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Deriving the Einstein Field-Equation Coupling Constant from Quantum Intrinsic Wormhole Networks

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Auteur principal: Wei, Zheng
Format: Recurso digital
Langue:anglais
Publié: Zenodo 2025
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QIW-EC, emergent gravity, Einstein coupling, Planck-scale discreteness, wormhole networks, RG flow.
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author Wei, Zheng
author_facet Wei, Zheng
contents <p>We derive the Einstein prefactor <span><span>8πG/c48\pi G/c^{4}</span><span><span><span>8</span><span>π</span><span>G</span><span>/</span><span><span>c</span><span><span><span><span><span><span>4</span></span></span></span></span></span></span></span></span></span> from the Quantum Intrinsic Wormhole–Einstein–Cartan (QIW-EC) framework using only Planck-scale discreteness. A coarse-grained phase potential <span><span>θ\theta</span><span><span><span>θ</span></span></span></span> obeys <span><span>∇2θ=−α δρw\nabla^{2}\theta=-\alpha\,\delta\rho_{w}</span><span><span><span>∇<span><span><span><span><span><span>2</span></span></span></span></span></span></span><span>θ</span><span>=</span></span><span><span>−</span><span>α</span><span>δ</span><span><span>ρ</span><span><span><span><span><span><span><span>w</span></span></span></span><span></span></span></span></span></span></span></span></span> with edge-energy <span><span>ε0=ℏc/ℓ⋆\varepsilon_{0}=\hbar c/\ell_\star</span><span><span><span><span>ε</span><span><span><span><span><span><span>0</span></span></span><span></span></span></span></span></span><span>=</span></span><span><span>ℏ</span><span>c</span><span>/</span><span>ℓ<span><span><span><span><span><span>⋆</span></span></span><span></span></span></span></span></span></span></span></span>. Matching to linearised GR in the Newtonian limit fixes <span><span>α=(8πG/c4)(ℏ/ℓ⋆)\alpha=(8\pi G/c^{4})(\hbar/\ell_\star)</span><span><span><span>α</span><span>=</span></span><span><span>(</span><span>8</span><span>π</span><span>G</span><span>/</span><span><span>c</span><span><span><span><span><span><span>4</span></span></span></span></span></span></span><span>)</span><span>(</span><span>ℏ/</span><span>ℓ<span><span><span><span><span><span>⋆</span></span></span><span></span></span></span></span></span><span>)</span></span></span></span>. We outline an action-level normalisation to the EC form, discuss torsion corrections, naturalness, mild RG running of <span><span>GG</span><span><span><span>G</span></span></span></span>, and a numerical validation concept (FFT-based Poisson solve). <strong>Figures:</strong> schematic flowchart and mock-data <span><span>⟨∣θ(k)∣2⟩\langle|\theta(\mathbf k)|^{2}\rangle</span><span><span><span>⟨</span><span>∣</span><span>θ</span><span>(</span><span>k</span><span>)</span><span>∣<span><span><span><span><span><span>2</span></span></span></span></span></span></span><span>⟩</span></span></span></span> vs <span><span>k−2k^{-2}</span><span><span><span><span>k</span><span><span><span><span><span><span>−2</span></span></span></span></span></span></span></span></span></span> (full runs pending).<br><strong>DOI:</strong> 10.5281/zenodo.16809182</p>
format Recurso digital
id zenodo_https___doi_org_10_5281_zenodo_16809182
institution Zenodo
language eng
publishDate 2025
publisher Zenodo
record_format zenodo
spellingShingle Deriving the Einstein Field-Equation Coupling Constant from Quantum Intrinsic Wormhole Networks
Wei, Zheng
QIW-EC, emergent gravity, Einstein coupling, Planck-scale discreteness, wormhole networks, RG flow.
<p>We derive the Einstein prefactor <span><span>8πG/c48\pi G/c^{4}</span><span><span><span>8</span><span>π</span><span>G</span><span>/</span><span><span>c</span><span><span><span><span><span><span>4</span></span></span></span></span></span></span></span></span></span> from the Quantum Intrinsic Wormhole–Einstein–Cartan (QIW-EC) framework using only Planck-scale discreteness. A coarse-grained phase potential <span><span>θ\theta</span><span><span><span>θ</span></span></span></span> obeys <span><span>∇2θ=−α δρw\nabla^{2}\theta=-\alpha\,\delta\rho_{w}</span><span><span><span>∇<span><span><span><span><span><span>2</span></span></span></span></span></span></span><span>θ</span><span>=</span></span><span><span>−</span><span>α</span><span>δ</span><span><span>ρ</span><span><span><span><span><span><span><span>w</span></span></span></span><span></span></span></span></span></span></span></span></span> with edge-energy <span><span>ε0=ℏc/ℓ⋆\varepsilon_{0}=\hbar c/\ell_\star</span><span><span><span><span>ε</span><span><span><span><span><span><span>0</span></span></span><span></span></span></span></span></span><span>=</span></span><span><span>ℏ</span><span>c</span><span>/</span><span>ℓ<span><span><span><span><span><span>⋆</span></span></span><span></span></span></span></span></span></span></span></span>. Matching to linearised GR in the Newtonian limit fixes <span><span>α=(8πG/c4)(ℏ/ℓ⋆)\alpha=(8\pi G/c^{4})(\hbar/\ell_\star)</span><span><span><span>α</span><span>=</span></span><span><span>(</span><span>8</span><span>π</span><span>G</span><span>/</span><span><span>c</span><span><span><span><span><span><span>4</span></span></span></span></span></span></span><span>)</span><span>(</span><span>ℏ/</span><span>ℓ<span><span><span><span><span><span>⋆</span></span></span><span></span></span></span></span></span><span>)</span></span></span></span>. We outline an action-level normalisation to the EC form, discuss torsion corrections, naturalness, mild RG running of <span><span>GG</span><span><span><span>G</span></span></span></span>, and a numerical validation concept (FFT-based Poisson solve). <strong>Figures:</strong> schematic flowchart and mock-data <span><span>⟨∣θ(k)∣2⟩\langle|\theta(\mathbf k)|^{2}\rangle</span><span><span><span>⟨</span><span>∣</span><span>θ</span><span>(</span><span>k</span><span>)</span><span>∣<span><span><span><span><span><span>2</span></span></span></span></span></span></span><span>⟩</span></span></span></span> vs <span><span>k−2k^{-2}</span><span><span><span><span>k</span><span><span><span><span><span><span>−2</span></span></span></span></span></span></span></span></span></span> (full runs pending).<br><strong>DOI:</strong> 10.5281/zenodo.16809182</p>
title Deriving the Einstein Field-Equation Coupling Constant from Quantum Intrinsic Wormhole Networks
topic QIW-EC, emergent gravity, Einstein coupling, Planck-scale discreteness, wormhole networks, RG flow.
url https://doi.org/10.5281/zenodo.16809182

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