Length contraction is not solely a mathematically assumed consequence of time dilation. Both length contraction and time dilation are actual physical effects predicted by the theory of special relativity.
According to the theory of special relativity, as an object moves relative to an observer, its length appears contracted in the direction of motion. This phenomenon is known as length contraction. It means that an object in motion will appear shorter in the direction of its motion when observed from a stationary reference frame. This effect becomes more pronounced as the object's velocity approaches the speed of light.
Length contraction is not merely a mathematical assumption to maintain a fixed measurement of the speed of light. It is a consequence of the fundamental postulates of special relativity, which include the constancy of the speed of light in all inertial frames of reference. The theory of special relativity describes how space and time are interconnected, and it predicts that objects in motion experience both time dilation and length contraction.
Time dilation, on the other hand, is the phenomenon where time appears to run slower for a moving object relative to a stationary observer. The combination of time dilation and length contraction ensures that the speed of light remains constant for all observers, regardless of their relative motion.
Experimental evidence, such as measurements of high-speed particles and the behavior of particles in accelerators, supports the predictions of time dilation and length contraction. These effects have been observed and verified in various experiments, providing strong evidence for the validity of the theory of special relativity.