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SUMMARY:The Bohrification of quantum logic - Klaas Landsman (Nijmegen)
DTSTART:20090403T130000Z
DTEND:20090403T140000Z
UID:TALK17695@talks.cam.ac.uk
CONTACT:Lawrence Ioannou
DESCRIPTION:A decade ago\, Isham and Butterfield proposed a topos-theoreti
 c approach to quantum mechanics\, which meanwhile has been extended by Doe
 ring and Isham so as to provide a new mathematical foundation for all of p
 hysics. Last year\, the speaker with Heunen and Spitters  redeveloped and 
 refined these ideas by combining the C-star-algebraic approach to quantum 
 theory with the so-called internal language of topos theory (see arXiv:070
 9.4364). The goal of the present talk (based on arXiv:0902.3201) is to ill
 ustrate our abstract setup through the concrete example of the C-star-alge
 bra M_n(C) of complex n x n matrices. In our approach\, the  nondistributi
 ve lattice  of projections  in M_n(C) (which forms the basis of the  tradi
 tional quantum logic of Birkhoff and von Neumann) is replaced by a specifi
 c distributive lattice\, whose elements correspond to 'Bohrified' proposit
 ions\,  in the sense that  to each  classical context  it associates a yes
 -no question (rather than being a single projection\, as in standard quant
 um logic). Distributivity is recovered at the expense of the law of the ex
 cluded middle\, whose demise is in our opinion to be welcomed\, not just i
 n intuitionistic logic in the spirit of Brouwer\, but also in quantum logi
 c  in the spirit of von Neumann.
LOCATION:MR14\, Centre for Mathematical Sciences
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