Temporal–Charge Factorization of the Aether Unit: Static Electrostatic Reference, Half-Spin Magnetic Realization, Five-Dimensional Space Resonance, and the Four-Fifths Physical Realization Law
Year: 2026
Type: preprint
Abstract: 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 $16\pi^2$; the electrostatic-to-magnetic square-charge relation $e^2=8\pi\alpha\, {e_{emax}}^{\,2}$; and the four forward-time loxodromic realization channels $\{L^-,L^+,R^-,R^+\}$. 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, $$\mathcal{L}_F=\mathbb{Z}_2^{(E)}\times\mathbb{Z}_2^{(LR)}=\{L^-,L^+,R^-,R^+\},$$ so that $$N_F=2_E\,2_{LR}=4.$$ Assigning a completed $2\pi$ loxodromic phase to each available forward realization gives $$\Omega_{E\leftrightarrow M}=2_E\,2_{LR}(2\pi_{\rm lox})=8\pi.$$ This reproduces the geometrical factor in the established QMU charge relation, $$e^2=8\pi\alpha\, {e_{emax}}^{\,2},$$ or equivalently, $${e_{emax}}^{\,2}=e^2\left(\frac12\right)\left(\frac1{4\pi}\right)\frac1{\alpha}.$$ The independent forward--backward temporal closure contributes a complete $2\pi$ phase, yielding the central temporal--charge factorization, $$\Omega_A=\Omega_{FB}\Omega_{E\leftrightarrow M}=(2\pi)(8\pi)=16\pi^2.$$ Equivalently, $$16\pi^2=2_E\,2_{LR}(2\pi_{FB})(2\pi_{\rm lox})=4(4\pi^2).$$ Thus the new factorization reproduces the independently established $4\pi^2$ measure of one Aether orientation state and the $16\pi^2$ 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 $$N_A=3_S+2_T=5,$$ whereas the forward physical realization has four independent loxodromic channels. Their ratio is therefore defined as the realization-capacity ratio $$D_F=\frac{N_F}{N_A}=\frac45.$$ 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 $\alpha_a$ acting over the rank-four forward representation has the same multiplicative realization measure as an equivalent isotropic scaling $\Xi_F$ over the rank-five Aether resonance representation, then $$\Xi_F^5=\alpha_a^4,$$ and therefore $$\Xi_F=\alpha_a^{4/5}.$$ 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, $$\mathrm{freq}=F_q,\qquad\mathrm{rson}=F_q^2,$$ the corresponding resonance realization is $$\Xi_R=\Xi_F^2=\alpha_a^{8/5}.$$ 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 $$\mathrm{dtrd}=\lambda_C^3F_q^2,$$ with the conditional realized form $$\mathrm{dtrd}_{\rm eff}=\mathrm{dtrd}\,\alpha_a^{8/5}.$$ 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 $$16\pi^2=(2\pi)_{FB}(8\pi)_{E\leftrightarrow M}=2_E\,2_{LR}(2\pi_{FB})(2\pi_{\rm lox}),$$ which connects the complete Aether geometry, the $8\pi\alpha$ 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 $\alpha_a^{4/5}\rightarrow\alpha_a^{8/5}$ realization sequence to cosmology is reserved for subsequent work.
Author: Thomson, David W.
Institution: Quantum AetherDynamics Institute
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7210276726