A Quantized Spacetime Based on $Spin(3,1)$ Symmetry

TL;DR

This paper proposes a novel quantization of spacetime using $Spin(3,1)$ symmetry inspired by string theory and loop quantum gravity, deriving a generalized uncertainty principle and demonstrating its holographic and fuzzy geometric properties.

Contribution

It introduces a new spacetime quantization framework based on $Spin(3,1)$ symmetry, linking string theory and loop quantum gravity concepts.

Findings

Derives a generalized uncertainty principle.

Shows the holographic nature of the theory.

Spacetime fuzziness is below astrophysical bounds.

Abstract

We introduce a new type of the spacetime quantization based on the spinorial description suggested by loop quantum gravity. Specifically, we build our theory on a string theory inspired $Spin(3,1)$ worldsheet action. Because of its connection with quantum gravity theories, our proposal may in principle link back to string theory, connect to loop quantum gravity where $SU(2)$ is suggested as the fundamental symmetry, or serve as a Lorentzian spin network. We derive the generalized uncertainty principle and demonstrate the holographic nature of our theory. Due to the quantization of spacetime, geodesics in our theory are fuzzy, but the fuzziness is shown to be much below conceivable astrophysical bounds.