Abstract quantum theory and space-time structure. I. Ur theory and Bekenstein-Hawking entropy

We discuss the close connection between a quantum theory of binary alternatives and the local Lorentzian structure of space-time, and outline v. Weizsaecker's concept of the ur-the quantized binary alternative. Then space-time is introduced mathematically as a symmetric space of the invariance group of the ur. It is physically interpreted as the cosmological space-time, the universe. In our model spacelike structures rest on the concept of hypermembranes - dynamical manifolds of codimension 1 in space-time. For a given number of urs a smallest length is introduced in this cosmic model by group-theoretic arguments. Already before introducing a dynamics the concept of isolated noncomposite objects can be given. They can be understood as simple models either for elementary particles or for black holes. Identifying the maximal localized states of many urs with a localized state of a particle, we get a good description of the large cosmological numbers and also a lower bound for a neutrino mass. A simple counting of the particle states given from the ur-theoretic ansatz allows an easy explanation of the Bekenstein-Hawking entropy