by jinydu » Fri Feb 11, 2005 8:44 am
Here's another way to understand this.
Suppose you're standing on a train, moving with a speed u relative to the ground. You throw a ball with speed v towards the back of the train, in your frame of reference. What is the speed of the ball, as seen by someone standing on the ground?
Newtonian mechanics would say u + v, but in Einstein's theory, the answer is instead:
(u + v)/(1 + (uv)/(c^2))
Notice that if u and v are much less than c, the bottom of the denominator is approximately 1, so Einstein's prediction is almost exactly the same as Newton's, which is what you'd expect, since Newton's theory was accepted for so long.
But if u and v are close to the speed of light, things are very different. Basically, the denominator prevents you from actually reaching c. For instance, if u = v = 0.99c, the value you get is not 1.98c but instead 0.999949c.