Hilbert Book Model Project

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This project is still in preparation phase. Translation is partly finished.

Introducing the Hilbert Book Model Project[edit]


Hans van Leunen is the initiator of this project.

The Hilbert Book Model Project is an ongoing project.

All its pages and sections may be revised.

Everybody is kindly invited to help to improve and to extend this project.

If you want to criticize or have other remarks, then you are kindly requested to use the Discuss tabs that appear at the top of the pages.

You can also react on my talk page.

In the opinion of the initiator a Wikiversity project is a perfect way for introducing new science.


If you want to become a collaborator, then please contact me.

This list is still empty.

Hilbert Book Model[edit]

The Hilbert Book Model Project governs the development of the Hilbert Book Model and its application.

The Hilbert Book Model is a purely mathematical model of the foundations and the lower levels of the structure of physical reality.

The model emerges from its foundations. This principle leads to the following implementation of the model.


The model bases on a simple foundation. In 1936 scientists discovered the structure of this foundation. The structure of the model emerges from this foundation. Mechanisms that exist external to this structure provide the geometric data that define the dynamic behavior of the model.

The model impersonates a creator that at the instant of the creation stores all dynamic geometric data of its creatures in a read-only repository.

All observable objects in the model are modules or modular systems. A set of pointlike elementary modules exists who's members configure all other modules.

This makes the creator a modular designer and a modular constructor. At every instant, the elementary object obtains a new spatial location that the repository stores together with the corresponding timestamp. A private stochastic mechanism generates the new location. All modules act as observers and can figure as actors in an observed event. Observers can only perceive information that comes from storage locations that possess a historic timestamp. That information is transferred from the storage location to the observer by vibrations and deformations of a continuum that embeds both the storage locations of the observed event and the current storage locations of the observer. The information transfer affects the format of the information that the observer perceives. The observer perceives in spacetime format. The Lorentz transform describes the format conversion from the Euclidean storage format to the spacetime format of the perceived information.

Relation to conventional physics[edit]

The Hilbert Book Model differs in many aspects from conventional physical theories. The reason bases on the fact that the Hilbert Book Model starts at its foundations and develops by extending these foundations, while most physical theories confine to concepts that can be verified by direct observations or via experiments. 

Only a tiny part of the Hilbert Book Model is accessible to observers and that includes observations that apply the most sophisticated instruments.

This situation makes the Hilbert Book Model an unconventional and unorthodox approach that offers an alternative to conventional physical theories where verification cannot apply direct or equipment aided observation.


The HBM restricts to the lowest levels of the structure of its target, which is physical reality.

The HBM does not explain the origin of the stochastic mechanisms. The HBM only applies these mechanisms.

The HBM does not explain the existence of bosons, other than warps, photons and non-elementary modules.

The HBM does not explain color confinement.

The HBM does not explain generations of elementary modules.

The HBM does not explain the diversity of masses of elementary module types.

Crucial differences[edit]

The HBM introduces a category of super-tiny objects that cannot be observed separately. This category contains shock fronts. The HBM calls them warps and clamps.

The HBM sees clamps as the objects that provide elementary modules with their mass.

The HBM sees strings of equidistant warps as the information messengers.

The HBM introduces the zigzag of elementary modules.

The HBM introduces the creator's view as alternative to the observer's view.

The HBM interprets the Lorentz transform in a special way

The HBM interprets its base model as a read-only repository.

The HBM introduces the scanning Hilbert space subspace.

The HBM introduces the embedding of the separable Hilbert space into its non-separable companion as an ongoing process.

The HBM introduces two quaternionic second order partial differential equations that describe the embedding process and the information transfer.


Introducing the Hilbert Book Model[edit]

This entry describes the discovery of the foundation of the model and explains how the purely mathematical model can derive from this foundation.

The model extends into a powerful platform that acts as a read-only repository. This base model merges function theory and differential and integral calculus with Hilbert space operator technology. In this way, the model introduces some new mathematics.

