Approaches to Quantum Gravity

468 S. Majidhas been called a ‘Planckian bound’ on spatial momentum. This is a generic featureof all bicrossproduct models based on noncompact groups. Moreover, the classicalgroup X = SO 4,1 in the model (24.1) acts on the momentum group M = R 3 >⊳Rand using this action one can come up with an entirely classical picture equivalentto the model. The action of G = SO 3,1 is highly nonlinear and given by certainvector fields in [23]. We will demonstrate a new phenomenon for the model comingfrom this nonlinearity with explicit global formulae in the 2D case coming fromSO 2,1 .Finally, a little knowledge can be a dangerous thing and certainly it is possibleto claim any number of nonsensical ‘predictions’ based on an abuse of the mathematics.If one is arguing as a phenomenologist then this does not matter; it doesnot matter where a formula comes from, one can just posit it and see if it fits thedata. However, for a theoretical prediction one must have an actual theory. For thisone has to address the following.• A somewhat complete mathematical framework within which to work (in our case thiswill be NCG).• Is the proposal mathematically consistent?• What are all the physical consequences (is it physically consistent?)Typically in NCG if one modifies one thing then many other things have to bemodified for mathematical consistency (e.g. the Poincaré quantum group does notact consistently on ordinary spacetime). There will be many such issues adopting(24.1) and after that is the interpretation of the mathematics physically consistent?If we suppose that a symbol p 0 in the mathematics is the energy then what elsedoes this imply and is the whole interpretation consistent with other expectations?Or we can suppose that p μ generators in the λ-Poincaré quantum group are thephysically observed 4-momentum and from the deformed Casimir||p|| 2 λ =⃗p2 e λp0 − 2 λ 2 (cosh(λp0 ) − 1) (24.3)claim a VSL prediction but how to justify that? Our approach is to look at noncommutativeplane waves (or quantum group Fourier theory) to at least begin toturn such a formula into a theoretical prediction [1]. The model (24.1) does thenhold together fairly well for scalar or U(1) fields. Spinors in the model remainproblematic and more theoretical development would be needed before predictionsinvolving neutrino oscillations or neutral kaon resonances etc. could haveany meaning.