The human brain is not capable to generate a theory that explains everything. In contrast, the discovery of a seed from which everything evolves might offer a useful result. This approach assumes that reality possesses structure and in addition it assumes that this structure has a foundation, which automatically evolves into more complicated levels of the structure of reality.Discovery is possible because foundations of structures are intrinsically simple. Thus a large chance exist that intelligent humans already discovered a similar structure. These humans were not searching for a foundation of reality. Instead, they are interested in general in similar structures. In 1936 Garret Birkhoff and John von Neumann reported what they called "quantum physics" and they showed in their paper that this lattice equals the lattice structure of the set of closed subspaces of a separable Hilbert space. Thus, the discovered lattice acts as a seed that automatically evolves in a platform that quantum physicists apply for modelling quantum physical systems.
This fact invites the investigation whether this seed poses restrictions and offers extensions that guides its evolution into an equivalent of what we know as reality.
Hilbert spaces can only cope with number systems that are division rings. Quaternions form the most elaborate division ring and quaternionic number systems exist in several versions that differ in the way that Cartesian and polar coordinate systems can order them.
The separable Hilbert space harbors operators that own countable eigenspaces. Thus these eigenspaces can only store the rational members of number systems.
Every infinite dimensional separable Hilbert space owns a unique non-separable companion that embeds its separable companion. The non-separable Hilbert space harbors operators that can store continuums in their eigenspaces. The version of the number system that the Hilbert space uses for specifying the inner product of pairs of Hilbert vectors plays a special role as the background parameter space of the Hilbert space. In a quaternionic separable Hilbert space this fact can be used to define a special reference operator that applies the rational members of the background parameter space as its eigenvalues and an orthonormal base as the corresponding eigenvalues. Now a selected real value can play the role of progression and define a subspace that the eigenvectors span, for which the real parts of the eigenvalues equal the progression value. This subspace scans over a dynamic base model that consist of the two Hilbert spaces. It divides the model into a historic part, a static status quo, and a future part.
This base model is like a fishbowl without fish.
The Hilbert Book Model fills the base model with floating platforms and with swarms and strings of shock fronts that present the basic quanta of the model.
See: Basic Quantum Field Theory,