Huh? Radiators are known technology. They have them on ISS; they have them on every Starlink satellite. This isn't like warp drive or antigravity.
Moreover, you can easily calculate how big of a radiator you need for a given power level and temperature. You can use the Stefan–Boltzmann law:
A ~ (1000 P) / (2 e k T^4)
Where A is the radiator area in square meters
P is the power in kilowatts
e is emissivity (usually 0.9)
k is the constant 5.67e-8
For a 1 kW test like Googles, you just need 1 square meter of radiators (assuming two-sided).For SpaceX's 175 kW satellites, they will need ~170 square meters of radiators.
None of this is impossible or even difficult to calculate. That's why I think this is the laziest argument against space data centers. There are so many other more reasonable arguments (like whether they will be economically competitive) but people love to latch on to this one for some reason.
To your last paragraph: when opposing something, it makes sense to use the laziest argument first. Only if that doesn't achieve your goals, would you move towards less lazy arguments. I forget what the term for this is, it's generally criticized ("you should just put your strongest arguments first").
sure, the physics is solved: we know how radiators work, and we can calculate the area needed, blah blah. but we haven't put sustained-AI-computer systems into space yet - heat is a genuine concern, and personally I'm curious if they are developing something beyond simple radiators. if a ~1m^2 radiator works, great. but if the current test can only run the TPUs for ~15-minute bursts before it has to stop and dump heat, this issue isn't exactly "solved" in my book.
> For SpaceX's 175 kW satellites
That's like a quarter of a rack of modern AI hardware. Modern AI datacenters are now in the multi-GW range.
I think you misunderstand the argument of the people worrying about cooling. I don’t think most people think it’s literally physically impossible, they just think that this will be the thing that makes it economically uncompetitive. It’s a combined argument.