Hilbert Book Model
paginated space-progression model
is strictly based on quantum logic
proceeds with fixed progression steps. It is a parameter that is more
fundamental than any other physical feature. It underlies all dynamics.
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
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
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.
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.
a paginated model, for all observed items the universe wide time clock has
the same value. Thus, in that model 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.
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
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
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 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.
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. Only the static
potentials are shown. 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
of the Hilbert Book Model
file of Hilbert Book Model
Spacetime model versus paginated
Entanglement in paginated space progression
The stochastic nature of
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
Schets van het
Hilbert Boek Model (Dutch)
Natuurkundige dilemma’s (Dutch)
Sketch of the Hilbert Book
On the hierarchy of objects
Hilbert logic slides
Hilbert logic slide comments
Deep Field Theory
Features of the
Hilbert Book Model
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of the Hilbert Book Model
Table of elementary particles