I don't see what he means by improving the quality of life while the GDP remains constant. I admit that GDP has imperfections, such as only measuring goods and services that are sold, but ignoring that any improvement in the quality of life is an improvement in the GDP. If it makes your life better, it's worth more.
I figure that economic growth would continue forever, but at a decreasing rate. The long-term growth would be more logarithmic, if not asymptotic, than exponential. Also, I think it could last longer than that physicist seems to think. Even assuming we don't leave the solar system, there's no reason to keep it in its current state. If we can do better in a thousand years by disassembling the planets, then at some point it will be worth while to mine from them to build space-stations, in which case we will disassemble the planets.
A dialogue discussing how thermodynamics limits future growth in energy usage, and that in turn limits GDP growth, from the blog Do the Math.
I think this is quite relevant to many of the ideas of futurism (and economics) that we often discuss here on Less Wrong. They address the concepts related to levels of civilization and mind uploading. Colonization of space is dismissed by both parties, at least for the sake of the discussion. The blog author has another post discussing his views on its implausibility; I find it to be somewhat limited in its consideration of the issue, though.
He has also detailed the calculations whose results he describes in this dialogue in a few previous posts. The dialogue format will probably be a kinder introduction to the ideas for those less mathematically inclined.