Gravitational Light Deflection as a Ratio of the Planck Force: A Bridge between General Relativity and Non-Equilibrium Dynamics

We derive a compact relation connecting the gravitational deflection of light in

General Relativity (GR) to the Planck force Fₚ = c⁴/G. Starting from the GR

deflection angle θ = 4GM/(c²b) and the Non-Equilibrium Dynamics (NED) photon

deflection formula θ = (lₚ/mₚ)F/c², we equate the two expressions and use the

identity c²mₚ/lₚ = c⁴/G = Fₚ to obtain: F_GR = θ_GR × Fₚ. The equivalent force on

a photon in GR equals the GR deflection angle multiplied by the Planck force.

Equivalently, the deflection angle is the ratio of the GR gravitational force on the

photon to the Planck force: θ_GR = F_GR/Fₚ. This result provides a new physical

interpretation of gravitational lensing: the bending of light is a direct measure of

how large the gravitational interaction is relative to the maximum force allowed

by nature. We verify the relation for the solar deflection (1.748 arcsec) and

discuss its implications for the unification of gravity and quantum mechanics.