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Reading about quantum mechanics, the probability wave is so that a particle can be everywhere. But when observed, it's probability wave collapses and the particle has to take a definite state.

The example were given for Schrödinger's cat, which is either alive or dead only after we open the box to look at it. Other examples could be that the moon might not exist in the sky if no one look at it. Or a tree falling in the forest is not really falling if no one checks it.

What is the power of the observer to dictate a behavior to a quantum particle? In other words, why would the state of dead/alive of Schrödinger's cat materializes only when I look at it while the cover of the box was actually staring at it the whole time?

In the case of the moon, how come it materializes at the same position while there are billions of different of conscious observers? And on top of that, its position is even predictable.

Thanks for any clarification.