The Majid-Ruegg model and the Planck scales

TL;DR

This paper introduces a new differential calculus for kappa-Minkowski space, explores its implications for quantum physics, and suggests potential observable effects on particle propagation speeds, linking noncommutative geometry with Planck scale physics.

Contribution

It develops a novel differential calculus with central inner product for kappa-Minkowski space and applies it to derive modified quantum equations with potential observable consequences.

Findings

Approximate numerical value for the deformation parameter linked to Planck scales.

Potential observable variation in propagation speed in Klein-Gordon equation.

Modified electrodynamics equations suggest frequency-independent speed of light.

Abstract

A novel differential calculus with central inner product is introduced for kappa-Minkowski space. The `bad' behaviour of this differential calculus is discussed with reference to symplectic quantisation and A-infinity algebras. Using this calculus in the Schrodinger equation gives two values which can be compared with the Planck mass and length. This comparison gives an approximate numerical value for the deformation parameter in kappa-Minkowski space. We present numerical evidence that there is a potentially observable variation of propagation speed in the Klein-Gordon equation. The modified equations of electrodynamics (without a spinor field) are derived from noncommutative covariant derivatives. We note that these equations suggest that the speed of light is independent of frequency, in contrast to the KG results (with the caveat that zero current is not the same as in vacuum). We end with some philosophical comments on measurement related to quantum theory and gravity (not necessarily quantum gravity) and noncommutative geometry.