This post is from one PA member to the other.
First, let me be clear that the interpretation problem in quantum theory is a real problem. Schroedinger's wave function does not match with our direct experience of reality. Several very different proposals have been made on how to solve this problem and in my opinion none of them is very convincing.
Furthermore, decoherence does not solve the measurement problem and this is all there is to say about that.
As for the many worlds proposal, the big problem is to get probabilities right but
if one is interested in consistent histories, there are two good papers about it. We read that
"their explanation of the apparent persistence of quasiclassicality relies on assumptions about an as yet unknown theory of experience".
I think this is the key. We don't have a theory of (conscious) experience and therefore there is an interpretation problem even in classical physics, but usually overlooked and well hidden.
Ernst Mach was one of the few who noticed it but he was pushed to the side long ago.
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