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An Intensional Probability Theory: Investigating the Link between Classical and Quantum Probabilities

Author

Listed:
  • Miloš Milovanović

    (Mathematical Institute of the Serbian Academy of Sciences and Arts, 11000 Belgrade, Serbia)

  • Nicoletta Saulig

    (Faulty of Engineering, Juraj Dobrila University of Pula, 52100 Pula, Croatia)

Abstract

The link between classical and quantum theories is discussed in terms of extensional and intensional viewpoints. The paper aims to bring evidence that classical and quantum probabilities are related by intensionalization, which means that by abandoning sets from classical probability one should obtain quantum theory. Unlike the extensional concept of a set, the intensional probability is attributed to the quantum ensemble, which is contextually dependent. The contextuality offers a consistent realization of the measurement problem, which should require the existence of the time operator. The time continuum by Brouwer has satisfied such a requirement, which makes it fundamental to mathematical physics. The statistical model it provides has been proven tremendously useful in a variety of applications.

Suggested Citation

  • Miloš Milovanović & Nicoletta Saulig, 2022. "An Intensional Probability Theory: Investigating the Link between Classical and Quantum Probabilities," Mathematics, MDPI, vol. 10(22), pages 1-16, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:22:p:4294-:d:974774
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    References listed on IDEAS

    as
    1. Antoniou, I. & Gustafson, K., 1999. "Wavelets and stochastic processes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 49(1), pages 81-104.
    2. Misra, B. & Prigogine, I. & Courbage, M., 1979. "From deterministic dynamics to probabilistic descriptions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 98(1), pages 1-26.
    3. Miloš Milovanović & Srđan Vukmirović & Nicoletta Saulig, 2021. "Stochastic Analysis of the Time Continuum," Mathematics, MDPI, vol. 9(12), pages 1-20, June.
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