I'm not sure what you mean. Isn't the "world we see" a subset of our awareness? Isn't it impossible by definition to know something outside of our awareness?
By reason, there has to be events occurring external to one's awareness. For example, something has to be responsible for the perception of change. As Paul said, we go away for a week and the grass has grown - since I wasn't conscious of this change in between, something external to my awareness dictated that difference. Even if it is in my own head, something keeps track of those differences.
Athon