I get my "demonstration" of time dilation from the textbook thought experiment.
A laser is mounted on a cart with a reflective ceiling. A $t=0$ the cart starts moving and the laser is fired. When the laser is reflected back at the starting point the (thought) experiment stops.
Now, two different observer, one sharing the frame of the cart and another standing on the ground perpendicular to the cart will observe two different things. For the first one the laser bounces back and then down in a straight line. For the second one the light travels in a triangular pattern which is longer then the path observed by the first guy.
Given that the speed of light is constant, time has to dilate/contract.
Why is the speed of light held constant here? Could we work out a physics were time is absolute but maximum speed of light variable?