As I mentioned yesterday, and against my better judgement, I am writing a long pedagogical document on magnitudes and how they work. I got to the bolometric-correction part and I realized that I didn't understand exactly why they are defined and how they are used. So I had a long think. The answer is: Theoretical models of stars are better at predicting the total bolometric luminosity output (energy per time) coming from a star than they are at predicting the detailed spectrum. Thus it makes sense to separate the belief about the total luminosity from the belief about the luminosity in any one band.
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