The Reversal
Before Lester Pelton, water turbines caught the jet in a cup. The water hit the bucket, pushed it forward, and spilled out the sides. The momentum transfer was straightforward: a mass of water moving at velocity v strikes a surface and stops. Momentum delivered equals mv. Efficiency hovered around fifty percent.
Pelton's 1878 design split each bucket with a central ridge. The incoming jet divides into two streams, each deflected backward along the bucket face, exiting nearly opposite to their entry direction. The momentum transfer is no longer mv. It is closer to 2mv — the initial momentum plus the momentum of the reversed flow. Efficiency jumped to ninety percent. The improvement did not come from better materials, tighter tolerances, or higher pressures. It came from sending the water back instead of merely stopping it.
When a photon strikes a black surface, it is absorbed. The surface receives the photon's momentum: p equals E divided by c. When a photon strikes a perfect mirror, it bounces back. The surface receives twice the momentum: the photon's original forward push plus the reaction from sending it backward. A mirror under the same illumination exerts exactly twice the radiation pressure of a black absorber.
This is why solar sails are reflective. A matte black sail and a polished reflective sail of the same area, catching the same sunlight, experience different forces. The reflective sail pushes twice as hard. The difference is not in what arrives. It is in what leaves. The black surface converts photons to heat. The mirror returns them. The return is what doubles the force.
When a moving billiard ball strikes an identical stationary ball head-on, the moving ball stops. The stationary ball leaves at the original speed. One hundred percent of the kinetic energy transfers from one to the other. This is what an elastic collision does: it reverses the relative velocity of the pair.
In an inelastic collision — where the two balls stick together — conservation of momentum still holds, but the combined mass moves at half the speed. Only fifty percent of the original kinetic energy survives as motion. The rest is spent deforming the materials at the contact point. The energy that goes into deformation is the energy that went into stopping the projectile without sending anything back.
Newton's cradle makes this visible in a line. Lift one ball, release it. It strikes the row and stops. The ball at the far end flies out. Energy crosses four intermediate balls with negligible loss because each collision is elastic — each ball reverses the relative velocity with the next. Replace the steel balls with clay and the first ball's energy dies at the first contact. Nothing is returned. Nothing propagates.
Stopping something extracts its momentum once. Reversing it extracts the momentum twice.