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There are a couple "interpretations" of QM in which there is no probability distribution.

One is the "Many Worlds" interpretation. (AKA, the Everett interpretation.) In this QM wave functions never collapse, and the only reason that we perceive there to be probability distributions is that the lack of collapse results in many different apparent worlds. Though in reality, there is really just one very big complicated world, but the difference parts of it stop effecting each other via a property called "decoherence".

Another deterministic interpretation is the Bohm interpretation, in which the particles are push around by a "pilot wave", which is the same wave function that never collapses in the Many Worlds interpretation. Since the "pilot waves" never collapse in the Bohm interpretation, one might wonder, then why you don't also end up with many worlds here too, but it is taken that the reality that we perceive is always determined by the particles that are being pushed around by the pilot waves.

One point of interest is that the Many Worlds interpretation and the Bohm interpretation are experimentally indistinguishable from each other.

Regarding the postulation of a multiverse, this is almost certainly true, if you ask me. It would seem to be the only way to explain the apparent "fine tuning" of the universe. Unless you believe that it was tuned by God, that is. But if that's the case, I have a few nits to pick with some of the choices that he or she made.



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