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Refinement of Adaptive Dynamical Simulation of Quantum Mechanical Double Slit Interference Phenomenon

Journal of Modern Physics 2024年第3期15卷 239-249页

作者： Tadashi Ando andrei khrennikov.ichiro yamato Department of Applied Electronics Tokyo University of Science Tokyo Japan International Center for Mathematical Modelling in Physics and Cognitive Sciences Linnaeus University V&aumlxj&oum Sweden Department of Biological Science and Technology Tokyo University of Science Tokyo Japan

We applied adaptive dynamics to double slit interference phenomenon using particle model and obtained partial successful results in our previous report. The patterns qualitatively corresponded well with experiments. Several properties such as concave single slit pattern and large influence of slight displacement of the emission position were different from the experimental results. In this study we tried other slit conditions and obtained consistent patterns with experiments. We do not claim that the adaptive dynamics is the principle of quantum mechanics, but the present results support the probability of adaptive dynamics as the candidate of the basis of quantum mechanics. We discuss the advantages of the adaptive dynamical view for foundations of quantum mechanics.

关键词： Double Slit Interference Adaptive Dynamics Quantum Mechanics Particle Model Simulation

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NON-ARCHIMEDEAN PROBABILITY: FREQUENCY AND AXIOMATICS THEORIES

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Acta Mathematicae Applicatae Sinica 1996年第1期12卷 77-92页

作者： andrei khrennikov(Department of High Mathematics, Moscow Institute of Electronic Engineering,103498, Moscow, K-498, Russian) Department of High Mathematics Moscow Institute of Electronic Engineering Moscow K-498 Russian

We propose a new theory of probability based on the general principle of the statistical stabilization of relative frequencies. According to this principle it is possible to consider the statistical stabilization not only with respect to the standard real topology on the field of rational numbers Q but also with respect to an arbitrary topology on Q. The case of p-adic (and more general non-Archimedean) topologies is the most important. Our frequency theory of Probability is a fruitful extension of the frequency theory of R. von Mises[18]. It's well known that the axiomatic theory of Kolmogorov uses the frequency theory as one of the foundations. And a new general frequency theory can be considered as the base for the general axiomatic theory of probability (Kolmogorov's theory is a particular case of this theory which corresponds to the real topology of the statistical stabilization on Q). The situation in the theory of probability becomes similar to that in modern geometry. The Kolmogorov axiomatics (as the Euclidean) is only one of the possibilities, and we have generated a great number of different non-Kolmogorov theories of *** applications to p-adic quantum mechanics and field theory are considered.

关键词： Frequency theory of probability of von Mises non-Kolmogorovean probability models p-adic numbers p-adic probabilities

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