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Some say that in the near future, it might become possible to accurately model currently complex things given sufficient computer advances . Assume then a very powerful computer that might be available within the next 100 years. Say like a big quantum computer or an iPhone 108 model.

Now we fire a single electron from a very accurate gun into an atom with it's orbiting electrons. Could we accurately predict the trajectory of the electron through and out of the atom, whether it hits another electron or not?

There is Is the universe fundamentally deterministic?, however it's a bit broad (Universe). More specifically though doesn't include the word electron anywhere in any of the answers. It would cover throwing dice too...

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At the specific scale of an atom's nucleus's radius, QM effects are significant. In fact it is QM that makes the periodic table look the way it does. So we need QM.

Computing power isn't really the root of indeterminism in QM, Heisenberg Uncertainty is. The uncertainties of incompatible quantities (position and momentum, energy and time, etc) are always h bar/2 no matter what technology we have. https://en.wikipedia.org/wiki/Uncertainty_principle Why this is the case is still an open question.

Local Hidden Variable theories (the idea that QM is not complete and we just need to find some other variables or perform better measurements) are no-go.https://en.wikipedia.org/wiki/No-go_theorem So there are only two possibilities for a deterministic universe: Superdeterminism, and breaking locality. Superdeterminism means everything is deterministic including us and our thoughts, locality - things can't travel faster than the speed of light and interact smoothly (in the technical sense) via fields. So yes, the universe could be deterministic, but then you have to believe all of it, including us is deterministic or break locality. https://en.wikipedia.org/wiki/Bell%27s_theorem

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