Gravity as the Emergent Acoustic Geometry of a Flowing Quantum Medium The Kinematic Origin of Light Bending and Newtonian Fall

Gravity originates in a light-speed flow of space, and the gravitational field is the effective geometry this flow produces. Space is a medium whose degrees of freedom stream at the speed of light; a mass densifies the streaming into an inward flow v=2GM/r. By the standard construction of analogue gravity, signals carried by the medium move on an effective Lorentzian metric, and the key point is what fills it: putting the flow speed into g_00=-(c^2-v^2) returns the Newtonian potential. For the densified river this metric is, by an explicit diffeomorphism, the Painlevé--Gullstrand form of Schwarzschild (K=48m^2/r^6). Light is unaffected by the conformal factor, so for light the geometry is exactly Schwarzschild and the deflection comes out as the factor of four; matter is carried by the flow, and since the flow speeds up as it falls inward it acquires exactly the Newtonian acceleration GM/r^2, the convective acceleration of the flow. Gravitational attraction and light bending are thus two responses to one flow's gradient --- light carried across it, matter carried inward along it --- and every step is checked by computer algebra. The strength of gravity may share this origin: the microscopic spacing a that sets the geometry would, if the geometry can be made dynamical, set its induced rigidity, with Gc^3a^2/ --- the observed value if a is the Planck length, so that the weakness of gravity is the fineness of the medium's quantum spacing. This is a conditional scaling; what it requires is a mechanism making the effective geometry dynamical, which the kinematics do not supply.