Quantum-Geometry Dynamics; an axiomatic approach to physics

This book addresses Hilbert's sixth problem — the axiomatisation of physics — directly and systematically. It presents Quantum-Geometry Dynamics (QGD), a physical theory derived from a minimal axiom set in which space is discrete, matter is constituted by fundamental kinetic particles called preons(+), and all physical change is governed by two opposing forces: p-gravity, the attractive force between preons(+), and n-gravity, the repulsive force between the fundamental spatial constituents, preons(−), whose mutual repulsion dimensionalises discrete quantum-geometrical space. From these axioms, without additional assumptions, QGD derives the full range of physical phenomena described by quantum mechanics, special and general relativity, and the Standard Model — while making novel predictions that distinguish it empirically from all three.

The foundational argument of the book is that existing physical theories — quantum mechanics, general relativity, and the Standard Model — are non-minimal frameworks. They introduce primitives that are not derivable from a minimal axiom set: the continuous wave function, continuous spacetime, probabilistic measurement, multiple fundamental particles, and numerous free parameters. Their persistent incompatibilities — above all the quantum gravity problem — are not deep facts about nature but structural consequences of their non-minimality. A theory derived from a genuinely minimal axiom set does not divide nature into a quantum sector and a gravitational sector, and therefore requires no reconciliation between them. The quantum gravity problem is not solved but dissolved.

The book develops QGD's account across nineteen chapters covering the derivation of quantum-geometrical space and its discrete geometry; the nature of matter as bound configurations of preons(+); the laws of momentum conservation and their consequences for all physical interactions; the derivation of relativistic effects including clock-rate changes, the bending of light, perihelion precession, and the mass-energy relation; the electromagnetic effects arising from the polarisation of the preonic field; quantum phenomena including interference, diffraction, atomic electron states, and the resolution of wave-particle duality without waves; QGD cosmology including dark matter as free preons(+), dark energy as repulsive n-gravity at cosmological scales, and the prediction of a finite bounded static universe; and the physics of mathematical practices, arguing that Gödel's incompleteness theorems, Turing's undecidability result, and the P vs NP distinction do not apply to physical reality because all three presuppose infinite domains that a finite physical universe does not instantiate.

Seven addenda extend the main text. Addendum A examines high-energy phenomena and reinterprets LHC results within the QGD framework. Addendum B assesses consistency of current LHC detections with QGD. Addendum C resolves the dark galaxy paradox through preonic dynamics. Addendum D presents QGD's deterministic account of Bell correlations: measurement physically alters the momentum of one particle, instantaneously updating the gravitational field acting on the distant particle, whose correlated outcome is a deterministic mechanical reaction governed by the laws of momentum conservation in discrete space — preserving absolute realism without sacrificing locality in the non-gravitational sense. Addendum E collects thirteen predictions unique to QGD, each with derivation references and Popper-level falsifiability criteria, spanning kinematics, gravity, quantum phenomena, cosmology, and high-energy physics. Addendum F proves the Uniqueness Theorem for Minimal Physically Derivable Theories: any two theories satisfying five conditions on minimality — one kind of fundamental matter, computationally representable space, momentum as primitive, exactly two opposing forces, and no axiom derivable from the rest — describe the same fundamental ontology and cannot differ in any derivation, description, or prediction. Addendum G develops the implications of the Uniqueness Theorem for quantum gravity, showing that QM and GR are incompatible not because nature is divided against itself but because both frameworks violate the minimality conditions, and that QGD, as the unique theory satisfying those conditions, is the theory from which both emerge as limiting approximations.

The book is intended for physicists, philosophers of physics, and mathematically literate readers interested in foundational questions. It is the primary source for the QGD framework and the basis for the author's associated papers on the Uniqueness Theorem, the physicality of logic, quantum computing under QGD, and the Bell correlations. It is published simultaneously in paperback and hardcover editions.

ISBN: [pending — to be assigned by Library and Archives Canada]