Abstract
In recent years, within the framework of the relational approach to the description of space-time and physical interactions, a number of studies have been carried out to substantiate the observed cosmological effects. In particular, it has been shown that the cosmological redshift described by the linear part of the Hubble law and the cosmic microwave background can be the result of contributions from emitted but not absorbed electromagnetic radiation. To describe the nonlinear part of the Hubble law, a logarithmic coordinate transformation was used, associated with the existence of a limiting observed distance, expressed by the gravitational radius of the observable Universe. The use of such a transformation must be justified by showing how it can be obtained in the derivation of space-time concepts for a system of a large number of emitters and absorbers. The article provides this rationale: it is shown that when deriving classical distances in the relational approach, there are two possibilities for determining the distance scale, they correspond to the scales of comoving and proper distances in cosmology, while the scale factor is expressed through the partition function of the configurations of emitters and absorbers.
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