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I am a retired physicist. In 2011, when I was 70, I started the Hilbert Book Model project. The project investigates the foundation and the lower levels of the structure of physical reality. The project is treated on https://www.researchgate.net/project/The-Hilbert-Book-Model-Project and on http://vixra.org/author/j_a_j_van_leunen.
A short introduction of the model is provided below.
Foundation and lower levels of the structure of physical reality.
This entry supposes that physical reality possesses structure and that this structure bases on one or more foundations.
Foundations are necessarily simple. Quite probably the foundations were discovered long ago by intelligent people. The discovered foundations became part of the mathematical library. These founding structures are not observable. An important property of foundations is that they extend into higher level structures. After sufficient extensions, facets of the structures of physical reality become observable. That this occurs is not straight forward. It appears to be typical for the structural evolution of physical reality.
For example, all observable massive discrete objects in the universe appear to be modules or modular systems. Sets of elementary modules exist that together configure all other modules and that themselves are not componentized. Another example is that precise clocks exist that despite the fact that they are not connected, keep in sync.
In 1936 two scientists Garrett Birkhoff and John von Neumann introduced a rather simple structure that can suit as a foundation of quantum physics. Because thus structure closely resembled the structure of classical logic, the duo named their discovery quantum logic. Mathematicians decided to name this structure an orthomodular lattice. The set of closed subspaces of a separable Hilbert space shares its relational structure with the orthomodular lattice. A set of atoms of the orthomodular lattice corresponds to the set of rays that the members of an orthogonal base of the Hilbert space span. Rays are one-dimensional subspaces.
Hilbert spaces can only cope with number systems that are division rings. In a division ring, every non-zero member owns a unique inverse. Three suitable division rings exist. These are the real numbers, the complex numbers, and the quaternions. If the quaternions are selected, then the separable Hilbert space can act as a structured repository for the storage of the dynamic geometric data of objects that occur in the model. These data consist of a timestamp and a three-dimensional location. Dedicated operators store these data in their eigenspaces as quaternionic eigenvalues. The eigenspaces of the operators in the separable Hilbert spaces are countable.
At every instant, a ray represents a location of an elementary module. The separable Hilbert space forms the platform on which the elementary particle resides. A large set of separable Hilbert spaces share the same underlying vector space. Each of these separable Hilbert spaces applies a private version of the quaternionic number system to specify the inner products of pairs of the Hilbert vectors. The elementary particles inherit their symmetry related properties from the selected version of the quaternionic number system. All separable Hilbert spaces that represent elementary particles float over a common infinite dimensional separable Hilbert space that acts as a background platform. Each separable Hilbert space owns a reference operator that manages a parameter space that is private to the platform. Thus all private parameter spaces float over the background parameter space. The background separable Hilbert space owns a unique companion non-separable Hilbert space. In the non-separable Hilbert space reside operators that can have eigenspaces, which are continuums. It is possible to consider the non-separable Hilbert space to embed all separable Hilbert space that float on top of its separable companion.
Depending on their dimension, number systems exist in many versions that differ in their ordering. A Cartesian coordinate system followed by a polar coordinate system can perform the ordering of a version of a quaternionic number system.The inner product of pairs selects one of these versions for specifying its values. Versions of number systems can act as parameter spaces and the Hilbert can store these parameter spaces as eigenspaces of normal operators.
The real part of the background parameter space corresponds to a subspace that scans over the whole vector space that underlies all separable Hilbert spaces as a function of progression. It divides the Hilbert space in a historical part, a static status quo, and a future part. It is possible to interpret the embedding of the separable Hilbert space into its non-separable companion as an ongoing process that occurs within the scanning subspace. Within the scanning subspace rays that are spanned by mutually orthogonal vectors represent the elementary modules.
A private mechanism that applies a stochastic process provides the location of the elementary module. Consequently, the elementary module hops around in a stochastic hopping path. After a while, the module matures statistically in a hop landing location swarm. The stochastic process owns a characteristic function. This function ensures the coherence of the swarm. The swarm owns a location density distribution and the characteristic function is the Fourier transform of that location density distribution. A gauge factor that acts as a displacement generator for the swarm can be added to the characteristic function. Consequently, the swarm behaves coherently and at first approximation, it moves as one unit.
The hop landings trigger a reaction of the embedding continuum in the form of a clamp. The name clamp is introduced by the author. A clamp is a spherical shock front. Its amplitude diminishes as 1/r with distance r from the trigger location. Clamps integrate into the Green's function of the embedding continuum. Due to the fact that they deform the embedding continuum, each clamp carries a standard bit of mass. However, the clamps are volatile. They quickly fade away. Only in dense swarms that are recurrently regenerated clamps can generate a persistent impression. This describes how elementary modules create a gravitation potential.
The platform on which the elementary module resides carries a parameter space that is private to the elementary module. The difference between the ordering of the private parameter space and the ordering of the background parameter space determines the symmetry flavor of the platform. The symmetry flavor corresponds to the symmetry-related charge of the platform. That charge locates at the geometric center of the platform. The elementary module inherits this symmetry-related charge and the charge interacts with the symmetry related field.
The model considers all modules as observers. Observers can read information that the creator stored at the instant of the creation of the model into the repository that consists of the combination of a series of infinite dimensional separable quaternionic Hilbert spaces and a non-separable companion Hilbert space of the background separable Hilbert space. The observers can only access information that is stored with an earlier timestamp. In addition, the transfer through the embedding continuum converts the originally Euclidean format of the stored dynamic geometric information about the observed event into the spacetime format that the observers perceive. The spacetime format features a Minkowski signature.
Quaternionic differential calculus describes the behavior of the embedding continuum and the interaction between this continuum and pointlike artifacts. The hopping elementary modules play the role of the pointlike artifacts.
I have started the Hilbert Book Model project. Hilbert_Book_Model_Project--HansVanLeunen (discuss • contribs) 12:12, 19 April 2017 (UTC) Updated by Hans van Leunen HansVanLeunen (discuss • contribs) 14:57, 26 May 2018 (UTC)
Please stop creating subpages of the Hilbert Book Model Project in main space. Subpages may be created by simply adding a forward slash in the title, such as Hilbert Book Model Project/Multi-mix Path Algorithm. If necessary, use the following to create a new project subpage:
Dave Braunschweig (discuss • contribs) 12:27, 25 April 2017 (UTC) Dave, Thanks for your advice. I now comprehend how to add subpages to the project. I will take your advice seriously. Greetings, Hans. --HansVanLeunen (discuss • contribs) 14:20, 25 April 2017 (UTC)
Hilbert Book Model Project[edit source]
Your resource the Hilbert Book Model Project appears to be well-developed and ready for learners! Would you like to have it announced in our Main Page News? Marshallsumter (discuss • contribs) 17:33, 9 October 2017 (UTC) Every initiative that leads to better knowledge of the purpose of the Hilbert Book Model project is welcome. I try to publish references to the Hilbert Book Model Project at ResearchGate, LinkedIn grouups, Quora and Science20.com as many as I can generate on those sites. So, I am pleased with your proposal. In the mean time I keep improving the Wikiversity Hilbert Book Model Project.HansVanLeunen (discuss • contribs) 19:36, 9 October 2017 (UTC)