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The Hilbert Book Model; in Concise Format

J.A.J. van Leunen

Published Dec 1, 2011• 0 citations
OpenAlex

Abstract

The Hilbert Book Model is a simple model of fundamental physics that is strictly based on the axioms of traditional quantum logic. It uses a sequence of instances of an extension of a quaternionic separable Hilbert space that each represent a static status quo of the whole universe.

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Essentials of the Hilbert Book Model

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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.

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Features of the Hilbert Book Model

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On the Hierarchy of Objects

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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.

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The Hilbert Book Test Model

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The Hilbert book test model is a purely mathematical test model that starts from a solid foundation from which the whole model can be derived by using trustworthy mathematical methods. What is known about physical reality is used as a guidance, but the model is not claimed to be a proper reflection of physical reality. The mathematical toolkit still contains holes. These holes will be encountered during the development of the model and suggestions are made how those gaps can be filled. Some new insights are obtained and some new mathematical methods are introduced. The selected foundation is interpreted as part of a recipe for modular construction and that recipe is applied 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 universe are configured from dynamic geometric locations. These items are stored 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. Both repositories are formed by quaternionic Hilbert spaces. The model offers two interesting views. The first view is the creator’s view and offers free access to all dynamic geometric data that are stored in the eigenspaces of operators. 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. This view sees the model as a spacetime based structure that stores its dynamic geometric data with a Minkowski signature.

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Hilbert Book Model Slides, Part 4

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Hilbert Book Model Slides, Part 3

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This is the third 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.

•Feb 1, 2013•0 citations
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.
The fundaments of quantum physics are still not well established. This book tries to find the cracks in these fundaments and explores options that were left open. This leads to unconventional solutions and a new model of physics. In order to optimize self-consistency, the model is strictly based on the axioms of traditional quantum logic. Traditional quantum logic is lattice isomorphic to the set of closed subspaces of an infinite dimensional separable Hilbert space. It means that the separable Hilbert space can be used as the realm in which quantum physics will be modeled. However, this would result in a rather
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 test model is a purely mathematical test model that starts from a solid foundation from which the whole model can be derived by using trustworthy mathematical methods. What is known about physical reality is used as a guidance, but the model is not claimed to be a proper reflection of physical reality. The mathematical toolkit still contains holes. These holes will be encountered during the development of the model and suggestions are made how those gaps can be filled. Some new insights are obtained and some new mathematical methods are introduced. The selected foundation is interpreted as part of a recipe for modular construction and that recipe is applied 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 universe are configured from dynamic geometric locations. These items are stored 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. Both repositories are formed by quaternionic Hilbert spaces. The model offers two interesting views. The first view is the creator’s view and offers free access to all dynamic geometric data that are stored in the eigenspaces of operators. 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. This view sees the model as a spacetime based structure that stores its dynamic geometric data with a Minkowski signature.