The short and honest answer is that we don’t really know. The later effects of radiation poisoning are well understood, and is explained by how the cells are killed as they try to divide. This is a relatively slow effect that manifests during cell division. But it doesn’t explain the reasons for the onset of prompt effects (e.g. vomiting, diarrhea).
There simply isn’t enough research on this, and as far as I know, there are no solid theories for why these effects occur. The best answer we have is that the intestines are very sensitive to radiation, and a huge dose of radiation will probably trigger something in that system, which in turn will respond in the only way it can: vomiting & diarrhea.
However this does not explain other common effects like nausea, metallic taste, fatigue, headache, etc.
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