Hilbert Book Model
paginated space-progression model
is strictly based on quantum logic
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
new view creates new insights !
I do this project purely for the fun of it and out of
curiosity to the lower levels of physics
Introduction to the
Hilbert Book Model
The role of the observer
The full slide show (in preparation)
The corresponding spoken text
Corresponding mp4 video
The concepts of
the Hilbert Book Model will be explained at the
DPG congress in Berlin at Tuesday march 18
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 2011.
he restarted the Hilbert Book Model project, the insights of the author
can follow this development via publications and his discussions on
ResearchGate, on Science2.0 and on LinkedIn.
November 2011 the author publishes on his e-print archive at http://vixra.org/author/j_a_j_van_leunen
proceeds with rather fixed progression steps. It is a parameter that is
more fundamental than any other physical feature. It underlies all
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.
a paginated space-progression model all observed time clocks are
synchronized. With other words in that model resides a universe wide time
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 static models.
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
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.
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.
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 observer.
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
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.
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.
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
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.
main criterion for the validity of the paginated model is the fact whether
all observed time clocks can be synchronized.
the paginated space-progression model exists, then this model and the
spacetime model can be considered to be two different views of the same
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.
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.
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.
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.
quantum 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.
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.
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 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.
tasks of the correlation mechanism are:
Embedding particles in the field that acts as the curved
Establishing the swarming conditions for elementary
Controlling the propagation of the wave fronts that
implement the potentials of the particles
Storing data in eigenspaces of operators and in quantum
Supporting entangled systems and
Stochastic nature of quantum physics
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 micro-path.
might agree that this comes close to the description of an elementary
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
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 principle.
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
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
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 waves.
The stuff from which we are made
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.
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.
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 distributions.
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
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 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.
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 I
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.
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 Book Model
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