Can Everettian Interpretation Survive Continuous Spectrum?

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Kim, Minseong
preprint description
This paper raises a simple continuous spectrum issue in many-worlds interpretation of quantum mechanics, or Everettian interpretation. I will assume that Everettian interpretation refers to many-worlds understanding based on quantum decoherence. The fact that some operators in quantum mechanics have continuous spectrum is used to propose a simple thought experiment based on probability theory. Then the paper concludes it is untenable to think of each possibility that wavefunction $\Psi \rangle$ gives probability as actual universe. While the argument that continuous spectrum leads to inconsistency in the cardinality of universes can be made, this paper proposes a different argument not relating to theoretical math that actually has practical problems.