Probability in Theories With Complex Dynamics and Hardy’s Fifth Axiom
L. Hardy has formulated an axiomatization program of quantum mechanics and generalized probability theories that has been quite influential. In this paper, properties of typical Hamiltonian dynamical systems are used to argue that there are applications of probability in physical theories of systems with dynamical complexity that require continuous spaces of pure states. Hardy’s axiomatization program does not deal with such theories. In particular Hardy’s fifth axiom does not differentiate between such applications of classical probability and quantum probability.
KeywordsProbability Complex dynamics Axiomatization
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- 1.Dakić, B., Brukner, Č.: Quantum theory and beyond: is entanglement special? arXiv:0911.0695v1 [quant-ph]
- 6.Hardy, L.: Quantum mechanics from five reasonable axioms. arXiv:quant-ph/0101012
- 7.Hardy, L.: Why quantum theory? In: Butterfield, J., Placek, T. (eds.): Proceedings of the NATO Advanced Research Workshop on Modality, Probability and Bell’ s Theorem, pp. 61–73. IOS, Amsterdam (2002) Google Scholar
- 9.Schack, R.: Quantum theory from four of Hardy’s axioms. arXiv:quant-ph/0210017v1
- 10.Duck, I.: Discovering quantum mechanics one again. arXiv:quant-ph/0307121v1
- 12.Abraham, R., Marsden, J.E.: Foundations of Mechanics. Benjamin/Cummings, New York (1980) Google Scholar
- 17.Landsman, N.P.: Mathematical Topics Between Classical and Quantum Mechanics. Springer, New York (1998) Google Scholar