On the interpretation of states as non-commutative measures in generalized probabilistic models

FEDERICO HOLIK

CABA

Workshop; International Workshop: Identity, indistinguishability and non-locality in quantum physics; 2017

We discuss generalized probabilistic models for which states do not necessarily obey Kolmogorov?s axioms of probability [1]. This is the case for standard quantum mechanics, where Type I factors are used. Other factors appear in the algebraic formulations of relativistic quantum mechanics and quantum statistical mechanics [2,3]. In this talk we discuss the relationship between properties and probabilistic measures in generalized probabilistic models, and explore some possible interpretations of these measures in terms of a modal ontology of properties [4,5].[1] Holik, F., Saenz, M., Plastino, A.: A discussion on the origin of quantum probabilities. Annals Of Physics 340(1), 293?310 (2014).[2] Halvorson, H., Müger, M.: Algebraic Quantum Field Theory. In: Butterfield, J.B., Earman, J.E. (eds.) Philosophy of Physics, Elsevier, Amsterdam, The Netherlands, pp. 731?922 (2006).[3] Bratteli, O., Robinson, D.W.: Operator Algebras and Quantum Statistical Mechanics: Volumes 1 and 2. Springer, Heidelberg (2012).[4] da Costa, N., Lombardi, O., Lastir, M.: A modal ontology of properties for quantum mechanics. Synthese 190(17), 3671?3693 (2013).[5] Holik, F., Fortin, S., Bosyk, G. and Plastino, A.: On the Interpretation of Probabilities in Generalized Probabilistic Models. J.A. de Barros et al. (Eds.): QI 2016, LNCS 10106, pp. 194?205, Springer, (2017). DOI: 10.1007/978-3-319-52289-0 16.