Unfortunately, physicists and philosophers disagree on what exactly the preferred basis problem is, what would constitute a solution, and how this relates (or subsumes) “the measurement problem” more generally. In my opinion, the most general version of the preferred basis problem was best articulated by Adrian Kent and Fey Dowker near the end their 1996 article “On the Consistent Histories Approach to Quantum Mechanics” in the Journal of Statistical Physics. Unfortunately, this article is long so I will try to quickly summarize the idea.
Kent and Dowker analyzed the question of whether the consistent histories formalism provided a satisfactory and complete account of quantum mechanics (QM). Contrary to what is often said, consistent histories and many-worlds need not be opposing interpretations of quantum mechanics Of course, some consistent historians make ontological claims about how the histories are “real”, where as the many-world’ers might say that the wavefunction is more “real”. In this sense they are contradictory. Personally, I think this is purely a matter of taste.a . Instead, consistent histories is a good mathematical framework for rigorously identifying the branch structure of the wavefunction of the universe Note that although many-worlders may not consider the consistent histories formalism the only way possible to mathematically identify branch structure, I believe most would agree that if, in the future, some branch structure was identified using a completely different formalism, it could be described at least approximately by the consistent histories formalism. Consistent histories may not be perfect, but it’s unlikely that the ideas are totally wrong.b . Most many-world’ers would agree that unambiguously describing this branch structure would be very nice (although they might disagree on whether this is “necessary” for QM to be a complete theory).… [continue reading]