OPTIMAL MATHEMATICAL MODEL FOR DESCRIPTION OF PHYSICAL PHENOMENA AND TECHNOLOGICAL PROCESSES

Subject of Research. The paper presents an approach that provides a numerical calculation of the absolute uncertainty of the measured physical quantity, which is capable of quantitatively estimating the minimum achievable discrepancy between the developed model and the object under study. The question of achieving a reasonable limit of measurement accuracy in engineering and science remains open, despite the use of powerful computers that take into account a huge number of quantities, and the latest mathematical methods of calculation. Since any physical and mathematical model contains a certain amount of information about the object under research, depending on the quantitative and qualitative set of the selected physical quantities, the optimal number of the chosen quantities must be found. Method. The principles of information theory are used to provide theoretical explanation and justification for the experimental results that determine the accuracy of various fundamental constants. We present the method of choosing a model with the optimal number of quantities considered and calculating the minimum achievable absolute and comparative uncertainties of the measured variable. The amount of information contained in the model is proposed as the criterion of optimality. Main Results. Within the framework of the information approach, the results show that the perfection of devices in physics and engineering is fundamentally limited. The limit of measurement accuracy calculated by the information method is much more stringent than is predicted by the Heisenberg uncertainty relation. The proposed metric provides numerical calculation of the absolute uncertainty, which is capable of quantitatively estimating the difference between the developed model and the object under study. The basic principles of the theory of measurements remain in force, and they can be used separately in the further stage of the specification and computerization of the model. Practical Relevance. The application of comparative uncertainty concept reduces the risk of selecting overestimated indicators of the equipment being designed, gives the possibility to reduce the time and cost of its development. Methodology application for calculating the relative uncertainty according to the information method will reduce significantly the financial costs of improving the International system of SI units.        

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