Discreteness of Space from Anisotropic Spin-Orbit Interaction

TL;DR

This paper proposes that anisotropic spin-orbit interaction, specifically Dresselhaus interaction, naturally leads to space quantization, suggesting a possible low-energy quantum gravity effect that breaks the continuum space assumption.

Contribution

It introduces a novel mechanism where spin-orbit interaction induces space quantization, linking quantum gravity concepts with condensed matter physics.

Findings

Space becomes quantized in units depending on particle mass and coupling constant.

Breakdown of continuum space occurs at tabletop experiment scales.

Spin-orbit interaction may serve as a low-energy quantum gravity effect.

Abstract

Various approaches to Quantum Gravity suggest an existence of a minimal measurable length. The cost to have such minimal length could be modified uncertainty principle, modified dispersion relation, non-commutative geometry or breaking of continuous Lorentz symmetry. In this paper, we propose that minimal length can be obtained naturally through spin-orbit interaction. We consider Dresselhaus anisotropic spin-orbit interaction as the perturbative Hamiltonian. When applied to a particle, it implies that the space, which seizes this particle, should be quantized in terms of units that depend on particle's mass. This suggests that all measurable lengths in the space are quantized in units depending on existent mass and the Dresselhaus coupling constant. On one side, this indicates a breakdown of the space continuum picture near the scale of tabletop experiments, and on the other side, it proposes that spin-orbit interaction is a possible quantum gravity effect at low energy scale that leads naturally to space quantization.