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 names
The Mathematics of Physical Reality
The Hilbert Book Model
Hilbert Book Model Project survey-book
You can bring this
file to a print shop and they can turn it in a US Letter size book
Quaternionic field equations (docx)
Quaternionic field equations (rtf)
Stochastic control versus forces
and force carriers
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
Shades of space
Behavior of basic fields
Origin of Gravity
Reality from its
Modularity in the
Generating Mass from
How Gravitation Works
Science with Blinders
Story About the Reality
Structure in Reality
Origin of Mass
Mother of all Field Equations
Rediscovered Dark Quanta
Basic Quantum Field Theory
A Simple Model
Thou Shalt Construct
in a Modular Way
Low Dose Rate Imaging
Mechanisms that keep reality coherent
of the Hilbert book model
the Hilbert Book Model project
The Hilbert Book Test
An unorthodox view on the foundations of physical reality
Generalized Field Equations
and integral calculus
Quaternionic versus Maxwell based differential calculus
Dirac equation in quaternionic
papers are partly replaced by newer papers
orthomodular base model:
Foundation of a mathematical model of physical reality
On the origin of
On the origin of
A consistent set of structured mathematical storage media
mathematical model of physical reality
The reverse bra-ket method
Fermion symmetry flavors
What drives reality?
and space-progression models:
The Lorentz transformation
Reality contains a network of
the Hilbert Book Model
HBM is a model that is based on a
recipe for modular construction
most fundamental law of physics cannot be stated in the form of a formula.
Instead, it is stated in the form of a commandment:
construct in a modular way”
Hilbert Book Model
a paginated space-progression model
dynamical coherence of the HBM is controlled by
a real time operating system
Hilbert Book Model does not offer another physical reality.
Hilbert Book Model offers an alternative view on physical reality
view differs from the view that is offered by
The new view creates new insights!
Three forms of models of physical reality can be discerned:
· Classical physics = set based
· Quantum physics = continuum based modularization
· Discrete physics = discrete object based modularization
The HBM focuses on discrete object based modularization
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
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 most basic aspect of this model is:
Each of the discrete
objects in this model can be represented by a closed subspace of an
infinite dimensional separable Hilbert space.
The foundation of the model represents a
recipe for modular construction.
The last e-book
previous manuscript (completed)
to the Hilbert Book Model
The role of the observer
traffic to this website became so intense that the costs surpassed my budget.
am now constructing alternatives via Google drive
Corresponding mp4 video
The full video mp4 flash(current version)
The Hilbert Book Model Game pdf (under
The full slide show (in preparation)
Full slideshow with voice.(Not yet ready)
The corresponding spoken text.(Not yet ready)
concepts of the Hilbert Book Model was explained at the DPG congress in Berlin at Tuesday march 18
What Image Intensifiers
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.
SPACE IS NOT STATIC
A model that starts with an existing concept of space and
an existing concept of progression is fooling us. SPACE IS NOT STATIC.
For those that deny that non-observable features and
phenomena exist and keep non-observable in the future: I challenge you to
design a model that contains subjects such as progression and space without
just stating them as already present concepts. Thus, these concepts must
emerge in your model.
I bed that you cannot design such model without accepting
non-observable features and phenomena that present a foundation of the
So, if I am right, then either all existing
"physical models" are cheating us or they must also contain a
foundation from which progression and space emerge.
Thus, if I am right, all models that do not support the
emergence of progression and space must be classified as non-physical.
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.
restarted the Hilbert Book Model project, the insights of the author
You can follow
this development via publications and his discussions on ResearchGate, on
Science2.0 and on LinkedIn.
2011 the author publishes on his e-print archive at http://vixra.org/author/j_a_j_van_leunen
Hilbert Book Model Project is documented in https://en.wikiversity.org/wiki/Hilbert_Book_Model_Project
overview of the highlights is presented in “Structure in Physical Reality”;
Very old stuff
with rather fixed progression steps. It is a parameter that is more
fundamental than any other physical feature. It underlies all dynamics.
Let us define
for convenience the concept of “observed time”. The observed time clock
ticks at the location of the observed item and travels with that item. We
suppose that all observable items own such clock.
