Physical reality


Open Access

The Hilbert Book Model project


This page is renewed on 3 May 2018


Author: Hans van Leunen

Retired physicist, chemist, software expert


Send your comments to “info” at this site


Hans van Leunen on ResearchGate


I discuss the Hilbert Book Model Project at


BaseModel.pptx at GoogleDrive

SpokenText by BaseModel presentatie at GoogleDrive


Related sites



Wikiversity project


Since March 2017, I have started the Wikiversity Hilbert Book Model Project. This online university project lectures the science of the Hilbert Book Model in an openly accessible and structured way. Everybody can read or participate. Participation requires acceptation of the Wikiversity rules. Wikiversity is part of the Wikimedia Foundation that also includes Wikipedia.




I offer a fine bottle of X.O. French cognac to the one that puts a significant argument, which disproves the Hilbert Book Model.

I also offer a fine bottle of X.O. French cognac to the one that adds a significant extension to the Hilbert Book Model


Send your responses to “info” at this site or post them on suitable LinkedIn groups or on




This website


The owner of this site (me) uses this medium as a public work pad. You will find my latest papers here. When they mature, then I upload the papers in pdf format to my e-print archive on That site only accepts papers in pdf format. I use it because Vixra provides a very efficient revision service. With that service, the reader can follow how the ideas behind the paper evolve in time. I prepare the papers in MS-Word docx format. MS-Word offers a powerful equation editor. For that reason, I keep the latest docx version of the papers also on this website. The papers do not enforce copyrights. Everybody may use the published texts.

My papers are quite unorthodox and often very controversial. They will not easily pass a biased peer-review barrier. In addition, the peer-review process cannot cope with the revision service that I use intensively. I do not want to disturb people with a request for endorsement as is required by the registration for The controversial and unorthodox character of my papers may pose too much burden for the endorsers. I also not use the open access journals that still ask a high fee to the authors. My retirement budget does not allow that. I have published a few papers on Their publication fee is acceptable low, and they are not afraid to publish controversial papers.


The web shows that several hundreds of so-called open access peer-reviewed journals are fighting for authors as well as for readers. I do not want to join that madness.


Cheaply printable books


These files contain easily readable and cheaply printable books. The font is set at 16 points and the number of colored paged is small. These pages are listed on the colophon page. If you take such file to your local print shop, then that service can produce an affordable ring band book.

The Mathematics of Physical Reality

De wiskunde van de Fysieke Werkelijkheid

Print on demand books

The books can be ordered as print-on-demand



and from






Een Zichzelf Scheppend Model van de Fysieke Werkelijkheid


De Wiskunde van de Fysieke Werkelijkheid


Natuurkundig Scheppingsverhaal


Witte Vlekken in de Natuurkunde




De Werkelijkheid vanuit zijn Beginselen


Massa uit het Niets


Structuur in de Fysieke Werkelijkheid


Wetenschap met Oogkleppen op


Het ongelofelijke verhaal over de realiteit


Structuur in de Werkelijkheid


De Eenvoud van de Werkelijkheid


Herontdekte Donkere Kwanta


Gij zult modulair construeren


De mechanismen die de realiteit coherent houden


Een wiskundig model van de realiteit


Opzoek naar witte vlekken

Keeping an e-book of about three hundred pages in sync with continuously deepening insights is a very laborious task. For that reason, my newest insights are reflected in “My newest paper”. This is a set of more dedicated papers that each have a certain focus. When the new insights mature, then I store the result on my personal e-print archive on Vixra.


My career as a developer of image intensifying devices offered me unique insights into the world of photons and elementary particles. See what image intensifiers reveal. Later in my career, I switched to the development of software and especially to the improvement of the software generation process. This last activity guided in the direction of modular software system construction.


The final book


I will collect the papers that are contained in the e-print archive into a book-sized pdf with name


A Self-creating Model of Physical Reality


The mathematical toolkit will be published in


Advanced Hilbert space technology



Representing Basic Physical fields by Quaternionic Fields




The following files contain quaternionic differential equations that will become readable in many of the web based editors


Quaternionic field equations (docx)


Quaternionic field equations (rtf)


