On 22 Feb 2013, at 04:10, Joseph Knight wrote:
Question: Why is the "derivation"* of the Born Rule in (Everett, 1957) not considered satisfactory**?
Good question. I asked it myself very often.
*Everett shows that the amplitude-squared rule for subjective probability is the only measure consistent with an agreeable additivity condition.
And that was shown by Paulette Destouches-Février some decade before. My study of Gleason's theorem (in Richard Hugues's book, Harvard press) convinced me, at that time, that the Born rule follows indeed from the formalism + a version of comp first person indeterminacy (implicit in Everett, I think). Given the time made by some people to grasp that first person indeterminacy, or even just the notion of first person in the comp setting, maybe the problem relies there. Wallace is close to this, though.
**It is apparently not satisfactory because there have been multiple later attempts to derive the Born Rule from certain other (e.g., decision-theoretic) assumptions in an Everett framework (Deutsch, Wallace). I have not yet studied these later works so cannot yet comment on them (but would appreciate any remarks/opinions that Everything-listers have to offer).
I did study them, but I think I miss something as I think that Everett, in his long paper (thesis) is more convincing, especially in quantum computing where high dimensional Hilbert Space is required. Gleason theorem requires three dimension at least. Now comp requires an arithmetical quantum logic on which "a Gleason theorem" should be working, and up to now, it looks like this is quite plausible, and then we got both the wave and the Born rule from arithmetic alone.
Bruno http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to firstname.lastname@example.org. Visit this group at http://groups.google.com/group/everything-list?hl=en. For more options, visit https://groups.google.com/groups/opt_out.