In a paginated
space-progression model, all observed time clocks are synchronized. With
other words in that model resides a universe
wide time clock. The reason
that the HBM is a paginated model is the fact that its foundation; the
skeleton relation structure that is called quantum logic, offers no means
to implement dynamics. A dynamic model uses an ordered sequence of these
In a paginated
model, the setting of the observed time clock equals the current value of
the progression step counter. The clock tick corresponds to a progression
consequence in that model, the universe can be considered to be proceeding
with universe wide progression steps from each static status quo to a
subsequent status quo. It means that universe can be considered to be recreated
at each progression step. This recreation occurs with a super-high
frequency. It is the frequency with which the universe wide time clock
ticks. Phenomena that occur with that frequency cannot be observed. Only
their averaged effects can be observed. It also means that every lower
frequency wave must be in synchrony with the universe wide clock or is
chopped and can only live on as a modulation of a super-high frequency
wave. Due to the unobservable super-high frequency progression seems to
flow. In fact, it steps. Time ticks.
Such a view on
space-progression is called a paginated space-progression model.
In this model, each static status quo of the universe is described in
a single page.
and the observed item are linked via an information path. Via this path,
the information is transported from the observed item to the observer.
Despite the fact that this path possesses characteristic attributes, these
attributes are usually not known by the observer.
Let us define
for convenience the concept of “observer’s time”. The observer’s time clock
ticks at the location of the observer and travels with the observer. We
suppose that all observers own such clock. The observer uses this clock in
order to estimate the time at the location of the observed item.
also owns an observed time clock. The readings of the observer’s time clock
and the observed time of the observed event will usually differ. The
difference depends on the characteristics of the path that information must
travel from observed item to observer.
physics uses the spacetime model. It uses the observer’s time instead of universe
wide time. The observer’s time clock ticks at the location of the observer.
In the spacetime model, space and
observer’s time are coupled via the local speed of information transfer. In
the spacetime model, the observer’s time clock can be selected freely.
the observed time setting at the location of an observed item cannot be
measured directly. If the path and the local speed that information takes
in order to arrive at the location of the observed item to the location of
the observer are known, then for a given observation it is possible to
derive an equivalent observer’s time. The path depends on space curvature.
In a paginated
model, for all observed items the universe wide time clock has the same
value. Thus, in that model, the observer’s time clock cannot be selected
freely but must be derived from the universe wide time value at the
observed event. This classifies the paginated space-progression model as a
fully deduced model. That does not say that the paginated model is not a
valid space-progression model.
criterion for the validity of the paginated model is the fact whether all
observed time clocks can be synchronized.
paginated space-progression model exists, then this model and the spacetime
model can be considered to be two different views of the same physical
Static status quo descriptors
significant argument for the existence of a paginated space-progression
model can be found in the foundations that were suggested at the advance of
quantum physics. In 1936 John von Neumann and Garret Birkhoff wrote their
famous paper about quantum logic and its lattice isomorphic companion; the
set of closed subspaces of a separable Hilbert space. Inspection of these
structures shows that they do not have a built-in means for implementing
dynamics. These proposed models can represent a static status quo of a
quantum physical system, but in order to represent dynamics, these models
must be extended. In contemporary physics, this is done by making either
wave functions or operators time dependent. However, it is also possible to
attach a progression parameter to the whole model. This last choice means
that the dynamic model is represented by an ordered sequence of sub-models
that each represent a static status quo. With other words, this dynamic model
is a paginated model.
In no way, a
model can give a precise description of physical reality. At the utmost, it
presents a correct view on physical reality. But, such a view is always an
reality is very complicated. It seems to belie Occam’s razor. However,
views on reality that apply sufficient abstraction can be rather simple and
it is astonishing that such simple abstractions exist. Complexity is caused
by the number and the diversity of the relations that exist between objects
that play a role. A simple model has a small diversity of its relations.
reality appears to have selected a skeleton relational structure as a means
to keep the complexity of its constructs within bounds.
structures might fit onto observed physical reality because its relational
structure is isomorphic to the relational structure of these observations.
The part of
mathematics that treats relational structures is lattice theory. Logic
systems are particular versions of lattice theory. Classical logic has a
simple relational structure. However, since 1936 we know that physical
reality cheats classical logic. Since then we think that nature obeys
quantum logic, which has a much more complicated relational structure.
logic seems to represent the skeleton relational structure that physical
reality has selected in order to reduce complexity.
offers structures that are lattice isomorphic to quantum logic. One of them
is the set of closed subspaces of a separable Hilbert space. However, this
set cannot be interpreted as a logic system. Interpreting the elements as
construction elements would fit better. The Hilbert space adds the
superposition principle to the skeleton relational structure of quantum
logic. Via the eigenspaces of its operators, it adds a storage place for
of this deliberation is that physical reality is not based on mathematics,
but that it happens to feature relational structures that are similar to
the relational structure that some mathematical constructs have. That is
why mathematics fits so well in the formulation of physical laws. Physical
laws formulate repetitive relational structure and behavior of observed
aspects of nature.
