Unified Chronoscalar Scaling Across Quantum Hall Systems, Graphene, Nematic FQHE, and Planetary Aurorae, with Machian Direction and Drift-Dynamics Derivation

Abstract

Ultra-clean quantum Hall devices, high-mobility graphene heterostructures, nematic fractional quantum Hall states, and planetary auroral plasmas exhibit persistent anisotropies and drift phenomena that cannot be reconciled within time-reversal-symmetric transport theories. Residual longitudinal resistivity floors survive in GaAs quantum Hall samples as T → 0, graphene breakdown fields display orientation locking even in ballistic regimes, nematic FQHE phases at ν = 7/3, 9/2, 11/2 form in the absence of any externally imposed symmetry-breaking field, and auroral emissions on Earth, Saturn, and Jupiter show long-lived dawn–dusk power asymmetries and inertial locking unexplained by solar-wind forcing or traditional MHD closure. Chronoscalar Field Theory (CFT) attributes all of these effects to a single underlying structure: a cosmologically imprinted gradient of a scalar condensate T(xμ) that defines an arrow of time at the level of the action. The chronoscalar gradient Tμ = ∇μT and its unit direction nμ = Tμ/|∇T| act as a universal, Mach-selected vector field that permanently breaks local time-reversal symmetry and induces a small but coherent anisotropy in every electromagnetic and transport observable. We show that the same gradient, with numerical value |∇T|⊕ = 1.36 × 10−14 m−1 as inferred from galactic rotation curves, lensing, and cluster dynamics in CFT III, produces a universal seed ϵCFT = |∇T|Leff which, when amplified by the appropriate collective dynamics, quantitatively matches the magnitude and direction of the observed anomalies from micron-scale Hall bars to planetary magnetospheres. The resulting scaling relation Δσ/σ ∝ |∇T|Leff spans over twelve orders of magnitude in Leff , yet remains consistent with existing QHE, graphene, nematic FQHE, and auroral datasets without introducing any new particles, hidden sectors, or higher-dimensional manifolds. Instead, an intrinsically asymmetric force of time—encoded in Tμ and its Hessian curvature Hμν = ∇μ∇νT—endows spacetime with persistence and a distinguished direction that is weak on microscopic scales but decisive once collective drift dynamics are taken into account.

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