Authors: Hans van Leunen
The Hilbert book test model is a purely mathematical test model that starts from a solid foundation from which the whole model derives by using trustworthy mathematical methods. The foundation restricts its extension. Also, the knowledge about physical reality serves as guidance, but the model is not claimed to be a proper reflection of physical reality. It is impossible to verify such claim. The mathematical toolkit still contains holes. These holes will appear during the development of the model and suggestions are made how those gaps can close. Some new insights and some new mathematical methods appear. The theory interprets the selected foundation as part of a recipe for modular construction, and that recipe applies throughout the development of the model. This development is an ongoing project. The main law of physics appears to be a commandment: “Thou shalt construct in a modular way.” The paper reveals the possible origin of several physical concepts. This paper shows that it is possible to discover a mathematical structure that is suitable as an extensible foundation. However, without adding extra mechanisms that ensure dynamic coherence, the structure does not provide the full functionality of reality. These extra mechanisms apply stochastic processes, which generate the locations of the elementary modules that populate the model. All discrete items in the universe configure from dynamic geometric locations. These items store in a repository that covers a history part, the current static status quo, and a future part. The elementary modules float over the static framework of the repository. Dedicated mechanisms ensure the coherent behavior of these elementary modules. Fields exist that describe these elementary modules. An encapsulating repository supports these fields. Quaternionic Hilbert spaces form both repositories. The model introduces a category of super-tiny objects that are shock fronts. The model gives them names, but mathematics knows these shock front already for two centuries as solutions of the wave equation. The model offers two interesting views. The first view is the creator’s view and offers free access to all historical, current, and future dynamic geometric data that store in the quaternion-based eigenspaces of operators. Quaternions store the data in a Euclidean space-progression structure. The second view is the observer’s view. The observers are modules that travel with the vane, which represents the static status quo. The observers only perceive information that comes from the past, and that is carried by the field that embeds them. The observer’s view sees the model as a spacetime based structure that presents its dynamic geometric data with a Minkowski signature.
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