Raum, Zeit und Wechselwirkung in der Quantentheorie der Ur-Alternativen

TL;DR

This paper explores a quantum theory based on fundamental logical alternatives called Ur-alternatives, proposing a new way to derive space, interactions, and internal symmetries from quantum information principles.

Contribution

It introduces a novel quantum framework where space and interactions emerge from Ur-alternatives, offering a background-independent approach to quantum gravity and electromagnetism.

Findings

Space arises as an indirect representation of relations between Ur-alternatives.

States in tensor space of Ur-alternatives can be mapped into 3D space.

A potential approach to incorporate internal symmetries using $G_2$.

Abstract

The quantum theory of Ur-alternatives of Carl Friedrich von Weizsaecker tries to constitute general quantum theory based on the concept of logical alternatives in time. Based on this interpretation of quantum theory the existence of free objects in space, their symmetry properties and their interactions shall be inferred. The alternatives are represented by binary alternatives, which are called Ur-alternatives because of their logically fundamental character. Through Ur-alternatives as elementary quantum theoretical units of information the Copernican revolution with respect to the question of space is realized in a consequent way. This means that not the objects of nature are in a given space, but the existence of space arises as a kind of indirect representation of relations between abstract quantum theoretical objects. The Ur-alternatives do not exist in a given physical reality, but the existence of space is constituted by Ur-alternatives at all. Such a concept of reality is implicitly contained within the uncertainty relation and can be seen especially in the EPR-paradoxon. It is shown in this thesis in a mathematical consistent way that a state in the tensor space of many Ur-alternatives can directly be mapped into a real three dimensional space which means that together with the dynamics a representation in a (3+1)-dimensional space-time becomes possible. By considering the $G_2$ an approach for the incorporation of the internal symmetries can be suggested. Furthermore the Ur-alternatives enable the constitution of a concept of interaction, which is based on quantum theoretical entanglement. By using this concept it is tried to obtain a purely quantum theoretical description of electromagnetism and gravity. This corresponds to a much more principle and in a radical sense background independent way of quantization.