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The interesting thing to me is that Randall describes a very similar system just a few What-Ifs earlier: https://what-if.xkcd.com/141/

Here he says very clearly that if you "bundled" all the light from the sun and aim it at the earth it would heat the atmosphere to millions of degrees (the surface of the sun is much less than that). It's not at all clear to me what he means by "bundled" and why it's not contradictory to what he says in the article here. Presumably some kind of lens / mirror system could be used?

It seems to me that in this article he has in mind some highly abstract system that's fully reversible. Of course, in that case, once the target object gets hot enough it will start emitting light and result in equilibrium. But it's not clear to me that this describes what would actually happen with a real optical system! E.g. (a) much of the light the target receives is going to be absorbed and reemitted away from the lens, (b) what if you removed the lens targeting system at the precise moment the light impacted the target, so that the system couldn't be reversed, etc.

Edit: one more thing. The surface of the lit side of the moon can reach 260 degrees F, and dry wood can potentially catch fire as low as 300 degrees F. And the moon has some reflectivity as well. So even taking Randall's claims on their face, I'm skeptical that you could not start a fire (in some materials at least) using moonlight.

Yeah, it does contradict that. You can't really "bundle" all the light from the sun like that and aim it at the Earth without violating thermodynamics. The way to do it would be something like wrapping the sun and the Earth together in a giant chamber made out of some perfect mirror (actually maybe the mirror isn't necessary), with the only exit being the dark side of the Earth. And that would heat up both the Earth and the Sun to millions of degrees.

Aha. I think you've helped me see the central issue with your point that it would also heat the sun to millions of degrees. Suppose there was some system that allowed you to collect the light of some source and dump it somewhere else: the drawing in the What-If seems to suggest a system of perfect mirrors with an "output tube" pointed at the earth, so that any photons leaving the tube hit the earth with a high degree of accuracy. What your point shows us is that even if we imagine an indestructible system of mirrors and lenses to do this, the result is that bottling up the energy that the source normally radiates away massively increases the temperature of the source (turning your mirrors into plasma and returning the system to normal, but we're ignoring that again). So entropy law isn't violated.

The reason I (and probably others) find Randall's explanation unhelpful is that obviously there's "enough" energy being reflected by the moon to start a fire (that's why people keep bringing up solar panels). The issue is that there's no way to optically redirect that energy into a small area without heating up your source to the same degree. Which is theoretically possible I suppose, but it's not the situation the What-If is talking about. Along with the issue that the light we see from the moon is mostly reflected rather than emitted (which changed the situation entirely), this makes the What-If explanation a little misleading.

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