>I'd imagine it will be running out pretty much the same way in 40 years, and 40 years after that.

It will run out, though. The only questions are when, and what the contingencies will be once it does.

Or it won't, since technology will replace the need for it long before that. We don't use horses to drive our cars not because we've run out of horses.

Well, there's some unsubstantiated optimism if I've ever seen it. Let's hope you're right, but right now the physics and economics do not support your exuberance.

It is substantiated by centuries of human history. And by physics and economics too. Particularly, economics teaches us that when resource's price raises, attractiveness of substitutes and thus investment into improving these substitutes raise considerably. And physicists are working on solving problems that block our progress for finding alternatives right now (e.g. on increasing energy density for electrical storage, increasing energy efficiency of solar cells) - and there are some encouraging signs there too. E.g. this one: http://www.nature.com/nature/journal/vaop/ncurrent/full/natu... may allow producing solar energy much cheaper than before.