Do parallel universes exist?
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This means there are infinitely many "parallel universes": cosmic patches exactly the same as ours (containing someone exactly like you), as well as patches that differ by just one particle's position, patches that differ by two particles' positions, and so on down to patches that are totally different from ours.
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The notion of "existence" should be accurately defined to make this question meaningful. For example, if something is not directly observable in principle; does it mean that this "something" does not exist (quark is a good example). Once you have an experiment and some theory explains accurately the result of this experiment plus, the same theory allows to predict the result of new experiment better then others competing theories then the wining theory approximates underling reality better; in this regards, Quantum mechanic is one of the most successful theories and in its pure form without extra assumptions or/and interpretations (such as collapse of wave function) it does tell that macro objects are not different from elementary particles therefore both Schrödinger's cats are equally real; thus the time is not one-dimensional but constantly branching realizations/evolution of observer. Quantum Universe does not split it remains in superposition state just it is not the Universe we used to consider as such it is a way more complex structure... Thus, how meaningful to ask if Hamiltonian in quantum mechanic "exists" - well, apparently it exists