Discreteness of space from anisotropic spin–orbit interaction

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.

Deformation of nanowires and nanotubes

“…For such materials, it has been explicitly demonstrated that the generalized Dirac structure which emerges beyond the linear regime is the GUP deformation of the usual Dirac structure [9]. It is also possible to obtain GUP deformation of the effective theory describing condensed matter systems using spin-orbit interaction [10]. It may be noted that GUP deformation occurs due to an intrinsic minimal length in the system [2,3].…”

EPR and Linear GUP

“…On the other hand, this simultaneous reality may be used to explain the instantaneous and non-local correlations when measuring the spin of two entangled particles as we explained above which was set by violation of Bell's inequalities. Possible conceptual connection between minimal length implied by Linear GUP and spin concept was studied in [34].…”