I'll start with the properties of light. Light always moves at the same speed to every observer, regardless of your frame of reference. This is not how ordinary matter works. If someone throws a ball at you at 20 m/s and you run away from them at 5 m/s, the ball will appear to be moving towards you at only 15 m/s. This is just common sense.
Now if they fire a laser at you at light-speed, and you fly away in a spaceship at half the speed of light, you would expect the laser to follow you at half the speed of light. But it doesn't. It still moves towards you at exactly the speed of light, whether you're running away or running towards it. This has some clear contradictions to it, but bear with me for a while.
Here's some other important ideas in relativity
1. When you're on a train with the windows boarded up, no noise, and no bumps on the track, you have no idea what speed you're going. You could be motionless or you could be going at half the speed of light. The inside of the train is always the same regardless of its speed.
2. When you move away from someone, it looks like they're moving away from you. Similarly, they think you are moving away from them. In fact, both are correct.
Now this is the tricky bit. Imagine a "light clock", where a photon bounces up and down between two parallel mirrors. When the photon hits the top, the clock "ticks" and when it hits the bottom, it "tocks". Let's say that one tick counts as one second. Here's a diagram: (sorry about the dots, I need them to stop the diagram from falling apart :wink:)
Path of photon relative to clock:
______
..../\.....
.....|.....
.....|.....
.....o.....
.....|.....
.....|.....
__\/___
Now what happens if we slide the light clock across the table at a high speed?
Path of moving clock:
.______.....>>>>...______.....>>>>...______
....................................................................
..................................o................................
....................................................................
....................................................................
....................................................................
.....o........................................................o....
.______.....>>>>...______.....>>>>...______
Now when we trace the path of the photon relative to the observer, we get a zigzagging pattern. The Pythagoras theorum tells us that this path is longer than the path of the photon in the stationary clock.
Path of photon relative to an observer:
...............o..............o
............./...\.........../..
........._/.......\......_/...
........./|......._\/..../|...
......./..............\../......
.....o.................o.......
(The lines in the middle are supposed to be arrows, by the way)
Now we know that
a) Light travels at the same speed relative to the observer as it does relative to the clock.
b) The clock is always the same on the inside, whether moving or not, so the distance the photon travels should be the same as in the stationary clock.
So we have the following problem:
To the obsever, the photon is moving a greater distance than inside the clock, but at the same speed.
Now speed = distance / time, and we are increasing the distance.
So to keep the speed of the photon constant, we have to slow down time inside the moving clock.
This is the fundamental result of special relativity, and it applies to every object, not just light clocks.
Time always slows down for an object in motion.
Sorry if I've got anything wrong, please tell me if you've studied relativity before and I've left something out. I find that when I read an explanation of relativity, I understand it perfectly for about 5 minutes. Then I forget some important detail from the explanation, inconsistencies start cropping up, and I have to read it again.
It's an exhausting topic to understand.
