length contraction
An object moving past you is measured to be shorter along its direction of motion than when it sits at rest. A spaceship streaking by, gauged in your frame, is squeezed in the front-to-back direction by the same Lorentz factor that slows its clocks. Its width and height, the directions across the motion, are untouched; only the length in the direction of travel shrinks.
Length contraction is the spatial twin of time dilation, and the two are inseparable partners. If moving clocks run slow and the speed of light is the same for everyone, then moving rulers must shorten by just the right amount to keep the books balanced. You cannot have one without the other; together they keep every observer measuring light at the same speed c.
The effect is real but symmetric and frame-dependent: the spaceship's crew see YOUR world flattened along their direction of motion, while finding their own ship perfectly normal. There is no objective 'true' length that one of you has wrong. To measure a moving object's length you must mark both ends at the same instant, and since observers disagree about simultaneity, they naturally disagree about length.
A vivid case is the same muon shower from the upper atmosphere. From the ground we explain the muons' survival by their slowed clocks. But riding alongside a muon, its clock is perfectly normal; instead the atmosphere itself is rushing up at near-light speed and is length-contracted to a thin shell, so there is far less distance to cross. Two descriptions, one consistent outcome.
A rest length L₀ is measured as the shorter length L in a frame where the object moves; only the along-motion dimension shrinks.
Contraction acts only along the direction of motion, and only on what you measure of a moving object; an object always has its full rest length in its own frame. A single camera snapshot also adds visual distortions that differ from this measured contraction.