Editing Openai/6897769e-4ee4-800f-aba5-69cca34f701c (section)

=== Quantitative, order-of-magnitude reality check (why the energy budget is the key problem) ===
# Local dark-matter energy density (what gravity needs). Observationally the local halo density near the Sun is typically quoted ≃ 0.3–0.6 GeV/cm³; commonly used number ~0.4 GeV/cm³. Converting: ρDM≈0.4 GeV/cm3≈7.1×10−22 kg/m3.\rho_{\rm DM}\approx 0.4\ \text{GeV/cm}^3 \approx 7.1\times10^{-22}\ \text{kg/m}^3.ρDM≈0.4 GeV/cm3≈7.1×10−22 kg/m3. The equivalent energy density (via u=ρc2u=\rho c^2u=ρc2) is uDM≈ρDM c2≈6×10−5 J/m3.u_{\rm DM}\approx \rho_{\rm DM}\,c^2 \approx 6\times10^{-5}\ \text{J/m}^3. uDM≈ρDMc2≈6×10−5 J/m3. (References and modern local-density reviews exist.) arXiv<ref>{{cite web|title=arXiv|url=https://arxiv.org/pdf/2012.11477|publisher=arxiv.org|access-date=2025-12-16}}</ref>
# Typical electromagnetic energy densities (order of magnitude). - Cosmic Microwave Background (CMB) radiation: uCMB≈4.2×10−14 J/m3u_{\rm CMB}\approx 4.2\times10^{-14}\ \text{J/m}^3uCMB≈4.2×10−14 J/m3. Wikipedia<ref>{{cite web|title=Wikipedia|url=https://en.wikipedia.org/wiki/Cosmic_microwave_background|publisher=en.wikipedia.org|access-date=2025-12-16}}</ref> - Interstellar starlight (local ISRF): order uISRF∼10−12–10−13 J/m3u_{\rm ISRF}\sim 10^{-12} \text{--} 10^{-13}\ \text{J/m}^3uISRF∼10−12–10−13 J/m3 (≈ 1 eV/cm³ ≈ 1.6×10⁻¹² J/m³). - Typical galactic magnetic energy (B ≈ a few μG): uB=B2/(2μ0)∼10−13 J/m3u_B = B^2/(2\mu_0)\sim 10^{-13}\ \text{J/m}^3uB=B2/(2μ0)∼10−13 J/m3. Compare: uDMu_{\rm DM}uDM is ~10⁷–10⁸ times larger than local EM energy densities. In words: the electromagnetic fields and radiation present in the ISM or in cluster plasma are many orders of magnitude too small to supply the mass-equivalent energy that dark halos appear to have. (Numbers above use standard values for CMB/ISRF/B fields.) Vaia<ref>{{cite web|title=Vaia|url=https://www.vaia.com/en-us/textbooks/physics/astronomy-a-physical-perspective-2-edition/chapter-21/problem-5-compare-the-energy-density-in-the-cosmic-microwave/|publisher=vaia.com|access-date=2025-12-16}}</ref>CERN Document Server<ref>{{cite web|title=CERN Document Server|url=https://cds.cern.ch/record/1693043/files/p85.pdf|publisher=CERN Document Server|access-date=2025-12-16}}</ref>
# Implication. If QAT wants EM exchanges to directly produce the gravitational field by the usual Gμν∝TμνG_{\mu\nu}\propto T_{\mu\nu}Gμν∝Tμν mapping in GR, the EM stress-energy available is insufficient by 7–8 orders of magnitude in many astrophysical environments. So either: - QAT finds a new channel that is not ordinary TμνT_{\mu\nu}Tμν bookkeeping (i.e., gravity emerges in a different way), or - QAT must rely on additional (non-EM) energy budget (e.g., vacuum energy, induced contributions, or hidden degrees of freedom), or - gravity is emergent but the emergent coupling (G) comes from microscopic UV physics (Sakharov-style), so the magnitude does not come directly from the classical EM energy density.