The correlation mechanism
measures, a paginated model will lead to dynamical chaos. An external
correlation mechanism must take care that sufficient coherence exists
between the subsequent sub-models. However, this coherence must not be too
stiff, otherwise again no dynamics will take place.
correlation mechanism must perform quite a lot of complicated tasks and it
is strange that contemporary physics assigns these tasks to quantum state
functions or operators. These actors are better suited as storage places
than as controlling bodies.
The tasks of
the correlation mechanism are:
· Embedding particles
in the field that acts as the curved operating space.
· Establishing the
swarming conditions for elementary particles
· Controlling the
propagation of the wave fronts that implement the potentials of the
· Storing data in
eigenspaces of operators and in quantum state functions.
· Supporting entangled systems and subsystems.
See: Stochastic nature of quantum physics
Poisson process can be coupled to an attenuating binomial process that is
implemented by an isotropic 3D spread function. This combined process can
be considered as a generalized Poisson process that locally has a lower
production rate. In this way, a 3D object distribution can be generated
that at large production rates will resemble a 3D Gaussian distribution.
That distribution can be described by two different descriptors. The first
is a continuous object density distribution that can be interpreted as a
probability density distribution. This descriptor has all aspects of the
squared modulus of a wave function. The second description uses the
sequence of generated objects. This sequence forms a stochastic path in 3D
space. It can be interpreted as a path that is walked by a single object.
Together, these descriptors describe an elementary building block that is
characterized by a wave function and that during each production cycle
walks along the mentioned stochastic micro-path.
agree that this comes close to the description of an elementary particle.
Extra restrictions set by the
extra restriction that is installed by the correlation mechanism is that
the coherent discrete distribution of step stones that belong to an
embedded particle can be characterized by a continuous step stone density
distribution that exists in the embedding continuum. Further, the mechanism
ensures that this continuous object density distribution can be
characterized as a probability density distribution. If this is the case,
then the object density distribution can be considered as the squared
modulus of the wavefunction of the considered object. This describes the
fundamental stochastic nature of the universe wide time clock model. These
extra restrictions are far from obvious. The consequence is that
the stochastic micro-path is generated in a recurrent fashion such that
important statistical attributes are reinstalled in a cyclic fashion.
after walking along the full micro-path the next walk keeps the average
location of the step stones at the same location, then the object is
considered to stay at rest or to take part in an oscillatory movement such
that the micro-path is stretched along the path of the oscillation. If that
is not the case, then the object is considered to move and the micro-path
is considered to be stretched along the path of that movement.
the correlation mechanism will put another restriction that concerns the
stretching of the micro-path along the movement or oscillation paths. This
must occur such that that the Fourier transform of the density distribution
of the step stones will reflect the probability distribution of the momenta
that characterize the motion. This restriction reflects the impact of
Heisenberg’s uncertainty principle.
these non-obvious additional restrictions present the model as a quantum
physical system and support the particle-wave nature of the objects that
are controlled by the correlation mechanism.
Universe wide time
Universe wide time ticks at a super-high frequency.
Phenomena, such as waves, that run at this super-high frequency cannot be
observed. Only their averaged effects can become noticeable. Potentials are
typical examples of such averaged phenomena.
Other processes may run in sync with
the universe wide time clock. These processes concern the recreation of
parts of the universe. Most of these processes run at a lower cycle time.
For example, the recreation of all aspects of a particle takes a large
number of progression steps.
In contemporary physics, red-shift is
measured and interpreted as space expansion. Further, the speed of
information transport appears to be constant. The HBM takes this speed as a
model constant. As a consequence space, expansion goes together with a
similar expansion of the progression step. With other words, the universe
wide time clock slows down as a function of progression.
Super-high-frequency waves are special.
