spacetime diagram
A spacetime diagram is a simple picture that turns the abstract ideas of relativity into geometry you can point at. It is a graph with space along the horizontal axis and time up the vertical axis, so that every point on the page is an event — a specific place at a specific moment. The whole history of an object becomes a line on this graph, called its worldline. Sitting still traces a straight vertical line (you go nowhere in space, but forward in time); moving at constant speed tilts the line; the faster you go, the more it leans.
Precisely: by convention the time axis is drawn as c times t so that both axes share units of length, and a light ray then travels along a 45-degree diagonal. Because nothing outruns light, every real object's worldline must stay steeper than 45 degrees — closer to vertical than the light line. Reading the diagram, the slope of a worldline encodes velocity, its curvature encodes acceleration, and the region a given event can influence is the wedge bounded by the 45-degree light lines, the light cone. Different inertial observers correspond to different tilted sets of axes drawn on the same picture, which is why they slice 'space' and 'time' up differently.
Spacetime diagrams are the physicist's favourite tool for reasoning about relativity because paradoxes that tangle the words untangle instantly in the picture. The twin paradox, for instance, becomes obvious: the two twins simply follow worldlines of different lengths between the same two meeting-events, and the one with the shorter proper time is the younger. Hermann Minkowski, Einstein's former teacher, introduced this geometric view in 1908.
On a spacetime diagram, a lamp switched on at the origin sends light out along two 45-degree lines. A person standing still is a vertical worldline; a spaceship at half light-speed is a line tilted halfway toward the light line — always steeper than 45 degrees, because it cannot catch the light.
Vertical worldline = at rest; tilted = moving; 45 degrees = light. Nothing tilts past the light lines.
A spacetime diagram is not an ordinary map: distances on it are measured with a minus sign between the space and time parts, so the geometry is 'hyperbolic', not the familiar Pythagorean kind. That sign flip is why a longer-looking worldline can actually carry less proper time.