Hi all, the question goes primarily to Bruno but all other input is welcome :-))

Bruno, you said you have already arrived at a quantum logic in your technical work? May I refer to the following two paragraphs?: We can read here: http://plato.stanford.edu/entries/qt-quantlog/ The Reconstruction of QM From the single premise that the “experimental propositions” associated with a physical system are encoded by projections in the way indicated above, one can reconstruct the rest of the formal apparatus of quantum mechanics. The first step, of course, is Gleason's theorem, which tells us that probability measures on L(H) correspond to density operators. There remains to recover, e.g., the representation of “observables” by self-adjoint operators, and the dynamics (unitary evolution). The former can be recovered with the help of the Spectral theorem and the latter with the aid of a deep theorem of E. Wigner on the projective representation of groups. See also R. Wright [1980]. A detailed outline of this reconstruction (which involves some distinctly non-trivial mathematics) can be found in the book of Varadarajan [1985]. The point to bear in mind is that, once the quantum-logical skeleton L(H) is in place, the remaining statistical and dynamical apparatus of quantum mechanics is essentially fixed. In this sense, then, quantum mechanics — or, at any rate, its mathematical framework — reduces to quantum logic and its attendant probability theory. And here we read: http://en.wikipedia.org/wiki/Gleason%27s_theorem Quantum logic treats quantum events (or measurement outcomes) as logical propositions, and studies the relationships and structures formed by these events, with specific emphasis on quantum measurement. More formally, a quantum logic is a set of events that is closed under a countable disjunction of countably many mutually exclusive events. The representation theorem in quantum logic shows that these logics form a lattice which is isomorphic to the lattice of subspaces of a vector space with a scalar product. It remains an open problem in quantum logic to prove that the field K over which the vector space is defined, is either the real numbers, complex numbers, or the quaternions. This is a necessary result for Gleason's theorem to be applicable, since in all these cases we know that the definition of the inner product of a non-zero vector with itself will satisfy the requirements to make the vector space in question a Hilbert space. Application The representation theorem allows us to treat quantum events as a lattice L = L(H) of subspaces of a real or complex Hilbert space. Gleason's theorem allows us to assign probabilities to these events. END QUOTE So I wonder - how much are you still missing to construct QM out of the logical results you have arrived at? Best Wishes, Günther --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-l...@googlegroups.com To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~----------~----~----~----~------~----~------~--~---