The effects of time dilation and length contraction in special relativity are not illusions, but rather consequences of the fundamental principles of the theory. While they may seem counterintuitive, they have been extensively confirmed by experiments and are essential for understanding the behavior of objects moving at high speeds relative to an observer.
In the context of the muon experiment, muons are subatomic particles that are created in the upper atmosphere when cosmic rays, high-energy particles from outer space, collide with molecules in the air. Muons are unstable and decay after a short time, but due to their relativistic speeds, they can travel significant distances before decaying.
From the perspective of an observer on the ground, muons moving at speeds close to the speed of light experience time dilation and length contraction. Time dilation means that the internal "clock" of the muon, which determines its decay rate, appears to run slower compared to a stationary observer. Consequently, the muon can travel a greater distance in its own "slow" time before decaying.
Similarly, length contraction refers to the apparent shortening of the muon's length as observed by the stationary observer on the ground. From the muon's perspective, it remains its usual length, while the surrounding environment, including the atmosphere, appears to be contracted in the direction of motion. This contraction effect allows the muon to cover greater distances relative to the observer's reference frame.
The key point to understand here is that these effects are not contradictory or paradoxical. They arise because the laws of physics, including the constancy of the speed of light, must hold true for all observers, regardless of their relative motion. Special relativity provides a consistent framework that explains how time, space, and other physical quantities transform between different inertial reference frames.
The observations made by the muon and the stationary observer are consistent within their respective reference frames. The muon's "view" of the atmosphere is not relevant to the ground-based observer's measurement of the muon's behavior.
It is worth noting that these relativistic effects become more noticeable as the relative speeds between observers increase, especially as objects approach the speed of light. In everyday life, these effects are negligible at the speeds we encounter, but they become significant in particle accelerators, space travel, and other high-speed scenarios.