Nonassociative operators probably have some subtle role that is different from what we currently understand. We might think of this as similar to noncommutative operators in quantum physics. Prior to the physical bais for quantum mechanics such structures had a limited role in classical mechanics. The only role they had was with angular momentum and related systems. It was with quantum mechanics the notion of [x, p] = iħ made physical sense. Then of course came spinors and then quaterionons and Clifford algebras. I think there is some underlying physics which is required to make sense of nonassociativity. The approach with G_2 I advocate here does not by itself impose nonassociativity onto physics, but is a way I think that S-matrix theory according to holography can be formulated.
Nonassociativity I think might emerge in the following way. The holographic principle or black hole complementarity exists on the basis that an asymptotic observer watches a string approach an event horizon in a way very differently from what an infalling observer records. The distant asymptotic observer records the string to time dilate and spread across the horizon. The transverse modes of the string slow down for a string with a tension T, and as a result appear to lengthen. Of course the infalling observer sees nothing like this as the string passes the event horizon. The holographic appearance of the string is worked on the tortoise coordinates
r* = r - 2m ln(|1 - 2m/r|)
which means the S-matrix theory (which is what string are) is on a domain of causal support appropriate for S-matrix theory. The infalling observer observes the string on a different causal domain. This means the two observers detect string physics on incommensurate bases of states.
The S-matrix theory is really a system of braids, knot theory, or Yang-Baxter equations. If there are two different causal domains with S-matrix theory over incommensurate states, this means there are two braid systems which are not related to each other by the Reidmeister operations of a braid group. So there is some sort of map m:g - ->g', between two quantum groups (braid groups), which is such that g'g^{-1} is not a unit. So the map requires there to be an additional element A such that g'A(e)g^{-1} = 1, and the information preserving aspects of quantum theory are preserved. The symbol A(e) acts on an associator ~ g(eg^{-1}) - (ge)g^{-1} to give a unit. The braid g - - g ( or elements a - - b for a & b in g) is extended to an associator g - - g" - -g', here g" = e, with a homotopy structure. This is a bit cryptic here, but the idea is that associative QM is a system which intertwines braids, or quantum groups.
The G_2 group that I am working with is a system of three forms on M^7, and this is a holonomy involved with brane wrappings and AdS/CFT. In this way I think that nonassociative structures might be shown to exist in quantum gravity.
Cheers LC