# Relativity paradox in exponentially accelerating train

## Main Question or Discussion Point

Using Einstein's train thought experiment, suppose a train is accellerating exponetially so that the engine remains forever ahead of a beam of light without it ever reaching the speed of light.

V = c[ 1 - e^(-t)] for the train

The light would approach the engine but never quite reach it. So it would pass the second car in a finite time. If you are sitting in the second car, you could wait til the light beam passes you outside, then get up and walk to the front of the engine. Your speed would be very slow relative to the train and fast but less than the speed of light relative to the ground.
But in doing this walk, you will have caught up to and passed a beam of light. This should be impossible!

So what prevents this from happening? Is it impossible to walk to the front of the train? If so, why? It is a short finite distance and the acceleration of the train is never infinite.

Jeff
kochanskij@yahoo.com

Related Special and General Relativity News on Phys.org
JesseM