The important thing to remember is that you are not going to experience yourself as going slower in time. You are always going to see something else as going slower in time.
So what are you going to observe relative effects relative to? Relative to yourself! So from your perspective, you are of course, never moving.
This might sound a little bit confusing when you are thinking about the twin paradox. When the twin is flying away, you see his clock as going slow, but he also sees your clock as running slow. So you and the twin just need to disagree, because neither is right until the twin changes speed.
When the twin changes speed, he sees all sorts of funky time changes in things that he is changing speeds relative to. The changes are more dramatic in distant objects. One of the effects he would see when he is, say, slowing down on his approach to Alpha Centauri, is to see time on Earth whip by very quickly. When he reaches the point that he is once again at rest relative to the Earth, both the twin and people on the Earth will agree that more time has passed on the Earth. It’s just that for the twin, most of that time passed in short burst.
You couldn’t get “stuck” at light speed, frozen in time forever, because it would require an infinite amount of energy to accelerate you to that speed. Any finite amount of energy will only get you to some fraction of that speed.
Asimov explains a lot of this stuff pretty well in * The Stars in Their Courses *, IIRC. What we have is limiting phenomena at relativistic velocities: as velocity --> C, mass --> infinity.
In theory, that happens on both sides of C, so not only is there not enough energy in the universe to boost a single electron to light speed, but if there are faster-than-light particles (going backwards through time), there isn’t enough energy to slow them down to light speed.
The only particles that can travel at light speed are those that have no mass whatsoever, and they’re trapped at that speed.
Also, at relativistic velocities, velocity isn’t additive: if you leave the Solar System at .6C in one direction, and I do the same in the opposite direction, we’re not traveling away from each other at 1.2C. I can’t recall the details of how it works right now, but that’s part of what Einstein figured out that Newton had no inkling that it was necessary to know. (No slam on Newton; he was brilliant. He just lived at the right time to be Newton rather than Einstein.)
