Authors: J.A.J. van Leunen
In order to support clear discussions, a simple self- consistent model of fundamental physics is constructed. It is strictly based on the axioms of traditional quantum logic and uses the isomorphism of the set of propositions of this logic system with the set of closed subspaces of a quaternionic separable Hilbert space. This primitive model cannot represent dynamics and does not include a representation of fields. For that reason the model also uses the Gelfand triple of the Hilbert space and a set of links that connect the eigenvectors of a particle location operator in the Hilbert space with the continuum eigenspace of a corresponding location operator in the Gelfand triple. These links are quaternionic probability amplitude distributions (QPAD’s) that will act as the quantum state functions of the particles. The combination of a quaternionic Hilbert space, its Gelfand triple and the set of linking QPAD’s still can only represent a static status quo of the universe. However, a dynamic model may consist of an ordered sequence of such sandwiches. The subsequent sandwiches form the pages of a book that we will call the Hilbert Book Model. The quaternionic derivative of a QPAD leads to a continuity equation that describes how the derivative is coupled to its source. When the strength of the coupling is made explicit, then the resemblance with linear equations of motion becomes apparent. This interpretation extends conventional quantum physics with quantum fluid dynamics. It throws an unprecedented view on the undercrofts of fundamental physics.
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