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

=== We test the plausibility numerically: can ordinary EM energy flux/momentum transfer produce Earth-scale gravity? ===

Earth example (very direct):
Earth mass M≈5.97×1024 kgM\approx 5.97\times10^{24}\ \mathrm{kg}M≈5.97×1024 kg. Its mass-energy Mc2≈5.37×1041 JMc^2\approx 5.37\times10^{41}\ \mathrm{J}Mc2≈5.37×1041 J. Typical radiative energy densities in the solar system are tiny: solar irradiance at Earth I⊙≈1361 W/m2I_\odot \approx 1361\ \mathrm{W/m^2}I⊙≈1361 W/m2, corresponding energy density u⊙∼I⊙/c≈4.5×10−6 J/m3u_\odot \sim I_\odot / c \approx 4.5\times10^{-6}\ \mathrm{J/m^3}u⊙∼I⊙/c≈4.5×10−6 J/m3. Compare:
* Required average local energy density to equal Earth mass-energy spread over Earth volume V∼1.08×1021 m3V\sim 1.08\times10^{21}\ \mathrm{m^3}V∼1.08×1021 m3 is uˉ∼Mc2/V∼5×1020 J/m3\bar u \sim Mc^2/V \sim 5\times10^{20}\ \mathrm{J/m^3}uˉ∼Mc2/V∼5×1020 J/m3.
* Ratio uˉ/u⊙∼1026\bar u / u_\odot \sim 10^{26}uˉ/u⊙∼1026. In other words, solar radiation is lower by ~26 orders of magnitude.

Conclusion: ordinary ambient radiation cannot supply the energy density needed to reproduce Earth’s gravitational field in a direct way.

What about momentum exchange (radiation pressure)?
Radiation pressure prad=I/cp_{\rm rad}=I/cprad=I/c. For sunlight p∼4.5×10−6 Pap\sim 4.5\times10^{-6}\ \mathrm{Pa}p∼4.5×10−6 Pa. Compare with Earth surface weight per unit area pg=ρgRp_g=\rho g R pg=ρgR (not directly comparable), but gravitational acceleration g=9.8 m/s2g=9.8\ \mathrm{m/s^2}g=9.8 m/s2 acting on kg mass is huge relative to pradp_{\rm rad}prad. The radiation pressure is negligible.

Bottom line: to obtain Newtonian gravity from straightforward radiation momentum flux, you need impossibly large energy densities or a new amplification mechanism.