A nice empirical demonstration of Galileo's principle of relativity: https://www.youtube.com/watch?v=GIMNS0YiHzY

If one replaces the person on the trampoline with a light beam bouncing up and down between two horizontal mirrors, and assumes that the speed of light is \(c\) in every inertial frame, one obtains (from Pythagoras) the well-known 'light clock" thought experiment of Einstein that derives the fact that such clocks slow down by a factor of √(1−𝑣²/𝑐²) when moving at a velocity \(v\).