Special Relativity dictates that as you approach c, time dilates, mass increases and length contracts such that, from your frame of reference, you appear to be accelerating at a constant rate even though your acceleration curve becomes asymptotic with the velocity c as the limit.
From my frame of reference? I don't know which one is it.
The only relevant frame of reference here is the earth's one, where people live. For them (for us, actually) there is no time dilatation nor length contraction as we are in the same frame of reference.
As Earth approaches c, always more energy is needed to continue accelerating, until infinite energy would be needed, which is impossible. Any massive object cannot reach c (regardless of the frame of reference by the way). So acceleration cannot go on forever.
I don't know what you heard about special relativity, but I don't think it means what you think it means.
RS is correct. SR does allow for the FE acceleration to continue indefinitely, but only with at least a centillion (10^303) joules, so far. Of course, that's just unreasonable.
I did oversimplify a bit. I meant: acceleration cannot go on forever
at g. I can agree on the asymptotic approach to c which means there could "always" be an acceleration, but never at g.
There is one huge problem, though: where does this tremendous energy come from? I mean, you're talking about a centillion joules but it's by far a gross underestimation. If you want to talk big numbers, try Graham's number, and still you wouldn't have enough energy to keep accelerating.
And even then, if I granted some magical energy to continue acceleration, and some magical law of physics that allows indefinite acceleration at g while never reaching c (after all, a FEer cannot adhere entirely to reality-based science, or he wouldn't be a FEer in the first place), there are still other problems: for example, I read on another thread that GPS do work with satellites. What makes
them accelerate? if they have to stay at the same altitude, they have to accelerate at the same rate as the earth, otherwise they would crash as earth accelerates towards them.