Universe as a Graph (Ramsey Approach to Analysis of Physical Systems)

Abstract

Ramsey theory is implemented to the analysis of physical systems. Physical interactions may be very generally classified as attractive and repulsive. This classification creates the premises for the application of the Ramsey theory to the analysis of physical systems. The basic notions of mathematical logic, such as transitivity and intransitivity, become key ones for understanding of physical systems. The Ramsey theory explains why nature prefers cubic lattices over hexagonal ones for systems built of electric or magnetic dipoles. The Ramsey approach may be applied to the analysis of mechanical systems when actual and virtual paths between the states in the configurational space are considered. Irreversible mechanical and thermodynamic processes are seen as directed graphs (digraphs). Chains of irreversible processes appear as transitive tournaments. These digraphs are acyclic; the transitive digraphs necessarily contain the Hamiltonian (or traceable) path. The set of states in the phase space of the physical system, between which irreversible processes are possible, is considered. The Hamiltonian path of the digraph arising from the graph uniting these states is a relativistic invariant. Applications of the Ramsey theory to the general relativity are possible. Reconsideration of the concept of “simultaneity” within the Ramsey approach is reported.