We often see 'time dilation is caused by something'. The 'something' may be true and unhelpful or true and misleading or true and unfathomable or downright wrong. Here I'm saying time dilation is caused by the geometry of spacetime. Could be any of the above. The assumptions are flat spacetime, no accelerations, no tricks and the simplest possible notation. The general idea is that the spacetime interval (I'm calling it 's') is the same in every frame - you might call it the invariant spacetime interval if you wanted to. I'll give it in full (simplest possible notation) and then tone it down to show how nice it really is. A # means 'comment'. In full, where x is the distance travelled in the x direction, y and z in y and z directions (all at right angles) and t is the measured time. s²=x²+y²+z²-c²t² # it's not as bad as it looks. This is all distances measured between events. Let's have some events. Alice starts her stopwatch (event A) and after time t she burps (event B). Two events, A and B which both take place in the same place in her frame so x=0,y=0,z=0 so we get the invariant spacetime interval s²=-c²t² # not so bad is it? Let's say some guys are driving past at speed v in the x direction. They get their own frame and I'm going to put a dash (') after everything relating to their frame. In the car frame Alice is moving past at velocity v' in the x direction, the time interval between Alice starting her stopwatch (event A) and burping (event B) is t'. so x'=v't' # distance*time (consult Newton for clarification if needed). Substituting v't for x' in the spacetime interval equation s²=v'²t'²-c²t'² # this is the guys spacetime interval We said (agreed?) the spacetime interval between events is the same for both the car guys and Alice - in her frame it was -c²t² so -c²t²=v'²t'²-c²t'² # Alice's spacetime interval = Guys spacetime interval change sign, divide by c²,extract t' and square root both sides c²t²=c²t'²-v'²t'² t²=t'²-v'²t'²/c² t²=t'²(1-v'²/c²) t=t'√(1-v'²/c²) as √(1-v'²/c²) is less than 1 it follows that the time in Alice's frame is less than the time in the Guys frame. So time dilation is a caused by the geometry of spacetime.