Theoretical physics still contains unresolved subjects. These deficiencies of the theory are caused by the way that physics was developed and by the attitude of the physicists that designed the current theory. Scientists take great care to secure the trustworthiness of their work, which ends in the publication of the results. They take measures to prevent that their publications get intermingled with badly prepared publications or even worse, with descriptions of fantasies. For that reason, they invented the scientific method . In applied physics, the scientific method founds on observations. Applied physics flourishes because the descriptions of observations help to explore these findings, especially when formulas extend the usability of the observations beyond direct observation. In theoretical physics, this is not always possible because not all aspects of physical reality are observable. The only way of resolving this blockade is to start from a proper foundation that can be extended via trustworthy methods that rely on deduction. This approach can only be successful if the deduction process is guided and restricted such that the extensions of the foundation still describe physical reality. Thus, if a mathematical deduction is applied, then mathematics must guide and restrict this process such that a mathematically consistent extension of the model is again a valid model of physical reality. After a series of development steps, this approach must lead to a structure and behavior of the model that more and more conforms to the reality that we can observe.
This guidance and restriction are not self-evident. On the other hand, we know that when we investigate deeper, the structure becomes simpler and easier comprehensible. So, finally, we come to a fundamental structure that can be considered as a suitable foundation. The way back to more complicated levels of the structure cannot be selected freely. Mathematics must pose restrictions onto the extension of the fundamental structure. This happens to be true for a foundation that was discovered about eighty years ago by two scholars. They called their discovery quantum logic . The scholar duo selected the name of this relational structure because its relational structure resembled closely the relational structure of the already known classical logic. Garrett Birkhoff was an expert in relational structures. These are sets that precisely define what relations are tolerated between the elements of the set. Mathematicians call these relational structures lattices, and they classified quantum logic as an orthomodular lattice . John von Neumann was a broadly oriented scientist that together with others was searching for a platform that was suitable for the modeling of quantum mechanical systems. He long doubted between two modeling platforms. One was a projective geometry, and the other was a Hilbert space   .Finally, he selected Hilbert spaces. In their introductory paper, the duo showed that quantum logic emerges into a separable Hilbert space. The set of closed subspaces inside a separable Hilbert space has exactly the relational structure of an orthomodular lattice. The union of these subspaces equals the Hilbert space. A separable Hilbert space applies an underlying vector space , and between every pair of vectors, it defines an inner product . This inner product can only apply numbers that are taken from an associative division ring  . In a division ring, every non-zero member owns a unique inverse. Only three suitable division rings exist. These are the real numbers, the complex numbers, and the quaternions. Depending on their dimension these number systems exist in several versions that differ in the way that Cartesian and polar coordinate systems sequence their members  .
In the Hilbert space, operators exist that can map the Hilbert space onto itself. In this way, the operator can map some vectors along themselves. The inner product of a normalized vector with such a map produces an eigenvalue. This turns the vector into an eigenvector. Together the eigenvalues of an operator form its eigenspace. This story indicates that mathematics guides and restricts the extension of the selected foundation into more complicated levels of the structure. It shows that the scholar duo started a promising development project.
However, this initial development was not pursued much further. Axiomatic models of physical reality are not popular. Most physicists mistrust this approach. Probably these physicists consider it naïve to suspect that an axiomatic foundation can be discovered that like the way that a seed evolves in a certain type of plant, will evolve into the model of the physical reality that we can observe.
Most quantum physicists decided to take another route that much more followed the line of the physical version of the scientific method. As could be suspected this route gets hampered by the fact that not every facet of physical reality can be verified by suitable experiments.
Mainstream quantum physics took the route  of quantum field theory , which diversified into quantum electrodynamics  and quantum chromodynamics . It bases on the principle of least action , the Lagrangian equation  and the path integral  However, none of these theories apply a proper foundation.
In contrast, the Hilbert Book Model Project intends to provide a purely and self-consistent mathematical model of physical reality  . It uses the orthomodular lattice as its axiomatic foundation and applies some general characteristics of reality as guiding lines. An important ingredient is the modular design of most of the discrete objects that exist in the universe. Another difference is that the Hilbert Book Model relies on the control of coherence and binding by stochastic processes that own a characteristic function instead of the weak and strong forces and the force carriers that QFT, QED, and QCD apply   .
Crucial to the Hilbert Book Model is that reality applies quaternionic Hilbert spaces as structured read-only archives of the dynamic geometric data of the discrete objects that exist in the model. The model stores these data before they can be accessed by observers. This fact makes it possible to interpret the model as the creator of the universe. The classification of modules as observers introduces two different views; the creator’s view and the observer’s view. Time reversal is only possible in the creator’s view. It cannot be perceived by observers because observers must travel with the scanning time window. ×