• Wednesday 13 December 2017 at Geneva – Karen Crowther (Geneva): When do we stop digging? Necessary conditions on a fundamental theory
Abstract: In seeking an answer to the question of what it means for a theory to be fundamental, it is enlightening to ask why the current best theories of physics are not generally believed to be fundamental. This reveals a set of conditions that a theory of physics must satisfy in order to be considered fundamental (although it is a further question whether a theory’s satisfaction of these necessary conditions is sufficient for it to be considered fundamental). Physics aspires to describe ever deeper levels of reality, which may be without end. Ultimately, at any stage we may not be able to tell whether we’ve reached rock bottom, or even if there is a base level–nevertheless, I aim here to draft a checklist to help us identify when to stop digging, in the case where we may have reached a candidate for a final theory. I begin by outlining some of the different conceptions of fundamentality associated with modern physics, before explaining why neither our current best theory of matter and forces (the standard model of particle physics), nor our current best theory of spacetime (general relativity), are generally considered fundamental. Following this, I present the necessary conditions that physicists apparently place on a fundamental theory, and I explore what these tell us about the nature of fundamentality. In terms of technical difficulty, this talk rates 1/5 
Beyond Spacetime 
Eighty years ago Garrett Birkhoff and John von Neumann discovered a candidate for an axiomatic foundation of physical reality. In their introductory paper, they showed that this orthomodular lattice emerges into a separable Hilbert space. They named their discovery “quantum logic” because its structure is quite like the structure of classical logic. However, the orthomodular lattice is not a logic system. Its elements are not logical propositions. Instead, the elements are closed subspaces of the separable Hilbert space and its atoms are rays that together span the Hilbert space. Some groups investigated this candidate, but these investigations stranded because they misinterpreted the elements of the orthomodular lattice. Much later John Baez gave a proper account of these trials. This does not mean that the duo did not find the proper foundation. Nobody explored the full potential of the separable Hilbert spaces as a development platform for physical theories. The secret is to define a set of separable Hilbert spaces that share the same vector space and use the fact that Hilbert spaces can cope with several versions of the quaternionic number system that differ in the way that coordinate systems sequence them. Also, the fact that infinite dimensional separable Hilbert spaces can embed in a non-separable Hilbert space is not explored properly. These possibilities lead to a powerful modeling platform that combines Hilbert space operator technology with quaternionic function theory and indirectly with quaternionic differential and integral calculus. The model implements a read-only repository in which reality can archive all of its dynamic geometric data in eigenspaces of quaternionic normal operators.
The Hilbert Book Model applies this model and the Hilbert Book Model Project.describes this model. https://en.wikiversity.org/wiki/Hilbert_Book_Model_Project.
http://vixra.org/author/j_a_j_van_leunen contains several excerpts that highlight aspects of the project.
As can be expected the Hilbert Book Model is very unorthodox and in relation to mainstream physics, the project is controversial.