Whence comes the experience of a present moment?

The after-the-fact processing done by the brain of the data accumulated in that moment, of course.

If that storage is disrupted - by sudden trama or an experiential shock, such as that which might occur in a car accident without leaving lasting damage - there are no experiences at all.

If there are no lasting consequences of an event that our physiology can react to, it's as though it never happened at all, at least as far as our awareness is concerned. If you have no high-level memory representation of an event, and no low-level physiological response resulting from it, as far as you're concerned it didn't happen.

Understanding this is key to recognizing how coherent perceptions arise from the utter chaos of the Library.