What does photon energy tell us about cellphone safety?

It has been argued that cellphones are safe because a single microwave photon does not have enough energy to break a chemical bond. We show that cellphone technology operates in the classical wave limit, not the single photon limit. Based on energy densities relative to thermal energy, we estimate thresholds at which effects might be expected. These seem to correspond somewhat with many experimental observations. Revised with appendix responding to critique published by B. Leikind.