No 2 (2020)

We discuss a quantum description of free particles in pseudo-Finslerian momentum spaces appearing in one of relational approaches to physics and geometry of space-time. It is shown that, for wave functions of such particles, we can define an invariant unitary scalar product which ensures the standard quantum mechanical probabilistic interpretation. As the simplest example, the description of a spinless particle is considered.

A model of physical space-time in the form of a trace from a random walk on the support of some finitely generated algebra is considered. The generating set of elements is considered as a set of initial events of the physical world, and all points generated by wandering are interpreted as their consequences. The special properties of such a model allow us to obtain interesting conclusions about the possible causes of the pseudo-Euclidean metric of our world and its 3 + 1 dimension. Such effects as the expansion of the Universe with low acceleration, gravitational deformation of the metric and the superposition of the states of quantum particles get their explanation. There is an effect of duality of the description of physical interactions as long-range or short-range interaction.

The consequences of the Wheeler hypothesis that bits are the primary elements of the universe are considered, provided that it is true. An information model of the universe should be created, as a hierarchy of information models of phenomena, which should be based on a single information theory of the microworld. The information model of the universe is relational from a physical point of view and idealistic from a philosophical one. According to a minimal assessment, the performance of a proton, as an information processing process, is comparable to the most powerful supercomputers, which gives an idea of the informational complexity of phenomena. To build information models of complex phenomena, it is necessary to develop a concept of the meaning of information as a physical characteristic. Physics develops along the path of identifying and analyzing elementary cause-effect relationships. The development of systems for working with big data opens up an alternative opportunity to study complex correlations and cause-effect relationships of phenomena that are currently out of sight, and to build relevant information models. Based on these models, it is possible to develop technologies for managing natural phenomena as information interaction. The information model of the universe leads to a view of universal evolution as an information process that can go into the stage of evolution of purely informational beings and the intelligent control of the universe.

What is the reason for a minor success of relational ideas in scientific and public society? Are they actually that weird as they seem at the first glance? Here we try to give a fresh-eye look to the relational cornerstones (secondary nature of space-time, action at a distance, and Mach’s principle). We consider some typical questions usually asked by the opponents, both physicists and wide audience, to find some new arguments in favor of this concept.

The article proposes an answer to those expressed in our group by L.G. Antipenko comments on the development of the relational picture of the world, as well as on the proposal of Antipenko, explain the foundations of binary pregeometry and show what has already been carried out in the framework of this research area.

In the review, in the context of the ideas of E. Mach, one of the key problems of modern natural science is touched upon: the correlation of “reductionism” and “holism”. If the idea of reductionism was unprecedentedly developed in the framework of the theory of sets and the Bourbaki program, then the Mach principle, as well as other ideas of the philosopher, are only on the rise. Nevertheless, there is a clear realization that the future lies behind these ideas and the book under review in this context seems extremely important.