One thought experiment that shows that time does in fact slow down is to imagine two inertial frames of reference- call them spaceships if you want- moving relative to each other. Say that each ship has a clock on board that has a beam of light bouncing back and forth between mirrors. Now, when you look at your own clock, you are not moving relative to it, and you simply see the beam following a straight path perpendicular to the mirrors. But when you look at the other person’s clock, between bounces the clock moves forward a little, and so the light is following a diagonal path that is longer than the path taken by the light in your own clock, according to the Pythagorean theorem. Light always travels at the same velocity no matter the frame of reference, so the light, from your perspective, must take longer between bounces. But the other person, who is not moving relative to their own clock, sees the light as traveling on a perpendicular path (identical to that in your own clock as seen by you) and therefore the time they observe between bounces is shorter than that you observe. As both observers are in inertial frames of reference, and all motion is relative, both observations are equally valid, and the only way to relieve the paradox is to say that time passes slower for the other spacecraft than for you. But of course the same can be said for them as well. However, when one ship decelerates their clock slows down from their perspective, and speeds up from the perspective of the observer, meaning that the clock on the ship that has kept a steady pace will have registered less time than the other when they meet. I think. Although that seems to contradict the twin paradox. Hmm…I’ll have to think on it a bit more.