The classic and pretty intuitive illustration is the light clock.
Imagine a clock that consists of two mirrors facing each other, with a beam of light bouncing between them. Like a ball.
Each bounce we will pretend is one second.
Standing still, light moves the distance between the mirrors in one second.
But what happens if we make the clock fly through space really fast?
In the frame of the clock, the light travels a fixed vertical distance. It’s still bouncing back and forth going the same distance in 1 second.
However, to an outside observer moving relative to the clock, [the light beam travels a longer, diagonal path due to the motion of the clock. ](https://i0.wp.com/www.isoul.org/wp-content/uploads/2023/06/Michelson-Morley-dilate2.jpg).
This results in the observer perceiving the clock’s time as running slower.
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