That slow white smear on the rooftops is lying. The rotating lamp inside the tower spins with nearly fixed angular velocity, so as distance grows, a tiny change in angle translates into an enormous linear jump across the town. The light itself travels at the speed of light; what moves along the roofs is only the intersection line between a narrow beam and a distant surface.
The odd part is not the physics, it is the audience. Human vision tracks angular speed, not the true linear velocity of that moving spot, so the sweep looks gentle because the angle at your eye changes smoothly and predictably. Across rooftops far away, the same small angular step spans hundreds of meters in almost no time, easily beating the speed of sound without violating any rule, since no material object or signal is racing along that path.
The mechanism is closer to a sliding laser pointer on a screen than to a car rushing down a street. Geometric optics and simple trigonometry set the pace: double the distance and you double the linear speed of the spot for the same angular rate. Your brain, tuned to follow solid objects with inertia and friction, quietly reinterprets this nonlocal sprint as a calm, orderly sweep over the town.
