The concept of length contraction arises from Einstein's theory of special relativity. According to this theory, the length of an object appears to contract when it is observed from a reference frame in relative motion to the object. This contraction effect is only noticeable when objects are moving at speeds close to the speed of light.
The formula for length contraction, also known as Lorentz contraction, is given by:
L' = L * √(1 - v^2/c^2)
Where: L' is the contracted length of the object as observed from the moving reference frame. L is the rest length of the object (i.e., its length when measured in its own stationary reference frame). v is the relative velocity between the object and the observer. c is the speed of light in a vacuum, which is approximately 299,792,458 meters per second.
The formula shows that as the relative velocity (v) between the object and the observer approaches the speed of light (c), the term inside the square root approaches 1, causing the contracted length (L') to approach zero. This implies that an object traveling at or near the speed of light would appear highly contracted or almost "flattened" when observed from a reference frame in relative motion.
It's important to note that length contraction is a relativistic effect and is not noticeable in everyday life because typical velocities we encounter are much lower than the speed of light. Length contraction becomes more significant as velocities approach relativistic speeds.