Daniel Burnstein

Why Space Has Three Dimensions: A Derivation from Minimal Axioms in Quantum-Geometry Dynamics

The dimensionality of space—the fact that the physical universe is three-dimensional rather than two, four, or any other number—is standardly taken as a brute empirical datum. While frameworks like String Theory attempt to explain macroscopic three-dimensionality via the dynamica...

The Physicality of Logic: The Structural Inapplicability of Incompleteness, Undecidability, and Computational Complexity Gaps to Finite Physical Domains

Three foundational results of twentieth-century mathematical logic — Gödel's incompleteness theorems, Turing's undecidability of the halting problem, and the P vs NP complexity gap — have been widely taken to impose permanent limitations on what a physical theory can achieve. Thi...

On the Uniqueness of Minimal Physically Derivable Theories

This paper proves a metatheorem concerning the class of physical theories derivable from minimal axiom sets. Rather than asking whether two given theories are equivalent — the direction taken by the existing literature on theoretical equivalence — it asks a prior question: given...

The Physicality of Scales: An Emergent Hierarchy from Minimal Axioms in Quantum-Geometry Dynamics

This paper proposes physically grounded definitions of object and scale within the framework of Quantum-Geometry Dynamics (QGD) and the Minimal Physically Derivable Theories (MPDT) programme established by the Uniqueness Theorem. Both definitions have been absent from the existin...

Physical Irreversibility in Quantum-Geometry Dynamics: Dynamics in Discrete Space as the Origin of the Arrow of Time, the Second Law, the Thermodynamics, the Measurement Problem, and the Limits of Quantum Computing

The fundamental laws of classical mechanics, quantum mechanics, and general relativity are time-symmetric, yet macroscopic experience is irreversible without exception. Standard physics bridges this gap with statistical argument: reversal is treated as merely improbable, not phys...