Today's mobile phone technology troubles 4158

Well, in the sense of a mathematically rigorous proof (the kind of logical exercise one fights thru in algebra II) you can't.

In practical terms you can calculate out the intermodulation and harmonic products that could occur from various combinations of the frequencies involved, and show that the power levels that the potentially interfering radio can generate will result in interfering signals weak enough to not be an issue. In the case of cell phones in planes, you'd have to spend a lot of time with various phones taking measurements of radiated power levels at various points in the plane, until you could be reasonably sure you could accurately predict the signal strength everywhere. And, to complicate matters, you'd have to buttume several phones could be in use at once. It would be very tedious to do (*).

You're generally allowed to buttume the equipment is in-spec for interferance testing. In the case of aircraft, because of the safety implications, you'd probably actually want to base the calculations on a reasonable "worst case" out of spec phone. Engineers are generally very cautious about this sort of thing; it hurts their egos if the real world results are worse than what they calculated.

John

(* or you just wait for the gov't to say "it doesn't look like there's a problem, let's try it and see what happens")