what do you mean by the term information?
My question is, rather, whether a system needs to be able to know it knows that information for it not to still be causal. Because it doesnt observe its whole wavefunction
Imagine, for simplicty sake, a world is a series of four switches which we can describe by 0 (off),1 (on).
Eg., world A at time 0 is 0000, at time 1, 0001, ...
Now a change from 0000 to 0001 is causal if in every physically possible world 0001 follows 0000, ie., P(0001|0000) = 1
Now suppose that we enumerate every possible world, ie., all the worlds containing only this kind of switch, and only four of them.
Now if 40% of the worlds had 0000->0001 and 60% had 0000->1000, then P(0001|0000) = 0.4
The question is how can it be that the fourth switch behaves randomly? Ie., without any necessary flip from 0 to 1. Nothing at all can cause that switch to flip, by definition, the world contains nothing else in it.
What property does the switch have such that it turns on 40% of the time? NONE.
Consider two resolutions to this problem: bite the bullet and say the switch is "miraculous in some sense" in that it "just turns on" sometimes; OR, say that this thought experiment is physically impossible and we're missing information.
Eg., that there's a hidden switch: 10000->10001 always, and 00000->11000 always, we just can't see the first switch, so it looks random.
If that's what the world is then there's no "we"