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The Hilbert Book Slides part 2

J.A.J. van Leunen

Published Feb 1, 2013• 0 citations
OpenAlex

Abstract

This is the second part of a slide presentation on the hierarchy of objects in the Hilbert Book Model. The HBM is strictly based on quantum logic. It uses a sequence of these logic systems in order to create a dynamic model. In order to establish coherence between the members of the sequence a correlation vehicle is used that maps the atomic propositions onto the base vectors of a Hilbert space. This leads to unprecedented insight in the undercrofts of physics.

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This is the second part of a slide presentation on the hierarchy of objects in the Hilbert Book Model. The HBM is strictly based on quantum logic. It uses a sequence of these logic systems in order to create a dynamic model. In order to establish coherence between the members of the sequence a correlation vehicle is used that maps the atomic propositions onto the base vectors of a Hilbert space. This leads to unprecedented insight in the undercrofts of physics.
The objects that occur in nature can be categorized in several levels. In this collection every level except the first level is built from lower level objects. This collection represents a simple model of nature. The model exploits the possibilities that mathematical concepts provide. Also typical physical ingredients will be used. The paper splits the hierarchy of objects in a logic model and a geometric model. These two hierarchies partly overlap. The underlying Hilbert Book Model is a simple self-consistent model of physics that is strictly based on quantum logic. This paper refines quantum logic to Hilbert logic such that it more directly resembles its lattice isomorphic companion, which is a separable Hilbert space. The HBM extends these static sub-models into a dynamic model that consists of an ordered sequence of the static sub-models. The paper is founded on three starting points: • A sub-model in the form of traditional quantum logic that represents a static status quo. • A correlation vehicle that establishes cohesion between subsequent members of a sequence of such sub-models. • The cosmological principle. Further it uses a small set of hypotheses. It turns out that the cosmological principle is already a corollary of the first two points. The paper explains or indicates the explanation of all features of fundamental physics that are encountered in the discussed hierarchy which ranges from propositions about physical objects until composites of elementary particles. Amongst them are the cosmological principle, the existence of quantum physics, the existence of a maximum speed of information transfer, the existence of physical fields, the origin of curvature, the origin of inertia, the dynamics of gravity, the existence of elementary particles, the existence of generations of elementary particles and the existence of the Pauli principle.
The Hilbert Book Model is the name of a personal project of the author. The model is deduced from a foundation that is based on quantum logic and that is subsequently extended with trustworthy mathematical methods. What is known from conventional physics is used as a guideline, but the model is not based on the methodology of contemporary physics. In this way the model can reach deeper into the basement of physics. The ambition of the model is rather modest. It limits its scope to the lowest levels of the physical hierarchy. Thus fields and elementary particles are treated in fair detail, but composites are treated marginally and only some aspects of cosmology are touched. Still the model dives into the origins of gravitation and inertia and explains the diversity of the elementary particles. It explains what photons are and introduces a lower level of physical objects and a new kind of ultra-high frequency waves that carry information about their emitters. Above all the HBM introduces a new way of looking at space and time.
In order to support clear discussions, a simple self- consistent model of fundamental physics is constructed. It is strictly based on the axioms of traditional quantum logic and uses the isomorphism of the set of propositions of this logic system with the set of closed subspaces of a quaternionic separable Hilbert space. This primitive model cannot represent dynamics and does not include a representation of fields. For that reason the model also uses the Gelfand triple of the Hilbert space and a set of links that connect the eigenvectors of a particle location operator in the Hilbert space with the continuum eigenspace of a corresponding location operator in the Gelfand triple. These links are quaternionic probability amplitude distributions (QPAD’s) that will act as the quantum state functions of the particles. The combination of a quaternionic Hilbert space, its Gelfand triple and the set of linking QPAD’s still can only represent a static status quo of the universe. However, a dynamic model may consist of an ordered sequence of such sandwiches. The subsequent sandwiches form the pages of a book that we will call the Hilbert Book Model. The quaternionic derivative of a QPAD leads to a continuity equation that describes how the derivative is coupled to its source. When the strength of the coupling is made explicit, then the resemblance with linear equations of motion becomes apparent. This interpretation extends conventional quantum physics with quantum fluid dynamics. It throws an unprecedented view on the undercrofts of fundamental physics.