Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Discreteness of Space from Anisotropic Spin-Orbit Interaction

Version 1 : Received: 3 February 2021 / Approved: 5 February 2021 / Online: 5 February 2021 (13:52:16 CET)

How to cite: Majumder, B.; Ali, A.F. Discreteness of Space from Anisotropic Spin-Orbit Interaction. Preprints 2021, 2021020162 (doi: 10.20944/preprints202102.0162.v1). Majumder, B.; Ali, A.F. Discreteness of Space from Anisotropic Spin-Orbit Interaction. Preprints 2021, 2021020162 (doi: 10.20944/preprints202102.0162.v1).

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.

Subject Areas

space quantization; Planck length; discreteness of space

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