2008-12-03

Running Aliens

Above Bengt's house floats a spaceship. It's big and round - basically what you would call a "flying saucer". It is held up by a force which exactly matches that of gravity, so that the spaceship stays hovering at the same height.
In the ship is a little green alien, who likes to get his exercise in the morning by running around the perimeter of the spaceship. Around and around in a circle, at an amazing speed. To avoid the spaceship starting to turn the other way, he has an identical friend alien who runs the other way. The other alien thinks this is a bit of a drag, but he still has the same physical properties.
The aliens are running so fast that you have to use relativistic equations to calculate their momentum. There are two ways of doing that; either it's m * v / gamma, or you use speed-dependent mass, which makes it m * v. Either way, the alien can never reach the speed of light, which is all good and well.
But if you use speed-dependent mass, the alien will get heavier. That means gravity on the spaceship as a whole increases, and it falls down. On the other hand, if you don't use speed-dependent mass, he doesn't get heavier, so it doesn't fall down.
    Which is it? Does the spaceship fall down, or not?