable lengths are quantized, with potential observable consequences beyond the Planck scale.

Contribution

It proposes a GUP compatible with key quantum gravity theories and demonstrates that space quantization arises naturally from this principle.

Findings

Space must be quantized when confined by the GUP

The fundamental length scale can be the Planck length

Possible observable effects at scales larger than Planck length

Abstract

Various approaches to Quantum Gravity (such as String Theory and Doubly Special Relativity), as well as black hole physics predict a minimum measurable length, or a maximum observable momentum, and related modifications of the Heisenberg Uncertainty Principle to a so-called Generalized Uncertainty Principle (GUP). We propose a GUP consistent with String Theory, Doubly Special Relativity and black hole physics, and show that this modifies all quantum mechanical Hamiltonians. When applied to an elementary particle, it implies that the space which confines it must be quantized. This suggests that space itself is discrete, and that all measurable lengths are quantized in units of a fundamental length (which can be the Planck length). On the one hand, this signals the breakdown of the spacetime continuum picture near that scale, and on the other hand, it can predict an upper bound on the quantum gravity parameter in the GUP, from current observations. Furthermore, such fundamental discreteness of space may have observable consequences at length scales much larger than the Planck scale.