Abstract
Quantum theory is a probabilistic theory that embodies notoriously striking correlations, stronger than any that classical theories allow but not as strong as those of hypothetical ‘super-quantum’ theories. This raises the question ‘Why the quantum?’—whether there is a handful of principles that account for the character of quantum probability. We ask what quantum-logical notions correspond to this investigation. This project isn’t meant to compete with the many beautiful results that information-theoretic approaches have yielded but rather aims to complement that work.
Similar content being viewed by others
Notes
One of John Wheeler’s ‘Really Big Questions.’
References
Clauser, J.F., Horne, M.A., Shimony, A., Holt, R.A. (1969). Proposed experiment to test hidden variable theories. Physical Review Letters, 23, 880–883.
Einstein, A. (1948). Quanten-mechanik und wirklichkeit. Dialectica, 2, 320–324.
Gleason, A.N. (1957). Measures on the closed sub-spaces of Hilbert spaces. Journal of Mathematics and Mechanics, 6, 885–893.
Jauch, J.M. (1968). Foundations of quantum mechanics. Reading: Addison-Wesley.
Jones, N.S., & Masanes, L. (2005). Interconversion of nonlocal correlations. Physical Review A, 72, 052312–052321.
Kochen, S., & Specker, E.P. (1967). On the problem of hidden variables in quantum mechanics. Journal of Mathematics and Mechanics, 17, 59–87.
Pawłowski, M., Patarek, T., Kaszlikowski, D., Scarani, V., Winter, A., Żukowski, M. (2009). A new physical principle: information causality. Nature, 461, 1101–1104.
Piron, C. (1976). Foundations of quantum physics. New York: W.A. Benjamin.
Popescu, S., & Rhorlich, D. (1994). Quantum nonlocality as an axiom. Foundations of Physics, 24, 379.
Stairs, A. (1983). On the logic of pairs of quantum systems. Synthese, 56, 47–60.
Stairs, A. (1978). Quantum mechanics logic, and reality. PhD dissertation, University of Western Ontario, 19878.
Tsirelson, B.S. (1980). Quantum generalizations of Bell’s inequality. Letters in Mathematical Physics, 4, 93–100.
Varadarajan, V.S. (2006). Geometry of quantum theory. Berlin: Springer.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Stairs, A., Bub, J. Correlations, Contextuality and Quantum Logic. J Philos Logic 42, 483–499 (2013). https://doi.org/10.1007/s10992-013-9272-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10992-013-9272-8