In the quest for a mathematical model, which could be a suitable tool to describe the geometry of small scale physics (or quantum gravity physics) one encounters noncommutative geometry. Though mathematically very attractive and physically well motivated these models lead to serious problems when considered in the physical, pseudoriemannian setup. The main one is how to define events and causality when we are dealing with "spaces" without points and the "time" itself might be noncommutative.
This lecture was delivered during the 16th Kraków Methodological Conference "The Causal Universe", May 17-18, 2012.
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