Die einheitliche Beschreibung der fundamentalen Objekte und Wechselwirkungen der Natur in der Quantentheorie der Ur-Alternativen

TL;DR

This paper explores a quantum logical framework based on Ur-alternatives, unifying fundamental interactions, including the standard model and gravity, within a purely quantum theoretical approach that offers new insights into the structure of nature.

Contribution

It introduces a unified quantum logical description of all fundamental objects and interactions, deriving gauge theories and gravity from the concept of Ur-alternatives.

Findings

Representation of structures in symmetric space in 3D real position space

Derivation of Yang-Mills gauge theories and gravity from quantum logical principles

Unification of standard model interactions and gravitation in a single framework

Abstract

In this research work the quantum theory of Ur-alternatives of Carl Friedrich von Weizs\"acker is considered. In This theory all objects and interactions in nature are constituted by abstract purely quantum logical relations in time. Such structures can be devided into binary alternatives, which are called Ur-Alternatives with respect to this principle meaning, and this leads to a tensor space of many Ur-alternatives. The indistinguishability of the Ur-alternatives yields two Hilbert spaces, the tensor space of symmetric and antisymmetric states under permutations of the Ur-alternatives. It is shown how the structures in the symmetric space can be represented in a three dimensional real position space connected to time according to special relativity. Accordingly this theory obtains ultimately a deep understanding of the EPR-paradox, since logic is independent of topological structures and causal relations in space. The antisymmetric space, which because of the Pauli principle contains much less degress of freedem, yields the additional quantum numbers of the elementary particles. Based on the demand for the highest possible symmetry in the tensor space, the Yang-Mills gauge theories of the standard model as well as a translational gauge formulation of general relativity in a purely quantum logical description are derived. The equations determine entanglements of states containing many Ur-alternatives and this concept is the analogue to classical pointwise interactions between separated objects. This means that the main structures of the SU(N)-interactions of the standard model of elementary particle physics as well as gravitation according to general relativiy are unified in a purely quantum theoretical conceptional framework. Finally it is derived an extended version of the E8-group, the biggest exceptional Lie-group.