Despite the success of the standard model Lagrangian (SM), the set of gauge theories consistent with current experimental constraints remains very large. It is a striking fact therefore that the SM is also a member of a much more restricted set of gauge theories that may be reinterpreted as arising from non-commutative geometry (NCG) in the sense of Connes. This fact raises the intriguing possibility of using the `geometry' of the fundamental constituents of matter to direct future experimental and cosmological searches for standard model extensions. Despite generating enormous interest however, many physicists are skeptical of this approach because: (i) NCG relies on a long list of axioms whose meaning is obscure to them; (ii) the NCG construction of spacetime and the laws of nature relies on a fishy step where several terms must be set to zero, essentially by hand, to get the desired result; and (iii) NCG predicts an incorrect mass for the Higgs. In attempting to further generalize NCG, I along with my supervisor Latham Boyle stumbled upon a reformulation of Connes ideas which, remarkably, fixes all three of these problems. With this improvement, Connes' approach becomes a tight and explanatory paradigm for exploring the underlying structure of spacetime.
For more information see: http://arxiv.org/abs/1408.5367, http://arxiv.org/abs/1401.5083 , and http://arxiv.org/abs/1303.1782 .