Let's imagine a rocket that travels straight path through space, accelerating gradually (or being boosted by outside force). The speed of rocket is such that 1st light year takes 1/2 hours in rocket's own frame 2nd light year takes 1/4 hours 3rd light year takes 1/8 hours 4th light year takes 1/16 hours 5th light year takes 1/32 hours and generally, nth light year takes (1/2)^n hours in rocket's own frame As it's seen, the sum of travel times form converging series that has limit 1. In the outside rest frame (the path frame), the rocket's speed approaches light speed and kinetic energy grows without bound, but light speed or infinite energy is never actually reached. However, in rocket's own frame, the passengers (strong enough to survive the acceleration) expect that they reach infinity at 1 hour and eagerly wait to see what happens and where they end up to. Will they be disappointed? Is there something in relativity why, at 1 hour, the passengers see that they still are far away from infinity, and actually will never reach it? Thanks.