Albert Michelson and Edward Morley tried to measure the properties of the aether. Light should propagate through the aether at a constant speed, so if one was moving with the light, it should appear to be moving slower, relative to the observer. Using an interferometer, they detected no effect.
George Fitzgerald and Hendrik Lorentz showed that moving objects would contract and that the observed time would dilate.
Einstein published On the Electrodynamics of Moving Bodies explaining these phenomena.
Penrose and Terrell notice that objects would appear rotated, not contracted as was originally assumed.