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    Johannes van Leunen's picture
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    Joined: May 26 2016
    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, http://vixra.org/abs/1708.0233
    Johannes vL

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    Zoran S. D.'s picture
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    Joined: Jan 14 2014

    "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 first few sentences you wrote make perfect sense.
    And then you sink into mathematical mysticism.
    Johannes van Leunen's picture
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    Joined: May 26 2016
    @Zoran,If you put some energy in comprehending the required math, then the next steps are not mysticism. They describe how reality evolves from a very powerful seed into a coherently behaving system.

    Lattices, Hilbert spaces and number systems are not complicated pieces of mathematics. Without these concepts it is very hard to tell the Hilbert Book Model as a good running story.


    Lattices are relational structures. Classical logic is a lattice of logic propositions. It is very similar to the orthomodular lattice, which is the foundation of reality that immediately leads to the Hilbert space because the set of closed subspaces of the Hilbert space has exactly the lattice structure of an orthomodular lattice. 
    Pia Maria Solèr proved not so long ago that Hilbert spaces can only cope with number systems for which every non-zero element has an inverse. The most complicated number system that fulfills that rule is formed by the quaternions. Because this number system is four dimensional, and every axis of the coordinate system can be ordered up or down, will sixteen versions of that number system exist. The HBM shows that the existence of these versions are responsible for the existence of the short list of electric charges and the color charges that elementary particles can have. 
    If you understand quaternionic Hilbert spaces, then you will comprehend that they implement repositories for data that can be stored in quaternions and quaternions are ideally suited to store combinations of time-stamps and spatial locations or real scalars and 3D vectors.

    At the instant of the creation the creator stores all relevant dynamic geometric data of his creatures in this repository, which at that instant becomes a read-only repository. His creatures may read this repository as observers, but these observers only get access to historic data. The observers live in a subspace that scans over the whole repository.
    Johannes vL

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