@Yogi DMT,
Not exactly. In the time it takes the light to travel two meters on your ship, it has travelled thousands of meters on George's ship. Visualize George's ship going past you - you're both in space, you can see it coming from 10,000 kilometers away. Lightbeam leaves origin point on George's ship, by the time it hits the mirror on the floor, the ship has moved several hundred thousand meters. And even though light moves pretty quickly, that difference is measurable.
So again, if George's ship is moving at millions of kilometers an hour, relative to you:
- From George's viewpoint, he sees the beam go straight down and straight back up
- From your viewpoint, if you could see the lightbeam in George's ship, you would see it travel obliquely for several hundred thousand meters in each direction, to 'keep up' with the motion of the ship
- So the distance the light beam has to travel, according to your frame of reference, is not two meters, but two hundred thousand meters (say)
And even though light is fast, the speed is finite, so it takes longer, from your frame of reference, for the beam on George's ship to make its return journey.
So time is
actually moving slower on George's ship. it is not an illusion, an appearance, or the way the clocks work. The faster you go, the slower time is for you, relative to a stationary observer.