Length contraction, also known as Lorentz contraction, is a phenomenon predicted by Einstein's theory of special relativity. It describes how the length of an object appears to change when observed from a reference frame in relative motion to the object.
According to special relativity, when an object is moving at a high velocity relative to an observer, its length in the direction of motion appears to contract or shorten as observed by the observer. This contraction is dependent on the relative velocity between the object and the observer.
The formula for length contraction is given by:
L' = L * sqrt(1 - v²/c²)
where: L' is the observed length of the object (contracted length), L is the rest length of the object (length when at rest), v is the relative velocity between the object and the observer, and c is the speed of light in a vacuum (approximately 3 x 10^8 meters per second).
The square root term (1 - v²/c²) represents a Lorentz factor, which approaches 1 as the relative velocity becomes much smaller than the speed of light. This means that at everyday velocities, the length contraction is negligible and not noticeable. However, at velocities close to the speed of light, the contraction becomes significant.
It's important to note that length contraction is a relativistic effect and only applies to objects moving at high velocities relative to the observer. At everyday speeds, the contraction is too small to be observable.