Special Theory of Relativity

Hi, I'm revising for HSC physics, and I'm a little confused. One of the postulates was that the speed of light is constant in all frames of reference. And this is because of the thought experiment Einstein conducted where, if the train is travelling at the speed of light, then an outside observer would see the light inside the train travelling at 2c, which was not possible as Maxwell had predicted that the speed of light in air was c.

But then, it got me thinking. why can't it travel at 2c? Say, for a train travelling at 20m/s and a guy in the train throws a ball at 20m/s, then an outside observer would see the ball travelling at 40m/s. How is this, then, possible? And what happens if the guy throws the ball at 20m/s when the train is travelling at the speed of light?

Please don't go into too much detail with your answers. Thanks.

This is a very good question.
I suppose you haven't read much of the relativity theory as the theory handles this question too.
The problem is that you are using the formula:
v = v1 + v2 for finding the net velocity with respect to observer.
While this formula is correct for small speeds , it fails at speeds close to the speed of light.
The actual formula for such speeds is:
v = (v1+v2)/(1+(v1*v2)/c^2)
For small v1 and v2 the denominator is approximately 1, but for large v1 and v2 , it is greater than 1.
Example : Let the speeds be .8c each.
According to the formula:
v = (.8c +.8c)/(1 +.64)
= 1.6c/1.64
So, we get a speed less than c.
No matter how many times you add a speed to another it will always be less than c.

It was proven during an eclipse. During an eclipse, the stars near the sun can be observed and thus calculate by how much the light beam from the stars are deviated due to the mass of the sun. Newtonian physics can calculate this, but is very inaccurate, usually half the actual answer.