The concept that time slows down as objects approach the speed of light is a prediction of Einstein's theory of special relativity. It has been extensively tested and confirmed through various experiments and observations.
One of the most well-known experiments demonstrating time dilation due to speed is the muon decay experiment. Muons are subatomic particles that are created in the upper atmosphere when cosmic rays collide with atoms. These muons have a short lifetime at rest, but due to their high velocities resulting from their creation in cosmic ray collisions, they can reach the Earth's surface before they decay.
If time didn't dilate with speed, most muons would decay before reaching the Earth's surface. However, experiments have shown that a significant number of muons do indeed reach the surface, indicating that their internal clocks, so to speak, run slower relative to a stationary observer on Earth. This observation is consistent with the predictions of special relativity.
Additionally, particle accelerators that accelerate particles to near-light speeds have also provided evidence for time dilation. For example, in the Large Hadron Collider (LHC), particles are accelerated to very high speeds, and their lifetimes are measured both at rest and at high velocities. The experiments have consistently shown that the accelerated particles have longer lifetimes, again confirming the time dilation effect.
It's important to note that when we say "clocks tick slower," it refers to the measurement of time itself. When objects move at high velocities relative to each other, their respective measurements of time will differ. From the perspective of an observer on a fast-moving object, time would appear to pass normally, while an observer in a relatively stationary frame of reference would observe the moving object's time to be dilated.
These experimental confirmations, along with the mathematical consistency of special relativity, provide strong evidence that time dilation occurs as objects approach the speed of light.