Een wiskundig model van de realiteit (in Dutch)
Op Zoek naar witte vlekken(in Dutch)
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”. When the new insights mature, then I store the result
on my personal e-print archive on Vixra. Vixra has an excellent revision
service that allows you to follow the development of my ideas. Only once
per year the e-book will be adapted.
A mathematical model of
Quaternions and Hilbert spaces
Skeleton relational structures
What drives reality?
Reality contains a network of mathematical
HBM is a model that is based on a
recipe for modular construction
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 =
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 wave function
Discrete physics treats objects and constructs that perform
below the wave function
“Above the wave function” = what uses the wave function
“Below the wave function” = what is described by the wave
underneath the wave function?
I do this HBM project purely for the fun
of it and out of curiosity to the lower levels of physics
The most basic law 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.
This law represents a recipe for modular
The last e-book
Introduction to the
Hilbert Book Model
The role of the observer
traffic to this website became so intense that the costs surpassed my
am now constructing alternatives via Google drive
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
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 reveal
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 model!
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.
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 industry. After his retirement the
author restarted the project in 2009. The project got its current name in
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 http://vixra.org/author/j_a_j_van_leunen
Time proceeds 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 step.
As a consequence in that model 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.
The observer 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
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.
The observer 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.
Contemporary 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.
In general, 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 from the location
of the observed item to the location of the observer is 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.
The main criterion for the validity of the
paginated model is the fact whether all observed time clocks can be
If the paginated space-progression model exists,
then this model and the spacetime model can be considered to be two
different views of the same physical reality.
status quo descriptors
Another 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 abstraction.
Physical 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.
Physical reality appears to have selected a
skeleton relational structure as a means to keep the complexity of its
constructs within bounds.
Mathematical 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
Thus quantum logic seems to represent the skeleton
relational structure that physical reality has selected in order to reduce
Mathematics 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 geometrical data.
The conclusion 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.
Without extra 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
The 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
Controlling the propagation of the wave fronts
that implement the potentials of the particles
Storing data in eigenspaces of operators and in
quantum state functions.
systems and subsystems.
nature of quantum physics
An original 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
You might agree that this comes close to the
description of an elementary particle.
restrictions set by the correlation mechanism
An 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 wave function 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.
If 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.
Here 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
Together 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
Universe wide time
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
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.
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
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 waves.
The stuff from
which we are made
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.
The behavior 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 distribution.
Quantum state 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
In quantum 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 called Palestra.
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
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 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 an
super-high frequency by a source that has a rather stationary location.
Together, these wave fronts form an SHF wave.
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 function.
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.
The overview of the involved objects is treated in
detail in the paper:
Work in progress:
Physics of the Hilbert Book Model
Sketch of the design of
the Hilbert Book Model
The stochastic nature of
file of Hilbert Book Model
PowerPoint file of HBM_Intro _part
PowerPoint file of HBM_part 2
Spacetime model versus paginated
Entanglement in paginated space progression
Oscillation of a HBM particle
Discoveries of the Hilbert Book
Abstract of the manuscript
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. 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 Model (Dutch)
Natuurkundige dilemma’s (Dutch)
Sketch of the Hilbert
On the hierarchy of objects
Hilbert logic slides
Hilbert logic slide comments
Deep Field Theory
Features of the Hilbert
You can download this manuscript free of charge
You may wish to buy a printed copy of the
This manuscript is of an earlier date.
of the Hilbert Book Model
Table of elementary particles