Einstein didn't set out to break time. He set out to fix an awkward inconsistency in how physics treated motion, and the broken-clocks part fell out of the maths whether he wanted it to or not. Special relativity is famous for feeling bizarre, but it starts from two rules that don't sound bizarre at all.
Two rules, taken completely seriously
Rule one: the laws of physics look the same to everyone moving at a constant speed, no exceptions for who's "really" moving and who's "really" still. Rule two, the strange one: everyone measures the speed of light as the same number, regardless of how fast they themselves are moving, or how fast the light source is moving. Fire a light beam from a spaceship going half the speed of light, and both the pilot and someone standing still watching it go by measure that beam travelling at exactly the same speed. Nothing adds on top of it. Nothing subtracts.
That second rule is the one every other bit of relativity theory follows from, once you refuse to treat it as a rough approximation and instead ask: what has to be true about space and time for that to actually hold?
Something has to give, and it's time
If light always measures the same speed no matter how fast you're moving, then distance and duration can't both stay fixed the way common sense assumes they do. Picture a "clock" made of a light beam bouncing between two mirrors, ticking once per bounce. Watch that clock from outside while it flies past you sideways, and the light has to travel a longer diagonal path to complete each bounce — but its speed can't have changed, so each tick has to take longer. From your outside vantage point, the moving clock runs slow. Not because anything mechanical inside it broke. Because the geometry of the bounce changed, and the speed of light didn't.
Not a rounding error, a measured one
The effect is genuinely tiny at ordinary speeds — you're not ageing detectably slower on a bike ride. But it isn't just theoretical. GPS satellites move fast enough, and sit far enough from Earth's gravity, that their onboard clocks drift out of sync with clocks on the ground by a measurable amount every day. The system corrects for it deliberately; skip the correction and GPS position errors would build up by kilometres within hours. Relativity isn't a thought experiment sitting in a textbook — it's a correction factor running quietly in a satellite over your head right now.
What we're still unsure about
"Everything is relative" is the popular one-line summary, and it's the part Einstein spent his life mildly regretting, because it's not quite what the theory says. The speed of light is the one thing that's absolute — fixed, the same for everyone, never relative. It's specifically because that one thing refuses to budge that space and time have to. The theory's real claim is closer to "one thing is absolute, and that's precisely why several things you assumed were absolute aren't" — which is a less catchy sentence, but the honest one.