Thought for the day:
Neils Bohr once challenged Albert Einstein to prove that the moon exists when no-one is observing it, after Einstein asked him whether he could really believe that it doesn't.
I don't have the math chops to do it. But, I believe it can be shown that for the Moon to not exist except when being observed would violate local causality. This is because the Moon is approximately 1.25 light-seconds away, and thus in order to be observable, the Moon would have to consistently begin existing at least 1.25 seconds before being observed.
(There is also a problem with the fact that the Moon exists in a specific, definable location, implying that it has independent existence even when not being observed. If we could call the moon into being simply by observing it, why can't we just observe it anywhere we choose, at any moment that the whim takes us? The simple fact that we can only observe the Moon "where it is" argues rather strongly that it, in fact, is.)