The Hilbert Book Test Model is a purely mathematical model of the lower levels of the structure of physical reality. Its base consists of an infinite dimensional separable Hilbert space and its unique non-separable companion Hilbert space. Both Hilbert spaces use members of a version of the quaternionic number system to deliver the values of their inner products. Thus also the eigenvalues of the operators that map Hilbert spaces onto themselves are quaternions. A special reference operator applies the rational members of the selected quaternionic number system to enumerate an orthonormal base of the separable Hilbert space. It uses the base vectors as its eigenvectors and the enumerators as the corresponding eigenvectors. The eigenspace can be used as a parameter space of a set of quaternionic functions and these functions can be used to define a category of defined operators that reuse the eigenvectors of the reference operator and apply the corresponding target values of the function as its eigenvalues. The same trick can be performed in the non-separable companion Hilbert space, but this time all members of the number system are used.
A scanning vane can be defined as a subspace of the separable Hilbert space that is spanned by the eigenvectors of the selected reference operator that share the same real part of the corresponding eigenvalues. The real value can be interpreted as progression. The vane splits the Hilbert space between a historic part, a static status quo (the vane), and a future part.
The non-separable Hilbert space can be considered to embed its separable companion. And the vane can be interpreted as the subspace where the ongoing embedding process occurs.
The model impersonates a creator. This idea eases the discussion about the creation of the universe, which is the living space of the discrete objects that appear in the model.
This simple dynamic model offers two views. One is the creator’s view. The creator has access to all dynamic geometric data that are stored in the Hilbert spaces.
The other view is the observer’s view. Observers are constituted from elementary modules that travel with the vane. In the vane, rays represent these elementary modules. Rays are one-dimensional subspaces. In the vane, each elementary module owns a private location that is presented by the imaginary part of a quaternion. A stochastic mechanism generates these locations. Therefore, the elementary modules appear to hop around in a stochastic hopping path. After a while, the hop landing locations have formed a coherent location swarm. The swarm and the hopping path represent the elementary module. A location density distribution describes the coherent swarm. This distribution equals the squared modulus of the wavefunction of the elementary module.
Together the elementary modules constitute all other modules and the modular systems that appear in the model.
The observers have no access to the future part of the model. They get their information via deformations of the embedding continuum or via information messengers that travel in the embedding continuum. The embedding continuum is the living space of the elementary modules. Thus, it is also the living space of all observers.
In the creator’s view, the elementary modules live in a tube that zigzags through the living space. The tube may just cross the vane, but it may also happen that the tube reflects against the vane. The reflection can occur at the historic side of the vane, but it can also occur at the future side. With other words, the tube may cross the vane multiple times. This means that the same elementary module can exist multiple times at the same instant in the vane. These appearances are entangled in a way that must be mysterious to the observers.
The observers will interpret the reflection against the historic side of the vane as the annihilation of a pair of an elementary module and its anti-module. The observers interpret the reflection against the future side of the vane as the creation of a pair of an elementary module and its anti-module.