Authors: Milovanović, Miloš 
Saulig, Nicoletta
Affiliations: Mathematics 
Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: An Intensional Probability Theory: Investigating the Link between Classical and Quantum Probabilities †
Journal: Mathematics
Volume: 10
First page: 4294
Issue Date: 2022
Rank: ~M21a
ISSN: 2227-7390
DOI: 10.3390/math10224294
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.
Keywords: measurement problem | quantum ensemble | quantum state | time continuum | time operator
Publisher: MDPI

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