Yes, there is substantial evidence that time dilation, a key prediction of the theory of relativity, exists. Time dilation has been confirmed through various experimental observations and measurements. Here are a few examples:
Particle Accelerators: Particle accelerators, such as the Large Hadron Collider (LHC), accelerate particles to very high speeds. These experiments involve particles moving at velocities close to the speed of light. By comparing the decay rates of particles at rest to those moving at high speeds, scientists have observed that the moving particles have a longer average lifetime. This experimental evidence supports the existence of time dilation.
Global Positioning System (GPS): The GPS system, which relies on precise timekeeping, provides another demonstration of time dilation. GPS satellites in orbit around the Earth move at high speeds relative to observers on the ground. The onboard atomic clocks on these satellites are designed to account for the time dilation effects predicted by relativity. If time dilation was not taken into account, GPS calculations would quickly become inaccurate.
Muons in Cosmic Rays: Cosmic rays, high-energy particles originating from outer space, often include muons. Muons are unstable particles with a short lifetime, but due to their high velocities, some of them can reach the Earth's surface before decaying. This phenomenon can be explained by time dilation, as the moving muons experience slower decay rates and thus have an increased chance of reaching the surface.
These experimental observations, among others, provide strong evidence for the existence of time dilation. They consistently demonstrate that time runs differently for objects in motion compared to stationary objects, confirming the predictions of the theory of relativity.