George_Weinberg2 comments on Heat vs. Motion - Less Wrong
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There's a way you could make the heat=motion concept much clearer to Carnot. When one studies kinematics, one generally makes the approximation that macroscopic bodies are rigid, and the motions of the body refer to center of mass motion, or perhaps rotation about some axis. If you explain that "heat" refers to the motion of the constituent particles relative to each other, I think a scientist of Carnot's day would understand the idea pretty quickly.
I think this sort of thing might be what people mean when they talk about a "bridging theory".