Abstract
The dynamics of the system in the space of random joint events is considered. The symmetric difference of events is introduced in space based on the Kolmogorov axioms. To describe quantum effects in the dynamics of the system, an additional axiom is introduced for random joint events: “the symmetric sum of random events.” In the generated space of random joint events, an equation is constructed for the probability of a system transition between two events. It is shown that for pairwise joint events it is equivalent to the equation of quantum mechanics.
Highlights
The development of modern information and computer technologies based on quantum theory stimulate its further study from the point of view of probability theory, for example, works [1] - [7], which present original results and reviews in this direction
We propose in this paper a model of the space of joint random events of classical and quantum physics, and equations for the probabilities of transitions between events
The proposed model of joint quantum random events and equations written in the space of these events allows us to describe processes in quantum mechanics, provided that the events are only pairwise compatible
Summary
The development of modern information and computer technologies based on quantum theory stimulate its further study from the point of view of probability theory, for example, works [1] - [7], which present original results and reviews in this direction. We propose to consider stochastic processes in the space of joint random events. The equations for the transition probabilities of systems in these spaces were proposed in [8] - [11]. We propose in this paper a model of the space of joint random events of classical and quantum physics, and equations for the probabilities of transitions between events. It is shown that the proposed equations for the probabilities of stochastic processes in the space of joint events, in the case when the events are only pairwise compatible, describe the dynamics of quantum processes
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