So China apparently invested over a hundred billion in fast rail. That's a lot of money. It is also a lot of cool infrastructure. Prosperity theory predicts that such public goods will accelerate the economy. It could also lead to los of empty but really fast trains. I wonder which one it is?

Both. The capacity needs to handle peak traffic during holiday season, so if you travel at a less busy time, you can easily end up in an almost empty train car with several empty rows of seats between each passenger. AFAIK, except for Beijing-Shanghai and maybe a few others in the wealthy, densely-populated east, most connections are operating at a loss. Connecting all the western provincial capitals was definitely just a prestige project.

But it did accelerate the economy for places that are now a lot more convenient to reach. I doubt that it's enough to justify the enormous construction costs, but it's also not nothing.