Now that we have a feel for the effects of special relativity, let's look at how fast things can go in this relativistic world. You'll recall from our previous segment on the speed of light, the classical transformation simply added the speed of movement in a reference frame to the speed of the reference frame itself. Here we see the person walking on the moving train. We simply added his walking speed to the train's speed to get the speed seen by an observer on the ground. In special relativity, the clock on the train is running a bit slower, and the distance the person walked is a little bit shorter as seen by the observer on the ground. So this calculation of the total velocity is a bit less than the Galilean calculation, but at these speeds it is too small a difference to notice. Now let's shift the super train into high gear and say his velocity is 8 tenths of the speed of light. And the person on the train kicks the ball at one half the speed of light. If the Galilean transformations were correct, the person on the ground would add these together and see the ball traveling faster than the speed of light. But to keep the speed of light a constant, the new relativistic equations tell us the person on the ground would see the ball traveling a lot slower than that at 9 tenths of speed of light. You can even see that with the relativistic equations if the train was traveling at point 8 times the speed of light, and a light was turned on, the person on the ground will see the light traveling at the speed of light, just like the person on the train will. In the most extreme case, suppose we had two photons traveling towards each other. Here's the northern hemisphere's summer triangle, the Vega, Altair, and Deneb. Let's say one photon is traveling from Deneb to Altair and the other one is traveling from Altair to Deneb. Of course each of them is traveling at the speed of light, so we would see their closing speed at two times the speed of light. And if we look at it from the point of view of one of the photons, we see that it sees them closing at the speed of light, not twice the speed of light.