Theoretical study demonstrates cosmological expansion rates in quantum measurement units, indicating a non-retuned derivation of dark energy density.
This paper develops a Quantum Measurement Units (QMU) formulation of cosmological Aether pressure and closure-asymmetry expansion, connecting the invariant QMU gravitational force scale, the Aether fine-structure constant, the four-to-five closure realization law, and the isotropic spatial response of the Aether. The starting point is the QMU Aether mass scale mₐ=λC³ Fq²G, with Fq=c/λC. The associated QMU gravitational force is Gforce=mₐλC Fq²=c⁴/G. The corresponding Aether mass density is masdA=mₐλC³. Using Ledger One, Aᵤ\,curl=Fq²λC², the native Aether pressure closes as presA=mₐFq²λC=masdA Aᵤ\,curl=GforceλC². This pressure is an invariant QMU reference scale rather than the directly observed cosmological vacuum-energy density. The cosmological problem is therefore reformulated as a realization problem: what dimensionless fraction of the native Aether pressure is physically expressed in the homogeneous cosmological sector? The required suppression factor is inherited from the Aether charge-capacity relation. The Aether fine-structure constant is αₐ=e²8π eₐ², where eₐ²=mₐλC³Fq²Aᵤ. The companion closure-measure analysis derives the first-order realization coordinate from a rank-four to rank-five representation transfer. Conservation of the extensive logarithmic realization measure gives ΞF=αₐ4/5. Because QMU resonance is quadratic, rson=Fq², the corresponding resonance realization is ΞR=ΞF²=αₐ8/5. The cosmological closure fraction is therefore defined as Ωcl=αₐ8/5. The exponent $8/5$ is not introduced by fitting cosmological observations and is not obtained by counting eight directed paths. It follows from the independently derived four-to-five closure transfer followed by the quadratic QMU resonance relation. The paper then audits the geometric origin of the isotropic expansion coefficient. The electrostatic representation of complete Aether closure is expressed as EA=S²₋× S²₊, with product measure ΩA(E)=(4π)₋(4π)₊=16π². The corresponding magnetic-temporal factorization is MA= Z₂(E)× Z₂(LR)¹FB¹ₗₒₓ, with total measure ΩA(M)=(2)(2)(2π)(2π)=16π². The equality ΩA(E)=ΩA(M)=16π² is an equality of complete closure measure, not a claim that the two configuration spaces are topologically identical. The electrostatic space is a connected four-dimensional product manifold, whereas the magnetic-temporal representation consists of four disconnected two-dimensional tori. The reciprocal relationship between electrostatic and magnetic charge projection is instead represented at the charge-ledger level by an explicit involution. With gq=8π, define Jg=pmatrix0 & 8π\\(8π)⁻¹ & 0pmatrix. Then Jg²=I₂. Including a physical realization parameter αₓ gives Jαₓ=pmatrix0 & 8παₓ\\(8παₓ)⁻¹ & 0pmatrix, with Jαₓ²=I₂. For qₓ=pmatrixe²ₓ²pmatrix, and αₓ=e²/8π eₓ², the QMU charge relation becomes the fixed-point condition Jαₓ qₓ= qₓ. This supplies a precise meaning for electrostatic--magnetic inverse realization at the projection-coordinate level without asserting an inverse topology between their full configuration spaces. The completed forward--backward temporal cycle is represented explicitly by S¹FB with measure 2π. Quotienting the magnetic-temporal closure by this completed cycle gives the exposed boundary representation BA= MA/S¹FB, and therefore ΩE↔ M=16π²/2π=8π. The transfer of this exposed boundary capacity into homogeneous three-dimensional spatial response is treated separately. For an isotropic spatial response tensor, define PB→ S(Ω)=Ω/3I₃. Under the Boundary-to-Spatial Trace Principle, the complete exposed boundary measure is preserved as the trace of the isotropic spatial response. Given trace preservation, linearity, and spatial isotropy, the response is uniquely C=8π/3I₃, giving ΓH=8π/3. The factor 8π/3 is therefore a conditional result rather than a consequence of charge geometry alone. Its derivation requires the physical premise that