Relativity in binary systems as root of quantum mechanics and space-time

Abstract

Inspired by Bohr's dictum that "physical phenomena are observed relative to different experimental setups", this article investigates the notion of relativity in Bohr's sense, starting from a set of binary elements. The most general form of information coding within such sets requires a description by four-component states. By using Bohr's dictum as a guideline a quantum mechanical description of the set is obtained in the form of a SO(3,2) based spin network. For large (macroscopic) sub-networks a flat-space approximation of SO(3,2) leads to a Poincare symmetrical Hilbert space. The concept of a position of four-component spinors relative to macroscopic sub-networks then delivers the description of 'free' massive spin-1/2 particles with a Poincare symmetrical Hilbert space. Hence Minkowskian space-time, equipped with spin-1/2 particles, is obtained as an inherent property of a system of binary elements when individual elements are described relative to macroscopic sub-systems.