Theoretical analysis demonstrates unified temporal-charge factorization in quantum measurement units, suggesting a four-fifths physical realization law governing space resonance.
This paper derives a unified temporal--charge factorization of the Aether unit within the Aether Physics Model (APM) and Quantum Measurement Units (QMU). The analysis connects three structures previously established separately in the QMU ledger: the complete Aether angular geometry 16π²; the electrostatic-to-magnetic square-charge relation e²=8πα\, eₑₘₐₓ\,2; and the four forward-time loxodromic realization channels ⁻,L⁺,R⁻,R⁺\. Electrostatic charge is identified as a one-spin spherical static temporal-reference degree rather than as an additional cyclic phase coordinate. Forward--backward temporal closure and left--right temporal torque provide the cyclic temporal structure. Importantly, the left and right temporal-torque routes are simultaneously available within the same quantum moment: they are alternative loxodromic routes, not successive temporal phases. Material occupation by a Ligamen Circulatus (LC) selects one route, while the complementary routes remain dormant geometrical capacities of the Aether unit. For the two electrostatic sphere polarities and two simultaneously available temporal-torque routes, LF=Z₂(E)₂(LR)=⁻,L⁺,R⁻,R⁺\, so that NF=2E\,2LR=4. Assigning a completed 2π loxodromic phase to each available forward realization gives ΩE↔ M=2E\,2LR(2πₗₒₓ)=8π. This reproduces the geometrical factor in the established QMU charge relation, e²=8πα\, eₑₘₐₓ\,2, or equivalently, eₑₘₐₓ\,2=e²(12)(14π)1α. The independent forward--backward temporal closure contributes a complete 2π phase, yielding the central temporal--charge factorization, ΩA=ΩFBΩE↔ M=(2π)(8π)=16π². Equivalently, 16π²=2E\,2LR(2πFB)(2πₗₒₓ)=4(4π²). Thus the new factorization reproduces the independently established 4π² measure of one Aether orientation state and the 16π² measure of the complete four-state Aether geometry without introducing an additional cyclic electrostatic phase or additional hidden material channels. The paper then distinguishes the five-dimensional Aether space-resonance representation from the exact four-character forward physical-realization representation. The Aether resonance structure has rank NA=3S+2T=5, whereas the forward physical realization has four independent loxodromic channels. Their ratio is therefore defined as the realization-capacity ratio DF=NF/NA=45. No Aether dimension is deleted by this relation. The complete five-dimensional Aether structure remains available, while a particular material LC occupies only one of four possible forward-time loxodromic channels. A conditional realization-measure law is then examined. If the common Aether fine-structure scaling αₐ acting over the rank-four forward representation has the same multiplicative realization measure as an equivalent isotropic scaling ΞF over the rank-five Aether resonance representation, then ΞF⁵=αₐ⁴, and therefore ΞF=αₐ4/5. This measure-equivalence condition is explicitly identified as a constitutive hypothesis rather than an inherited QMU identity. The ranks four and five are structural; deriving the conservation law that equates their multiplicative realization measures remains an open theoretical problem. Because QMU distinguishes frequency from resonance, freq=Fq,=Fq², the corresponding resonance realization is ΞR=ΞF²=αₐ8/5. Hence the exponent $8/5$ does not require eight material paths. It arises as the resonance square of the $4/5$ forward-realization scaling. The associated QMU domain-resonance quantity is dtrd=λC³Fq², with the conditional realized form dtrdeff=dtrd\,αₐ8/5. The paper also introduces the dormant-sector principle: occupation of one loxodromic channel does not remove the unused electrostatic or temporal-torque capacities of the Aether unit. This suggests a possible application to superconducting pairing in which normally dormant electrostatic sectors participate in mutual particle organization and potentially produce an Aether-space pinching or shared-space configuration. This superconductivity application is presented as a research direction rather than as a derived prediction. The principal new result is therefore the unified factorization 16π²=(2π)FB(8π)E↔ M=2E\,2LR(2πFB)(2πₗₒₓ), which connects the complete Aether geometry, the 8πα electrostatic--magnetic charge conversion, and the four forward loxodromic realization channels within one consistent temporal geometry. The paper deliberately stops short of deriving a cosmological expansion law; application of the conditional αₐ4/5→αₐ8/5 realization sequence to cosmology is reserved for subsequent work.
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David J. Thomson (2026) studied this question.
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