Ioannidis, G. S.Syros, C.Raptis, G.The chrono-topology, as introduced axiomatically in a different context, is also supported by Liouville's theorem of statistical mechanics. It is shown that, if time is quantized, the distribution function (d.f.) becomes real. An elementary solution, g, of the classical Liouville equation has been found in phase-space and time, which can be used to construct any differentiable d.f, F(g), satisfying the same Liouville equation. The conditions imposed on F(g) are reality and additivity. The reality requirement, {Im F(g)=0) quantizes: (i) F(g) and makes it time-independent, (ii). The time variable, (iii) The energy. As a verification of chronotopology, the Planck constant h has been calculated on the basis of the time quantization. The d.f. F(g) becomes, after the time quantization, a real generalized Maxwell-Boltzmann d.f, F(g) = exp[g(p, g; l1,l2,..,lN)], depending on Ν quantum numbers. These facts are significant for quantum theory, because they uncover an intrinsic relationship between Liouville's theorem and quantum mechanics.application/pdfhttps://eproceedings.epublishing.ekt.gr/index.php/hnps/article/view/279810.12681/hnps.2798engHellenic Nuclear Physics Society (HNPS)Πνευματική ιδιοκτησία (c) 2020 C. Syros, G. S. Ioannidis, G. RaptisAnnual Symposium of the Hellenic Nuclear Physics Society2654-00882654-007XAnnual Symposium of the Hellenic Nuclear Physics Society; Τόμ. 9 (1998): HNPS1998; 395-419HNPS Advances in Nuclear Physics; Vol. 9 (1998): HNPS1998; 395-419Liouville's theorem and quantum mechanics - time quantization and realityinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersion2020-02-11Πυρηνική φυσικήNuclear Physicsisi - Physics, Nuclear includes resources on the study of nuclear structure, decay, radioactivity, reactions, and scattering. Resources in this category focus on low-energy physics. High-energy physics is covered in the PHYSICS, PARTICLES & FIELDS category.Άρθρο συνεδρίουConference articleΕπιστημονικό άρθροScientific articleHellenic Nuclear Physics SocietyGreek Aggregator OpenArchives.gr | National Documentation Centre (EKT)other