In his latest post
, Alain Connes comments on the canonical nature of time evolution for noncommutative spaces. In M Theory, the analogue should be a whole heirarchy of Planck constants. For example, the Weyl relations of the quantum torus depend on the parameter $\hbar$. These spaces are studied in a very nice paper
from 1993 by Alan Weinstein, where $\hbar$ is associated to time evolution for a particle on an ordinary torus. The particle is initially concentrated at a point, for $\hbar = 0$, but quickly becomes non-localised.Louise Riofrio
also has many fascinating posts on an emergent thermodynamic Time associated to Planck's number. In M theory we may view this as an approximation to a 3-Time picture, which brings to mind the twistor triality of Sparling
, or the 2-Time
theory of Itzhak Bars. It seems that wherever we look, the canonical Arrow raises its head.