Lo! is it not unto Allah that belongeth whosoever is in the heavens and whosoever is in the earth? Those who follow aught instead of Allah follow not (His) partners. They follow only a conjecture, and they do but guess.
Times are computed by method; your mosque's timetable governs the adhan. Every text carries its source and grade. Nothing here is a fatwa, a prediction, or a substitute for a doctor: your own scholar decides what is contested, and the tradition itself says the practice is alongside treatment, never instead of it.