-- The train cant travel at c, because only massless fields can do that. But even if it could, the addition of relativistic velocities will give youv = (1 + v₂)/(1 + 1•v₂) = 1, which is c, no matter what v₂ is.......
• "And what happens if the guy throws the ball at 20 m/s when the train is traveling at the speed of light?" -- The train can't travel at c, because only massless fields can do that. But even if it could, the addition of relativistic velocities will give you
v = (1 + v₂)/(1 + 1•v₂) = 1, which is c, no matter what v₂ is.
For the train traveling at 20 m/s and the guy who throws the ball at 20 m/s, you would indeed expect an outside observer to measure the ball's velocity at 40 m/s. This follows common sense and is an example of Galilean Relativity. However, while this seems true for slow objects like trains and balls, it breaks down when you approach the speed of light. In reality, the outside observer would measure the velocity to be 39.99999... m/s.
If someone aboard a train going close to the speed of light were to throw a ball at close to the speed of light as well, an outside observer would see only an modest increase in the ball's velocity.
"But then, it got me thinking. why can't it travel at 2c?"
Because any inertial observer measures it to be c, as required by Maxwell's relations.
"And what happens if the guy throws the ball at 20m/s when the train is travelling at the speed of light?"
Easy, the train cannot go the speed of light. So let it go 1 m/sec less than the speed of light. The guy on the train sees the ball moving forward at 20m/sec... but his length is contracted and his time is dilated, and we'd see the ball traveling faster than the train but slower than c.
