I don't think that's the case. Suppose we deal with real numbers- so $10,000 represents my fraction of the static population's static energy consumption. If my consumption grows from $100,000 to $200,000, the fraction of my consumption that energy represents is now 5% instead of 10%. That means that energy is really getting cheaper- if I continued spending 10% of my consumption on energy, I would get more energy (in whatever form it's useful to me in, which may actually represent less watts).
That is, your statement- that energy prices rise with GDP and other prices don't- is not what the physicist is ruling out. The physicist is ruling out that all prices rise. If they don't, then in order for some prices to rise other prices must fall- for GDP growth to continue but energy to have a smaller share of GDP, energy must be getting cheaper, which seems odd for a scarce resource.
I think the economist should argue that energy prices will rise but energy quantities will stay stagnant. It seems to me that you could have a future scenario in which almost all of income is spent on energy.
Indeed, what happens if, instead of talking about this in terms of dollars, we talk about it in terms of watts? (I'm using watts instead of joules because income is typically dollars / year, instead of just dollars.) If energy is scarce, it's a natural store of value. We've built a Dyson sphere, we've grown the population such that the average person has an income of 1 kW. GDP per capita is now stuck at 1 kW forever- but the sort of goods and services that I can buy with my income of 1 kW will get more and more impressive over time. The price of an experience in terms of Joules will decrease as time goes on. Right?
Much of the value increases he's describing- that the physicist later calls "development" rather than "growth"- strikes me as the sort of "inflation" that he's ruling out. Really, what's going on with a static store of value like that chasing higher and higher utilities is deflation. George Selgin put out a book called Less Than Zero that's relevant.
[edit]Hm, thinking about this again, depending on how you count up "GDP" this might depend on how frequent trading is. I'm presuming you count it in terms of net income plus consumption, rather than net revenue; the first is the more physical quantity but the second is easier to measure.
Claim A: "If the price of energy rises as fast as GDP, then this GDP growth is inflation rather than real growth."
Claim B: "If the price of energy and all other prices rise as fast as GDP, then this GDP growth is inflation rather than real growth."
Claim C: "For GDP to continue really growing (exponentially) given constant energy, the price of energy must continue falling (exponentially) relative to GDP."
I claim that C follows from A, and that the physicist asserts A and deduces C, but I claim that A is false and that C is also...
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.