The entry introduces modular design and construction of modules whose footprint is generated by stochastic processes.

The model accepts a storage view and an observer's view. These views can mix.

Hilbert Book Model

Relational structures[edit]

The most important foundation of the Hilbert Book Model is a relational structure that mathematicians call an orthomodular lattice. This lattice extends into a separable Hilbert space

The orthomodular lattice incorporates a modular configuration lattice. A subspace of the separable Hilbert space represents this sublattice.

Relational Structures

Modules and modular systems[edit]

The creator appears a modular designer and constructor. Modular system generation can occur in stochastic way and as soon as intelligent species arrive, then locally, intelligent modular design may replace part of the stochastic modular design. The creator teaches these designers some important lessons.

Modules and Modular Systems


Due to the fact that the base model of the Hilbert Book Model applies quaternionic Hilbert spaces, will quaternions play a major role in the project.


Quaternionic Hilbert Space[edit]

Quaternionic Hilbert spaces constitute the base model of the Hilbert Book Model.

Hilbert spaces can only cope with number spaces that are division rings. The HBM selects the most versatile division ring.

Hilbert spaces exist as separable Hilbert spaces and non-separable Hilbert spaces.

Every infinite dimensional separable Hilbert space owns a unique companion non-separable Hilbert space that embeds its separable companion.

The two selected companions constitute the base model of the Hilbert Book Model.

Quaternionic Hilbert Spaces

The behavior of continuums[edit]

This section describes the behavior of continuums by applying the first and second order partial differential equations of the quaternionic functions that define these fields.

The document interprets the solutions of homogeneous second order partial differential equations.

The relations between volume integrals, surface integrals, loop integrals and corresponding differential equations relate balance equations to continuity equations.

Finally, the document explains the Lorentz transform.

Quaternionic Field Equations

Nabla operators[edit]

The quaternionic nabla and the spatial nabla play an essential role in the behavior of fields.

Nabla Operators


Waves, warps, clamps and plops are solutions of the quaternionic second order partial differential equations. These solutions play an essential rule in the Hilbert Book Model.


Quaternionic Fourier Transform[edit]

Fourier transforms play a significant role in the assurance of dynamical coherence and in the binding of modules.

Quaternionic Fourier Transform

Stochastic Location Generators[edit]

Each module owns a private mechanism that at every instant generates the locations that constitute their footprint. The mechanisms apply statistic processes that own a characteristic function.

In this way the mechanisms ensure dynamical coherence.

Stochastic Location Generators

Perceptibility and Recognition at Low Dose Rate[edit]

Measuring the perceptibility of images that generated at a low dose rate show the nature of the mechanisms that produce the objects, which constitute the image.

Perceptibility and Recognition at Low Dose Rate

The Extended Stokes Theorem[edit]

The extended Stokes theorem extends the generalized Stokes theorem, which combines the relations between volume integrals and surface integrals.

The applied integration appears to be sensitive to the ordering symmetries of the applied parameter spaces. This effect is the source of the symmetry-related charges of the platforms on which elementary modules reside. The symmetry-related charges generate the symmetry-related field. The interaction between the symmetry-related charges and the symmetry-related field controls part of the dynamics of the model.

Extended Stokes Theorem


The universe can be divided into compartments.



In the creator's view, the elementary modules can zigzag in the direction of progression.

Observers perceive the reflection instants as annihilation events of a particle in combination with a creation event of the corresponding anti-particle. Both events go together with the emission or absorption of two information messengers that operate in opposite directions.


Information Messengers[edit]

The Hilbert Book Model supports several types of strings of warps that act as information messengers. Each type features its own emission duration and corresponds to an elementary module type.

Information Messengers

Multi-mix Path Algorithm[edit]

This algorithm is HBM's alternative to the well-known Path Integral.

Multi-mix Path Algorithm

Dirac equation[edit]

Dirac investigated a way to interpret the Klein-Gordon equation in a special way. That action resulted in the Dirac equation.

This equation introduced antiparticles.

Dirac Equation