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SUMMARY:Quantum theory from simple physical principles for single systems 
 - Howard Barnum (University of New Mexico)
DTSTART:20150305T141500Z
DTEND:20150305T151500Z
UID:TALK57643@talks.cam.ac.uk
CONTACT:William Matthews
DESCRIPTION:We describe simple physically and informationally meaningful p
 rinciples that give rise to the quantum description of finite-dimensional 
 systems terms of density matrices and positive operator-valued measures.\n
 \nThe first three principles characterize finite dimensional formally real
  Jordan-algebraic systems: real\, complex\, and quaternionic quantum theor
 y\, plus systems whose state spaces are balls\, and one exceptional\ncase.
  The principles are (1) a generalized spectral decomposition\, (2) a high 
 degree of symmetry\, and (3) that there is no irreducible three (or more) 
 path interference.  We'll explore the physical\nimplications of the princi
 ples\, individually and in various combinations.\n\nComplex quantum theory
  then follows from "local tomography": that the state of a composite syste
 m be determinable from the statistics (including correlations) of local ob
 servables.  But one may obtain quantum theory without considering composit
 e systems\, by requiring (4)\n"energy observability": the generators of re
 versible dynamics are observables.\n\nDropping (3) might allow systems enj
 oying many properties of quantum physics\, but exhibiting higher-order int
 erference\; we'll discuss properties of such theories\, in particular whet
 her they support good notions of entropy and a reasonable statistical mech
 anics\, and whether they are possible candidates for new physics encompass
 ing quantum theory as a limiting case.\n\nTime permitting\, the possibilit
 y and properties of composites of systems satisfying (1-3) (Jordan-algebra
 ic systems) will be discussed.
LOCATION:MR4\,  Centre for Mathematical Sciences\, Wilberforce Road\, Camb
 ridge
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