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

This paper demonstrates that physical irreversibility is a necessary consequence of dynamics in discrete space as formalized in Quantum-Geometry Dynamics (QGD). The argument does not rest on statistical mechanics, coarse-graining, or any appeal to special initial conditions. It follows from three features of QGD's ontology taken together: the discreteness of quantum-geometrical space, the strict causal succession of physical states, and the instantaneous and universal scope of gravitational interaction. All non-gravitational momentum transfer in QGD operates through a unified emission-absorption mechanism: a particle or structure emits preons⁺ that are absorbed by another, with the absorbed preons⁺ becoming constituents of the receiving structure. This mechanism — instantiated in collisions, electromagnetic interactions, and photon absorption — is shown to be irreversible on three independent local grounds: absorbed preons⁺ cannot be selectively recovered; post-event momentum vectors cannot spontaneously reverse under the principle of strict causality; and the trigger conditions for the emission-absorption process cannot recur with identical conditions. A fourth, global ground follows from QGD's instantaneous universal gravity: every local event irreversibly shifts the gravitational configuration of the entire universe, making all prior states causally unreachable. Each ground is independently sufficient; their conjunction is conclusive. This single result is shown to dissolve four problems that mainstream physics treats as separate: the arrow of time, which is the direction of causal succession in discrete space and requires no special initial conditions; the second law of thermodynamics, which follows from the categorical irreversibility of structure formation from an initial state of zero entropy rather than from statistical arguments over macrostates; the quantum measurement problem, which does not arise in QGD because measurement is a determinate irreversible physical interaction with no wave function, no superposition, and no collapse; and the assumption of reversible gate operations in quantum computing, which is shown to be physically impossible independently of and in addition to the argument against ontological superposition developed in Burnstein (2026d). The paper is explicitly positioned within the Minimal Physically Derivable Theories (MPDT) programme established by the Uniqueness Theorem (Burnstein 2026a) and the broader QGD framework developed in Burnstein (2026e). It also engages directly with Lucien Hardy's reconstruction of quantum theory from five reasonable axioms, showing that QGD's categorical irreversibility stands in direct tension with Hardy's fifth axiom — the existence of continuous reversible transformations between pure states — and raises a precise question about whether Hardy's causaloid framework can be understood as an epistemic representation of QGD's definite causal structure.