I've heard arguments that cooling will be a hard technical challenge and, given current equipment weights and launch costs, they would be uneconomical. But is there an obvious reason space data centers would be impossible?

Most technologies start out looking hard and economically infeasible. But if you invest in development, you might be able to get a few breakthroughs, and suddenly, it's viable.

If they do get things to work, the benefits seem obvious: 24/7 access to clean energy, not upsetting the people who'd rather not have a datacenter next door (or in the same state), and plenty of space to scale up.

Literally no one is saying it’s impossible. Of course it’s possible, and it may one day even be economically viable.

But Elon’s claim that by 2027, the cheapest place to put data centers will be in space? Yeah, that’s impossible. But then again, only a fool would believe him at this point.

I highly doubt that space data centers will be more advantageous than terrestrial before 2035, and that’s very optimistic.

I agree with you about Elon Musk's claims, but that's not what we're discussing here.

If it takes until 2035 or even 2045 for space data centers to have an economic advantage, it still seems like a good investment for someone in Google's position.

And FWIW, there are quite a few people claiming that they'd "go against the laws of physics", etc. For example: https://news.ycombinator.com/item?id=49838152