Some people, motivated by category theory and traditional NC geometry, still seem to believe that ordinary $C^{*}$ algebras are the key to quantum gravity, despite their clear inadequacy as a basis for constructive number theory. As we have seen, non associative Jordan algebras are much closer to the physical requirements of quantum topology, best described using braided structures for categories.
The fact that quantum mechanics is well enough described using symmetric structures is a poor argument for ignoring braidings, given that quantum gravity cannot be an ad hoc concoction of QM and causality a la GR. This fact is remarkably underappreciated in the social industry of academic paper mills. Any decent CERN theorist, or topological quantum field theorist, knows that braid diagrams are ubiquitous in modern twistorial techniques for perturbative supergravity, and are unlikely to disappear in the non perturbative regime, if diagram techniques have any power at all.
14 years ago
I once heard a Fields Medallist (not a physicist) say that symmetric structures are where it is at ... but you see, at that time planar operads were the coolest things around and $4$-categories the most sophisticated idea with physical applications. Now note that twistorial gravity requires $6$-categories, which we begin to investigate with braided structures, albeit adding a third product structure and imagining three singular levels beneath the braided surfaces (ribbons).
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