Since all lower frequency waves are chopped, the super-high frequency waves
are carrier waves for all other waves. These other waves are modulations or
temporal averages of the super-high frequency waves. The background field
that acts as our curved space is modulated by the super-high frequency
The stuff from which we are made
Quantum fluid dynamics
The medium in
which light propagates is space. This space can curve. The curvature is not
static. So, this space moves. It can be treated as a field. Particles are
embedded in this continuum.
of this combination can be analyzed by a kind of fluid dynamics. Let us
call this method quantum fluid dynamics. It differs from conventional fluid
dynamics in the medium that is treated. In conventional fluid dynamics,
this is a gas or a fluid. Fluid dynamics concerns density distributions and
currents. In quantum fluid dynamics these are space location density
distributions and space location current density distributions. They can be
combined in quaternionic distributions, where the real part is the space
density distribution and the imaginary part is the space current density
functions are probability amplitude distributions. They can be specified as
complex functions or as quaternionic functions. In the last case, they fit
the purpose of quantum fluid dynamics. In fact, they are a special type of
quaternionic distributions that we call quaternionic probability amplitude
fluid dynamics the quaternionic probability amplitude distributions act on
the continuum in which they are embedded. The shared parameter space of all
quaternionic probability amplitude distributions comprises the whole
universe. It is the arena where everything occurs. In the HBM this arena is
The Hilbert Book Model
The Hilbert Book Model (HBM) is a simple model of the
lowest levels of fundamental physics. The HBM is strictly based on quantum
logic. The concepts in the following text are directly or indirectly
derived from this foundation.
In the Hilbert Book Model (HBM) nature steps with universe
wide progression steps from one static status quo to the next static status
quo. Progression conforms to universe wide
time. In the HBM all observed time clocks are synchronized.
In the HBM nature's building blocks (elementary
particles) are represented by coherent sets of what I call step stones. The
step stones are placeholders of locations where the building block can be.
The set is generated by a stochastic process.
At every progression instant, only one step stone is
used. In this way, even at rest, the building block walks along a
micro-path. At every arrival at a step stone, the building block emits a wave
front that carries information about the presence and the properties of the
building block. This wave front propagates with light speed away from its
source. The wave front slightly folds and thus curves the embedding
continuum. This explains the origin of space curvature. The wave fronts
that were emitted by ALL building blocks that existed in the universe,
together form a huge background field. This field acts as the embedding
continuum that we observe as our curved space. It is not a potential. It
has no unique source. The background field implements inertia. (It
counteracts acceleration of embedded particles).
The wave fronts that are emitted by a single particle are
thus generated at slightly different locations. Already at a small
distance, they seem to be generated at a super-high frequency by a source
that has a stationary location. Together, these wave fronts form an SHF
At small scales, the wave fronts that are emitted by a
building block interfere. Together they form a set of rather static potentials
that represent the averaged effect of the wave fronts. The contribution to
a potential by a wave front is characterized by a dedicated Green's
A sudden change of the energy of the building block goes
together with a temporary modulation of the wave fronts. We know such
modulations as photons. The duration of the modulation equals the duration
of a complete micro-walk.
Such occasions occur with electrons inside atoms. There
the electrons walk along a micro-path that is stretched along the path of a
spherical harmonic oscillation. Due to this stochastic motion, the
electrons potentials act as if the electron is free. With other words, the
oscillation is completely hidden by the stochastic stepping. Only the
static potentials are shown. The extra movement is accounted in the mass of
the electron. However, if the electron switches its energy level, then this
goes together with the emission or absorption of a photon that corresponds
to the energy jump.
The fact that the energy quantum is reflected in the
frequency of the photon leads to the conclusion that the photon is
created/annihilated in a fixed number of progression steps. That number
conforms to the duration of a complete micro-walk.
At the start of quantum physics, this phenomenon looked
strange to physicists that expected EM waves that correspond to the
spherical harmonic oscillation.
of the involved objects is treated in detail in the paper:
Work in progress:
Physics of the Hilbert Book Model
of the design of the Hilbert Book Model
stochastic nature of quantum physics
PowerPoint file of Hilbert Book Model
file of HBM_Intro _part I
file of HBM_part 2
versus paginated model
Entanglement in paginated
space progression models
Oscillation of an
the Hilbert Book Model
Abstract of the manuscript
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. It explains entanglement and the Pauli principle. Above all the
HBM introduces a new way of looking at space and time. Where contemporary physics applies the spacetime model, the HBM
treats space and progression as a paginated model.
author’s e-print archive is at
also HAL (Hyper Articles en Ligne)
Schets van het Hilbert Boek
Natuurkundige dilemma’s (Dutch)
of the Hilbert Book Model
On the hierarchy of objects
Hilbert logic slides
Hilbert logic slide comments
Deep Field Theory
the Hilbert Book Model
You can download this manuscript free of charge
You may wish to buy a printed copy of the manuscript.
This manuscript is of an earlier date.
Essentials of the Hilbert Book Model
Table of elementary