By Sandro Sozzo, Claudio Garola, Arcangelo Rossi
This quantity offers a special review of modern Italian experiences at the foundations of quantum mechanics and similar ancient, philosophical and epistemological themes. a meeting of students from diversified cultural backgrounds, the convention supplied a discussion board for a desirable alternate of rules and views on more than a few open questions in quantum mechanics. the various nature of the papers during this quantity attests to the success of that target with many contributions supplying unique options to demonstrated difficulties by way of bearing in mind concepts from diversified disciplines.
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Extra info for The Foundations of Quantum Mechanics: Historical Analysis And Open Questions, Cesena 2004
Example text
3 of Sec. 1 and in its explanation). Then, with WA= {WA= trs(V(Ws® WA)V*) | Ws G WHS} and with reference to Propositions 1 and 2 respectively, we say that: • (final) (quantum) component system semibooleanity (semimacroscopicity, objectivity) is satisfied (by the External Quantum Model) whenever LTA expresses a semiboolean structure for (HA,W ); • (final) (quantum) component system Booleanity (macroscopicity) is satisfied (by the External Quantum Model) whenever LTA expresses a Boolean structure for (HA,\V ) , that is, equivalently, the mapping i —> IIAei — an identification — an identification — an inclusion (troughp^ enables e Lr = LJJAH, Wr« = WIJAC, W C Wr» = ZiPFSi ~^WA = ^pf*UA%).
The aim of this section is to try to display the basic concepts that are needed in a careful, but not formalized way. 25 We refer to the usual framework within which theoretical physicists develop any treatment using observables and states only. Concerning Quantum Theory, to simplify matters, we restrict the set of the observables to the set (lattice) of the "attributes", and we identify this (observational) set with the set (lattice) V(H) of the orthogonal projectors in the relevant Hilbert space H.
For its elements. The set £(S) carries the natural ordering a < & O- a(a) < b(a) for every a £ S, as well as a notion of partial addition: if 0 < a(a) + b(a) < 1 for every a £ S then the function S 3 a -»• a(a) + b(a) is again an effect, denoted a + b, and called the (partial) sum of a and b. Two effects are said to be orthogonal when their sum exists. The mentioned algebraic structure of £ (S), that fits the notion of effect algebra [7,8], makes it possible to define effect-valued measures (EV measures).