A particle lives longer because it is moving

Cosmic-ray muons reach the ground in numbers that only make sense if their clocks run slow. Their half-life in flight matches special relativity.

The proper lifetime is 2.2 μs. At rest, a muon barely crosses a room. The ones made by cosmic rays are moving so close to light speed that time dilation stretches that life, in the lab frame, by a factor of ten or more. Rossi and Hall, and later Frisch and Smith on Mount Washington, counted the flux at two altitudes. The survival was the relativistic one, not the Newtonian one.

This is the twin paradox without the biography. The travelling clock really does record less time. GPS corrects the same fact on purpose. The muon is the correction, caught in the wild.