On Mon, Apr 24, 2017 at 10:38:51PM -0700, Brent Meeker wrote: > > > On 4/24/2017 7:49 PM, Russell Standish wrote: > >On Mon, Apr 24, 2017 at 07:12:38PM -0700, Brent Meeker wrote: > >> > >>On 4/24/2017 2:15 AM, Bruno Marchal wrote: > >>>>This world is 'objective' in the sense that there is > >>>>intersubjective agreement about it. > >>>That happens in multi-user video games, and all the multi-user > >>>games are implemented by all universal numbers, with all players > >>>in arithmetic. The only problem is the relative measure, but we > >>>have already that the measure one obeys a quantum logic. > >>How do we "have" that? Can you derive, from computationalism, that > >>the description of the world must be in terms of vectors in a > >>complex Hilbert space? > >> > >I looked into that claim, so maybe I can offer a different > >perspective. Quantum logics are the logic of events in a complex > >Hilbert space that have probability 1, ie the logic of Hilbert > >subspaces. For example, if x is the statement that the system is in > >subspace X and y the statement that the system is in subspace Y, we > >can speak of x∧y being the statement that the system is in the > >subspace X∩Y, and x∨y being the statement that the system is in X⊕Y > >(X∪Y is not a subspace). It turns out that these logics (apparentally > >a family of them, all quite distinct from classical logic) satisfy the > >same axioms as Z and X, modal logics describing two of Bruno's hypostases > >(that of the believer and the observer IIRC). > > If you can explain why the state of systems should be described by > vectors in a complex Hilbert space, the derivation of Born's rule > might follow from Gleason's theorem. >
Bruno's theory does not (at best it is somewhat compatible). The derivation I came up with (published in "Why Occam's Razor, and also appendix D of "Theory of Nothing") does show why the state of systems should be described by a Hilbert space - the only issue being why a complex field, and not some more general measure, such as quaternions. The derivation of Born's rule also appears in that appendix - it appears to be independent of Gleason's theorem. Cheers -- ---------------------------------------------------------------------------- Dr Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders Visiting Senior Research Fellow [email protected] Economics, Kingston University http://www.hpcoders.com.au ---------------------------------------------------------------------------- -- 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 [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
