The phenomenon of time dilation at relativistic speeds has been experimentally verified through several experiments and observations. One of the most well-known experiments that confirmed time dilation is the Hafele-Keating experiment conducted in 1971.
In the Hafele-Keating experiment, atomic clocks were flown in commercial airliners traveling in opposite directions around the Earth. The experiment aimed to test the effect of both speed and gravitational fields on time dilation. The clocks on the planes were compared to synchronized reference clocks on the ground. The results showed that the moving clocks on the planes had indeed experienced time dilation, and the effect was consistent with the predictions of special relativity.
Another example comes from particle accelerators, where high-speed particles are accelerated to speeds approaching the speed of light. In these experiments, the particles have relatively short lifetimes and decay into other particles. By measuring the lifetimes of these particles at rest and when they are moving at high speeds, scientists have observed that the moving particles have longer lifetimes, indicating time dilation.
Furthermore, modern technologies such as GPS (Global Positioning System) rely on the principles of relativity, including time dilation, for their accurate functioning. The clocks on GPS satellites are adjusted to account for both the gravitational time dilation caused by Earth's gravity and the time dilation resulting from the satellites' orbital speed.
These experimental observations and practical applications provide strong evidence for the existence of time dilation at relativistic speeds. The predictions of special relativity, including time dilation, have been consistently supported by experimental data, confirming the validity of Einstein's theory.