The Majid-Ruegg model and the Planck scales

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.

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