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

===== Problem: In fluid analogues, in-phase pulsators attract and out-of-phase repel. Gravity is always attractive. How to get consistent attraction at cosmological scales if microscopic EM phases vary? =====

Key idea to salvage: If the gravitational effect is built from quadratic gauge-invariant quantities (energy density, E2+B2E^2+B^2E2+B2, and stress-tensors) then phases average out and the resulting source is positive definite (roughly). So attractivity can be preserved only if the emergent coupling depends on phase-averaged quadratics, not linearly on amplitude/phase.

Mathematics hint: TμνEMT_{\mu\nu}^{\rm EM}TμνEM is quadratic in fields → phase independent. Show microscopically that many boundary events rebuild ⟨E2⟩,⟨B2⟩ \langle E^2\rangle,\langle B^2\rangle⟨E2⟩,⟨B2⟩ rather than phase-sensitive quantities.