The possibility of constructing a relativistic space of information states based on the theory of complexity and analogies with physical space-time

TL;DR

This paper explores constructing a relativistic space of information states using complexity theory and physical space-time analogies, revealing how information dynamics can mirror relativistic physics principles.

Contribution

It introduces a novel framework linking information complexity with relativistic space-time concepts, including Lorentz transformations and the principle of least action.

Findings

Information trajectories follow Lorentz transformations.

Optimal compression separates regular and random information parts.

Analogies with physical space-time clarify information dynamics.

Abstract

The possibility of calculation of the conditional and unconditional complexity of description of information objects in the algorithmic theory of information is connected with the limitations for the set of the used languages of programming (description). The results of calculation of the conditional complexity allow introducing the fundamental information dimensions and the partial ordering in the set of information objects, and the requirement of equality of languages allows introducing the vector space. In case of optimum compression, the "prefix" contains the regular part of the information about the object, and is analogous to the classical trajectory of a material point in the physical space, and the "suffix" contains the random part of the information, the quantity of which is analogous to the physical time in the intrinsic reference system. Analysis of the mechanism of the "Einstein's clock" allows representing the result of observation of the material point as a word, written down in a binary alphabet, thus making the aforesaid analogies more clear. The kinematics of the information trajectories is described by the Lorentz's transformations, identically to its physical analog. At the same time, various languages of description are associated with various reference systems in physics. In the present paper, the information analog of the principle of least action is found and the main problems of information dynamics in the constructed space are formulated.