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Do you think of reality in terms of different "timelines"?
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Laplace's Demon is just a thought experiment, and has nothing to do with alternate timelines.
Anyway, multiple timelines are definitely not incompatible with our understanding of physics and causality. Look into the many worlds interpretation of quantum mechanics. (in my opinion, the most reasonable explanation of quantum physics)
Why is adding an additional unprovable postulate to quantum mechanics (the universal wave function) and believing we live in an invisible infinite-dimensional infinitely branching multiverse more reasonable than just accepting that quantum mechanics is a time-symmetric theory?
I mean referring to the parallel universe concept. Unless everyone here believes in free will, the thinking goes universes that start out the same are going to play out the same, requiring any differences to be caused by external interference.