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Evaluates Lorentz compliance in local matter models, indicating implications for quantum stability.
Preferred-frame tests, loop stability, and the missing ABC vector This paper audits the Lorentz question raised by any theory with an absolute source clock: if the substrate has an ordering clock, why do local laboratory experiments see Lorentz-invariant matter and light? The answer developed here is expressed in the language used by precision tests: the local Einstein-gauge matter action contains no laboratory ABC vector, no anisotropic kinetic tensor, and no direction-dependent propagation coefficient. The local matter face is \[ Sₘₐₜₜₑᵣˡᵒᶜ = ∫ d^4x\,√-g\, LSM(gμν,ψ), \] so the minimal SME coefficients vanish at tree level in the local Einstein-gauge sector: \[ { a_μ=b_μ=cμν=dμν=Hμν=0. } \] The Lorentz factor is not imported as a postulate. It is read as the A6 finite-speed budget: \[ { v^2+c_W^2=c^2, dτ/dT=c_W/c = √1-v^2/c^2, γQTT=1{√1-v^2/c^2}. } \] The radiative-stability part answers the Collins-style loop objection. The legal Artian regulator class is four-dimensional and covariant, \[ Δ V_4=4π_A^4, Λ_*=(8π)1/4_A⁻¹, t_*=_A^2/48, F(t_*Δ_E), \] with \(F\) an entire scalar profile. For this class, the low-dimensional Lorentz-violating SME projection of the regulated one-loop effective action is \[ { ΠSMELV [ Γ1PIArtian - Γ1PIᶜᵒᵛ ]d≤4 =0. } \] The zero is not obtained by Planck suppression. A deliberately illegal ellipsoidal regulator gives the exact response \[ { Δ c(ξ)= e^2(ξ-1)/16π^2 ∫_0^∞ {y^2\,dy}{(1+y)3/2(ξ+y)5/2}, Δ c'(1)=α/12π. } \] Thus a genuine microscopic anisotropy would percolate at loop size; the QTT null is a symmetry/domain result, not a small-number hiding place. The theorem is scoped to the current A1--A7 local matter/gauge Einstein-gauge constructor. It explicitly excludes a later promoted dynamical ABC clock field, an anisotropic four-measure, quantum-metric loops, and full nonperturbative reconstruction. If one of those objects is added, it requires a separate theorem and a new SME audit. Main status labels: SIGMA-ABC-INDEX-NON-PROMOTION-CLOSED SIGMA-A1-A7-PREFERRED-INDEX-COMPLETENESS-CLOSED SIGMA-FOUR-CAPACITY-REGULATOR-CLASS-CLOSED SIGMA-ONE-LOOP-MINIMAL-SME-PROJECTION-CLOSED SIGMA-COLLINS-NEGATIVE-CONTROL-EXACT SIGMA-LOCAL-MATTER-GAUGE-LORENTZ-COMPLIANCE-GREEN Related QTT anchors: Main book v10.01: 10.5281/zenodo.17527179 Radiative-stability companion theorem: 10.5281/zenodo.21301312 A2 Einstein-field dynamics: 10.5281/zenodo.20763263 Artian time framework: 10.5281/zenodo.20761499 QTT website: quantumtraction.org Lexicon: ABC clock, quantized Lorentz boost ledger Included files: Main PDF paper, version 2.0 Reconstruction ZIP containing LaTeX source, verifier, machine certificate, render audit, scientific audit, source-anchor ledger, and checksum manifest
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Attar Ali (2026) studied this question.
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