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Cyan comments on Open Thread: February 2010 - Less Wrong
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If I understand the Many-Worlds Interpretation of quantum mechanics correctly, it posits that decoherence takes place due to strict unitary time-evolution of a quantum configuration, and thus no extra collapse postulate is necessary. The problem with this view is that it doesn't explain why our observed outcome frequencies line up with the Born probability rule.
Scott Aronson has shown that if the Born rule doesn't hold, then quantum computing allows superluminal signalling and the rapid solution of PP-complete problems. So we could adopt "no superluminal signalling" or "no rapid solutions of PP-complete problems" as an axiom and this would imply the Born probability rule.
I wanted to ask of those who have more knowledge and have spent longer thinking about MWI: is the above an interesting approach? What justifications could exist for such axioms? (...maybe anthropic arguments?)
ETA: Actually, Aronson showed that in a class of rules equating probability with the p-norm, only the 2-norm had the properties I listed above. But I think that the approach could be extended to other classes of rules.
Non-Born rules give us anthropic superpowers. It is plausibly the case that the laws of reality are such that no anthropic superpowers are ever possible, and that this is a quickie explanation for why the laws of reality give rise to the Born rules. One would still like to know what, exactly, these laws are.
To put it another way, the universe runs on causality, not modus tollens. Causality is rules like "and then, gravity accelerates the bowling ball downward". Saying, "Well, if the bowling ball stayed up, we could have too much fun by hanging off it, and the universe won't let us have that much fun, so modus tollens makes the ball fall downward" isn't very causal.
This reminds me of an anecdote I read in a biography of Feynman. As a young physics student, he avoided using the principle of least action to solve problems, preferring to solve the differential equations. The nonlocal nature of the variational optimization required by the principle of least action seemed non-physical to him, whereas the local nature of the differential equations seemed more natural.*
I wonder if there might not be a more local and causal dual representation of the principle of no anthropic superpowers. Pure far-fetched speculation, alas.
* If this seems vaguely familiar to anyone, it's because I'm repeating myself.