The "many worlds" approach to quantum physics posits that when one possible subatomic event happens, alternate outcomes that did not occur in this universe have materialized in alternate, diverging universes with their own timelines. The epistemology of this metaphysical notion of the universe is at best horrendously unsound, as anyone who believes that any aspect of physics, quantum or macroscopic, supports this idea of many worlds rooted in diverging events has leapt from one idea to another that does not logically follow from it at all. This non sequitur is blatantly obvious to any sincere, rational thinker, not that any competent. rationalist would ever suppose that a quantum-based multiverse is anything more than one unprovable possibility put of several.
There is also absolutely nothing about quantum physics in particular that makes a "many worlds" concept of the external world a particularly relevant subject. If different possibilities at the subatomic scale branch off into literally different universes with their own diverging quantum events, what about different possibilities at the macroscopic level? Why would there need to be a difference? Thinking about even a single macroscopic example can show just how fallacious any sort of science-based endorsement of the "many worlds hypothesis" always is. Any example would suffice, but the following one has to do with a basic natural phenomena.
A leaf from a given tree might or might not fall within another few moments. Either outcome is logically possible at all times, even if one of them is determined by God or nature to occur at a specific time. It would take the embrace of an enormous non sequitur fallacy to get from recognizing the possibility of a quantum or macroscopic event to believing that each possibility that does not come to fruition takes place in an alternate universe, perhaps in a timeline and cosmos that branches off of something in our universe. Perhaps there are many worlds in such a manner as this, but it is not because it could not have been any other way.
Is it possible for this conception of a multiverse to be true? Yes, but only in the sense that anything that does not contradict the laws of logic is possible. Just as it is possible for the external world to only exist in small fragments as it is perceived or for my own consciousness to be the uncaused cause no matter how much it seems otherwise, it is possible for a specific particle to behave one way in our universe and somehow trigger an alternate behavior, but one still constrained by the same laws of physics present in our universe, in a separate version of the external world.
Logical necessity and logical possibility are distinct from each other and from the epistemologically and metaphysically inferior laws of logic. Possibility alone does not mean something must be true; they mean there is nothing that would logically render a concept or event incapable of being part of reality either as it is or part of reality if non-necessary truths (necessary truths are purely logical truths like logical axioms) had been different. No one is staying where reason brings them if they truly believe, especially based on mere hearsay from scientists, that quantum physics in any way requires, evidences, or proves a multiverse where an event that happens in one universe is at odds with the absence of that event in another universe.
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