Interrelation Between the Fractional Dimensions of Measurands and Fractal Dimensions

The article examines the possibility of an informal relationship between the two concepts of dimensions — dimension of the measurand and the fractal dimension of objects, specifically in relation to the fractional dimension. Measurement results having nonzero type I and II error probabilities can be considered as external impact when comparing the measurand with measures. From the perspective of quantum theory, it is impossible to reliably predict the measurement outcome (only the probability of the outcome) since the object is affected by the measuring instrument (scale nonuniformity). The fractional dimensions of units of electrical and magnetic quantities exist in the CGS system of units (centimeter, gram, second). Noninteger, including fractional, fractal dimensions are observed when considering the structure of complex nonlinear objects. The commonality of the two different concepts of dimension lies in the measurement procedure in both definitions. It is shown that the relationship between the fractional dimensions of measurands and fractal dimensions is manifested as a result of representing the measurement process in the form of a generalized impact characterizing the interaction of objects. The obtained results can be used to expand the application of the fractal approach in measurement practice.