PIRSA:12080007 Scientific Series Mathematical physics

DOI10.48660/12080007

Series: Quantum Foundations

Ududec, C. (2012). The closest cousins of quantum theory from three simple principles. Perimeter Institute. https://pirsa.org/12080007

Ududec, Cozmin. The closest cousins of quantum theory from three simple principles. Perimeter Institute, Aug. 07, 2012, https://pirsa.org/12080007 

@misc{ pirsa_PIRSA:12080007,
  doi = {10.48660/12080007},
  url = {https://pirsa.org/12080007},
  author = {Ududec, Cozmin},
  keywords = {Mathematical physics},
  language = {en},
  title = {The closest cousins of quantum theory from three simple principles},
  publisher = {Perimeter Institute},
  year = {2012},
  month = {aug},
  note = {PIRSA:12080007 see, \url{https://pirsa.org}}
}

Abstract

A very general way of describing the abstract structure of quantum theory is to say that the set of observables on a quantum system form a C*-algebra.  A natural question is then, why should this be the case - why can observables be added and multiplied together to form any algebra, let alone of the special C* variety?  I will present recent work with Markus Mueller and Howard Barnum, showing that the closest algebraic cousins to standard quantum theory, namely the Jordan-algebras, can be characterized by three principles having an informational flavour, namely: (1) a generalized spectral decomposition, (2) a high degree of symmetry, and (3) a requirement on conditioning on the results of observations.   I'll then discuss alternatives to the third principle, as well as the possibility of dropping it as a way of searching for natural post-quantum theories.

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