Weak-Field Light Bending (General Relativity)

$$n(r) \approx 1 + \frac{2GM}{c^2 r}, \quad \theta \approx \frac{4GM}{c^2 b}$$

Status: Proven.

This is General Relativity’s real, weak-field prediction for how much a light ray is deflected passing a mass $M$ at impact parameter $b$. It follows from solving the geodesic equation for light in the Schwarzschild metric to first order — the factor of 2 relative to the naive Newtonian light-bending estimate (which a corpuscular treatment of light gives half of this value) is specifically a GR effect, from spatial curvature contributing equally with time dilation.

Real, independent confirmation: famously confirmed during the 1919 solar eclipse expedition (Dyson, Eddington & Davidson) for light grazing the Sun ($\theta\approx1.75’’$); see General Relativity for the fuller confirmation record, now extending to sub-1%-precision very-long-baseline radio interferometry.

Used in: Paper 2 and Paper 12, where PBT reproduces this exact real number via aether refraction rather than spacetime curvature — a deliberate consistency check with GR’s own confirmed prediction, not an independent test.