Quantum Force Mediation: Virtual-Particle Exchange

This 2D simulator visualizes the force between two particles the way a physicist draws a Feynman diagram: a stream of virtual quanta spawns along the line connecting them and fades outward, its rate tied directly to the mediator's propagator e^(−m·r)/r. The particles themselves move under the exact closed-form Yukawa force, F(r) = g·e^(−m·r)·(1/r + m)/r, derived from the potential V(r) = −g·e^(−m·r)/r. Set the mediator mass m to zero and the force becomes the familiar infinite-range Coulomb law; raise it and the force — and the visible stream of exchanged quanta — collapses into a short, exponentially screened range, the same mechanism that separates the massless photon from the weak force's massive W and Z bosons. A live inset graph traces F(r) across the visible separation range so you can watch the curve itself reshape as you tune the controls.