exposed boundary capacity is conserved as spatial trace. A second and logically distinct physical premise is required to convert the dimensionless closure fraction into an expansion rate. The Spatial Resonance Response Law is stated as Rᵢⱼ=Fq²Ωcl Cᵢⱼ. For a unit spatial direction nⁱ, Hcl²(n)=nⁱ Rᵢⱼnʲ. Spatial isotropy then gives Hcl²=8π/3Fq²αₐ8/5, and hence Hcl=Fqαₐ4/5√8π/3. The Spatial Resonance Response Law is explicitly identified as a constitutive principle. Dimensional analysis alone does not derive it. Deriving this law from native QMU volume--resonance dynamics remains a principal open problem. For comparison with conventional cosmology, the Einstein equation is used only as a bridge, Gab+Λ gab=8π/GforceTab. The conventional cosmological vacuum-energy density then becomes uDE=GforceΛ/8π. Dividing by the invariant Aether pressure eliminates the force scale: ξDE=uDEpresA=ΛλC²8π. Thus the comparison separates three quantities: the native Aether pressure scale, the closure-resonance residual, and the boundary-to-spatial projection. Using the inherited QMU values λC=2.42631023538×10⁻¹²\ m, Fq=1.23558996549×10²⁰\ s⁻¹, and αₐ=2.0345684859×10⁻⁴⁸, the paper obtains Gforce=1.2102555643×10⁴⁴\ N, presA=2.0558168791×10⁶⁷\ J\,m⁻³, Ωcl=4.9380524811×10⁻⁷⁷, uDE⁽ᶜˡ⁾=1.0151731640×10⁻⁹\ J\,m⁻³, Λcl=2.1081567552×10⁻⁵²\ m⁻², and Hcl=2.5131101589×10⁻¹⁸\ s⁻¹=77.5464768\ km\,s⁻¹\,Mpc⁻¹. No cosmological parameter is used to retune αₐ, the $4/5$ closure exponent, the $8/5$ resonance exponent, or the conditional 8π/3 spatial coefficient. Two cosmological interpretations are therefore kept explicitly separate. In the pure-Λ branch, the microscopic closure sector is identified directly with the cosmological vacuum sector: ξDE=Ωcl. In the total-expansion branch, the closure fraction represents the complete homogeneous expansion sector, so the vacuum component is weighted by the conventional vacuum fraction: ξDE=Ω_ΛΩcl. The observational comparison gives R_Λ=ξDE⁽ᵒᵇˢ⁾Ωcl≈0.519. The pure-Λ branch predicts R_Λ=1, corresponding to an order-unity discrepancy of approximately $1.93$. The total-expansion branch predicts R_Λ=Ω_Λ≈0.687, reducing the discrepancy to approximately $1.32$. Neither residual is absorbed into an adjustable packing factor or efficiency coefficient. The predicted value Hcl≈77.55\ km\,s⁻¹\,Mpc⁻¹ is also retained as an expansion-sector diagnostic. Its position relative to lower early-universe inferences and higher late-time determinations may help discriminate the physical interpretation of the closure sector, but it is not used retrospectively to select a branch or fit the prediction. The provenance of the result is also made explicit. Although αₐ is independent of H₀ and Λ, it inherits the measured gravitational constant through ²,Aᵤ,λC,Fq,G\ₐeₐ²αₐ. The construction is therefore cosmologically unfitted but not independent of gravitational empirical input. The paper leaves several physical questions deliberately open. The equation of state wA=-1 is presently an Einstein-bridge requirement rather than a native APM derivation. The Casimir--nuclear microscopic source inventory is not yet independently closed. Local Aether space-density gradients associated with gravitation and the homogeneous cosmological realization of Aether pressure are treated as distinct physical sectors and require independent experimental tests. The resulting framework provides a no-retuning cosmological pipeline from QMU Aether scales and charge-capacity closure to a quantitative expansion residual. It also makes the failure conditions explicit. The remaining factor-of-order-unity discrepancy is retained as a falsifiable target rather than absorbed into an adjustable coefficient, while derivation of the Spatial Resonance Response Law, the cosmological expansion-sector assignment, and the native Aether equation of state remain the principal next steps.
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David J. Thomson (2026) studied this question.
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