christopherj comments on The Statistician's Fallacy - Less Wrong
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Microwaves are almost certainly safe, but just FYI, the point about there being 'no plausible mechanism' is wrong, and a common misconception. Photons don't need to have enough energy to directly cause DNA breakage, in order to be dangerous. Microwaves seem have effects on proteins beyond that caused by thermal excitation, which means they could plausibly be carcinogenic, e.g. if they interfere with DNA repair enzymes. There's some evidence that pumping enough microwaves at cells in culture can turn them cancerous.
The epidemiological evidence though, is that they don't cause cancer.
http://www.ncbi.nlm.nih.gov/pubmed/11088227
The more obvious plausible mechanism for cell phones causing cancer, is that people with a certain lifestyle are more likely to buy and use a cell phone, or that owning a cell phone increases stress or somehow contributes to a different lifestyle, or some other mechanism that doesn't involve dim sources of low energy photons.