The quick answer is that time in the surrounding environment appears to slows down and the physical dimension of space in the direction of motion appears shortened. The faster one goes, the more profound the effect. At the speed of light, which an object with mass cannot attain, time would...
OK, thanks, didn't notice the date. I am a physicist and know the answers, was frankly mostly getting on folks for being so unhelpful to the original poster.
The original poster is just trying to understand the nature of time and space at very high speeds, so let's just re-phrase the question this way:
As a THOUGHT EXPERIMENT, if I have an infintesimal mass, and am traveling at the maximum speed an infintesimal mass can travel, how would I...