Loxodromic Chirality Ledger in QMU: Sign Rules for Toroidal Non-Reciprocity at Zero Field
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| Natura: | Recurso digital |
| Lingua: | inglese |
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Zenodo
2025
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| _version_ | 1866901349519589376 |
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| author | Thomson, David |
| author_facet | Thomson, David |
| contents | <p>This paper formalizes “loxodromic chirality” in the Aether Physics Model (APM) as a physically operative (signed and dimensional) ledger quantity tied to the Aether unit and curl geometry. Motivated by recent experimental demonstrations of geometry-induced spin chirality and remanent non-reciprocal wave transport in a geometrically chiral, but materially non-chiral, ferromagnet, we provide an APM-native framework that separates (i) chirality as a real mirror-odd circulation bias from (ii) dimensionless laboratory readouts such as intensity-asymmetry ratios.</p> <p>Ledger anchor (Aether rotational closure):<br>$$A_u\cdot \mathrm{curl}={F_q}^2{\lambda_C}^2.$$</p> <p>Definition (dimensional chirality carrier along the loxodrome):<br>$$\mathcal{C}_{\mathrm{lox}} \equiv (\tau_{\mathrm{geo}}\lambda_C)\,(A_u\cdot \mathrm{curl})<br>= (\tau_{\mathrm{geo}}\lambda_C)\,{F_q}^2{\lambda_C}^2,$$<br>where $\tau_{\mathrm{geo}}$ is the signed geometric torsion of the loxodromic centerline (right/left-handed screw).</p> <p>State variables:<br>$s_{\mathrm{lox}}\in\{+1,-1\}$ (structural handedness), $m_{\mathrm{rem}}\in\{+1,-1\}$ (remanent branch selected by magnetic history),<br>and $p_k\in\{+1,-1\}$ (propagation direction sign).</p> <p>Core sign rules (APM chirality ledger):<br>$$\mathrm{sgn}(\mathbf{T}_{\mathrm{tor}})=s_{\mathrm{lox}}\,m_{\mathrm{rem}},$$<br>$$\mathrm{sgn}(\Delta f/F_q)=p_k\,s_{\mathrm{lox}}\,m_{\mathrm{rem}},$$<br>where $\mathbf{T}_{\mathrm{tor}}$ is the emergent toroidal circulation bias and $\Delta f=f_{+k}-f_{-k}$ is the non-reciprocal dispersion splitting.</p> <p>QMU geometry controls (SI-free ingestion):<br>$$\tilde{r}=r/\lambda_C,\ \tilde{p}=p/\lambda_C,\ \tilde{k}=k_z\lambda_C,$$<br>with the natural pitch-set choice $\tilde{k}=2\pi/\tilde{p}$.</p> <p>The paper also provides a two-channel scaling template for non-reciprocity versus downscaling in fully QMU-normalized form, and it outlines falsifiable tests: handedness inversion, remanent reprogrammability, propagation-direction parity, and downscaling enhancement. Finally, we discuss how $\mathcal{C}_{\mathrm{lox}}$ can enter binding-energy ledgers as a geometry-selected state variable, enabling controlled “mirror-odd” corrections in rotational/torsional APM energy closures.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17979385 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Loxodromic Chirality Ledger in QMU: Sign Rules for Toroidal Non-Reciprocity at Zero Field Thomson, David QMU Aether Physics Model Aether unit curl loxodrome torsion chirality toroidal moment non-reciprocity magnonics geometry-induced chirality remanence binding energy sign rules <p>This paper formalizes “loxodromic chirality” in the Aether Physics Model (APM) as a physically operative (signed and dimensional) ledger quantity tied to the Aether unit and curl geometry. Motivated by recent experimental demonstrations of geometry-induced spin chirality and remanent non-reciprocal wave transport in a geometrically chiral, but materially non-chiral, ferromagnet, we provide an APM-native framework that separates (i) chirality as a real mirror-odd circulation bias from (ii) dimensionless laboratory readouts such as intensity-asymmetry ratios.</p> <p>Ledger anchor (Aether rotational closure):<br>$$A_u\cdot \mathrm{curl}={F_q}^2{\lambda_C}^2.$$</p> <p>Definition (dimensional chirality carrier along the loxodrome):<br>$$\mathcal{C}_{\mathrm{lox}} \equiv (\tau_{\mathrm{geo}}\lambda_C)\,(A_u\cdot \mathrm{curl})<br>= (\tau_{\mathrm{geo}}\lambda_C)\,{F_q}^2{\lambda_C}^2,$$<br>where $\tau_{\mathrm{geo}}$ is the signed geometric torsion of the loxodromic centerline (right/left-handed screw).</p> <p>State variables:<br>$s_{\mathrm{lox}}\in\{+1,-1\}$ (structural handedness), $m_{\mathrm{rem}}\in\{+1,-1\}$ (remanent branch selected by magnetic history),<br>and $p_k\in\{+1,-1\}$ (propagation direction sign).</p> <p>Core sign rules (APM chirality ledger):<br>$$\mathrm{sgn}(\mathbf{T}_{\mathrm{tor}})=s_{\mathrm{lox}}\,m_{\mathrm{rem}},$$<br>$$\mathrm{sgn}(\Delta f/F_q)=p_k\,s_{\mathrm{lox}}\,m_{\mathrm{rem}},$$<br>where $\mathbf{T}_{\mathrm{tor}}$ is the emergent toroidal circulation bias and $\Delta f=f_{+k}-f_{-k}$ is the non-reciprocal dispersion splitting.</p> <p>QMU geometry controls (SI-free ingestion):<br>$$\tilde{r}=r/\lambda_C,\ \tilde{p}=p/\lambda_C,\ \tilde{k}=k_z\lambda_C,$$<br>with the natural pitch-set choice $\tilde{k}=2\pi/\tilde{p}$.</p> <p>The paper also provides a two-channel scaling template for non-reciprocity versus downscaling in fully QMU-normalized form, and it outlines falsifiable tests: handedness inversion, remanent reprogrammability, propagation-direction parity, and downscaling enhancement. Finally, we discuss how $\mathcal{C}_{\mathrm{lox}}$ can enter binding-energy ledgers as a geometry-selected state variable, enabling controlled “mirror-odd” corrections in rotational/torsional APM energy closures.</p> |
| title | Loxodromic Chirality Ledger in QMU: Sign Rules for Toroidal Non-Reciprocity at Zero Field |
| topic | QMU Aether Physics Model Aether unit curl loxodrome torsion chirality toroidal moment non-reciprocity magnonics geometry-induced chirality remanence binding energy sign rules |
| url | https://doi.org/10.5281/zenodo.17979385 |