Shape in an atom of space: exploring quantum geometry phenomenology

A phenomenology for the deep spatial geometry of loop quantum gravity is introduced. In the context of a simple model of an atom of space, it is shown how purely combinatorial structures can affect observations. The angle operator is used to develop a model of angular corrections to local, continuum flat-space 3-geometries. The physical effects involve neither breaking of local Lorentz invariance nor Planck-scale suppression, but rather only rely on the combinatorics of SU(2) recoupling. Bhabha scattering is discussed as an example of how the effects might be observationally accessible.