In preparation




My newest papers


The Standard Model of Particle Physics and the Hilbert repository

The docx of the document

The author uses MathType to format formulas and Grammarly to check the grammar


Representing basic physical fields by quaternionic fields


Base Model pptx

TextToReadAloud Can be used with ReadAloud app


Quaternionic Field Theory


A Self-creating Model of Physical Reality


All About Mass and Gravitation


Steps to the Hilbert Book Model


Stochastic control versus forces and force carriers


Dark Objects


Relational structures


Physical Creation Story


White spots in physics


Mass and Field Deformation


Tracing the structure of physical reality by starting from its fundaments


Generating the Universe from Scratch


Pure Energy






64 Shades of space




Behavior of basic fields


Structure of physical reality


Exploring the Origin of Gravity


Reality from its Basics


Modularity in the Universe


Modeling Platform


Generating Mass from Nothing


Structure in Physical Reality


How Gravitation Works


Science with Blinders


The Incredible Story About the Reality


Structure in Reality


Explanation of gravitation


Origin of Mass


Mother of all Field Equations


Rediscovered Dark Quanta


Physical Simplicity


Basic Quantum Field Theory


A Simple Model


Thou Shalt Construct in a Modular Way


Low Dose Rate Imaging


Mechanisms that keep reality coherent


Review of the Hilbert book model


Report of the Hilbert Book Model project


The Hilbert Book Test Model


An unorthodox view on the foundations of physical reality




Generalized Field Equations


Merging Methods


Differential and integral calculus


Quaternionic versus Maxwell based differential calculus


The generalized Stokes theorem


Dirac equation


Dirac equation in quaternionic format


About the Hilbert Book Model


The HBM is a model that is based on a
recipe for modular construction


The most fundamental law of physics cannot be stated in the form of a formula. Instead, it is stated in the form of a commandment:


“Thou shalt construct in a modular way”


The Hilbert Book Model

is a paginated space-progression model


The dynamical coherence of the HBM is controlled by
a real time operating system


This Hilbert Book Model does not offer another physical reality.


The Hilbert Book Model offers an alternative view on physical reality


That view differs from the view that is offered by
contemporary physics


The new view creates new insights!



In a simplified description:

Quantum physics treats objects and constructs that perform above the wavefunction

Discrete physics treats objects and constructs that perform below the wavefunction


“Above the wave function” = what uses the wave function

“Below the wave function” = what is described by the wave function



What exists underneath the wavefunction?




I do this HBM project purely for the fun of it and out of curiosity to the lower levels of physics







The concepts of the Hilbert Book Model was explained at the DPG congress in Berlin at Tuesday march 18



Nearly all tools that quantum physicists use are in some way based on the concept of the wave function. This means that such tools deliver a blurred view of the fine grain structures and fine grain behavior that these tools describe.

See: What is underneath the wave function.



Insights change

The Hilbert Book Model started during the study of the author in the sixties on the TUE university in Eindhoven. The project paused during the author’s career in the industry. After his retirement, the author restarted the project in 2009. The project got its current name in 2011.

Since he restarted the Hilbert Book Model project, the insights of the author changed significantly.

You can follow this development via publications and his discussions on ResearchGate, on Science2.0 and on LinkedIn.

Since November 2011 the author publishes on his e-print archive at

The Hilbert Book Model Project is documented in

An overview of the highlights is presented in “Structure in Physical Reality”;



The author’s e-print archive is at







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Older versions:




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Features of the Hilbert Book Model


You can download this manuscript free of charge


Beschrijving: Support independent publishing: Buy this book on Lulu.

You may wish to buy a printed copy of the manuscript.




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What image intensifiers reveal

At low dose rates it becomes apparent that radiation is not built from waves, but from separate quanta that move in un-sharp corridors (clouds), which may be shaped as waves or wave packages.


A short film of the output of an X-ray image intensifier made at a very low dose.

Provided by Philips Healthcare

  • The pixel size is about 200μm
  • The number of pixels is about 500 * 600
  • The average number of X-ray quanta per pixel per frame in the mid-gray area is circa 1
  • The range inside this picture is about 20
  • The direct radiance is about 5 quanta per pixel per frame
  • The dark regions get <<1 quanta per frame
  • The number of pictures is 33


Other pictures: . Low-dose X-ray image of the moon. ; Hailstorm. Warning, this is NOT a video of an external object. It is constructed by coupling two night vision goggles. There is no input image. What is shown is the cold emission of the photocathode of the first goggle at different temperatures. Very low dose photos.


At low dose rates, I never saw any sign of a wave. At the utmost, I saw detection patterns that looked like interference patterns.


Why is that so? Remember that for (elementary) particles the squared modulus of the wavefunction is a probability density distribution that indicates the probability of finding the particle at the location defined by the parameter of the wave function!

This distribution has a Fourier transform, which makes it a wave package! This establishes the wave behavior of the particle. The wave package is recurrently regenerated when the hop location swarm is regenerated.


Photons also have detection location density distributions that represent detection probability density distributions and have Fourier transforms. Thus, the detection probability density distribution is a wave package. However, these waves differ from the structure of a photon!

The detection probability density distribution establishes the particle behavior of a set of photons!!


The Hilbert Book Model states that photons are formed by strings of shape keeping fronts that each carries a fixed amount of energy. In free space, the string moves with light speed and the shape keeping fronts also keep their amplitude. At a given instant of progression, the passage of the complete string takes a fixed number of progression steps.








Hans is active in

ResearchGate  and in LinkedIn,