Dissolving the Mentaculus: How Quantum-Geometry Dynamics Accounts for Time's Arrows Without a Statistical Postulate

Abstract

Albert and Loewer’s Mentaculus is an ambitious unification project that aims to account for the reversibility problem, the thermodynamic arrow of time, the epistemic arrow, the influence and causal/counterfactual arrows, the applicability of statistical reasoning to macroscopic regularities, and the compatibility of objective probability with determinism. This companion note evaluates each of these explananda through the apparatus of Quantum-Geometry Dynamics (QGD) and the Minimally Physically Derivable Theories (MPDT) programme. The central result is that QGD dissolves the reversibility problem at its root. Because QGD’s fundamental dynamics is categorically asymmetric rather than time-symmetric, the inference that the Past Hypothesis and Statistical Postulate are jointly designed to block never arises. The thermodynamic arrow at cosmological scale follows as a direct theorem of preonic binding; the Statistical Postulate is shown to be a modelling residual rather than a further fundamental law. QGD’s own isotropic initial state S0 S_0 S0 remains necessary but is immune to the continuum fine-tuning charge that the Mentaculus literature itself acknowledges for the Past Hypothesis. The epistemic arrow receives an independent non-statistical account of records, while a practical residual for finite observers is openly acknowledged. The causal, counterfactual and influence arrows are treated only as a sketch; a developed counterfactual semantics remains an open item. Objective probability under determinism is sidestepped rather than solved, because QGD treats probability as strictly epistemic. This is an ungrounded companion note to the QGD / MPDT Problem Register and is not assigned a portfolio (P-series) number.