QGD / MPDT and Loop Quantum Gravity: Achievements, Structural Challenges, and a Minimal Axiomatic Alternative

Loop Quantum Gravity (LQG) represents the most sustained and mathematically sophisticated attempt to quantise geometry without a background spacetime. Its central achievements are genuine: area and volume quantisation, background independence, and the partial dissolution of the ultraviolet divergence problem. This paper addresses the LQG researcher directly, with the aim of showing that the problems LQG cannot solve from within its own framework — the Barbero–Immirzi parameter, the classical limit problem, the temporal import in spin foam models, and the non-derivability of three-dimensionality — are not technical obstacles awaiting better mathematics. They are structural consequences of LQG’s founding commitment: quantising an inherited continuum structure rather than deriving a discrete one from axioms. The Quantum-Geometry Dynamics (QGD) framework, developed within the Minimally Physically Derivable Theories (MPDT) programme, begins where LQG’s motivations point but its derivations cannot reach. Space is not quantised — it is constituted by discrete preons(−) as a primitive axiomatic commitment. The result is a framework in which LQG’s genuine achievements survive as effective approximations, its structural challenges dissolve without replacement, and a precise translation dictionary connects the two programmes’ technical vocabularies. The paper closes with differential empirical predictions that distinguish the two frameworks at experimentally accessible scales.