Why passengers cannot use mobile phones on planes
As everybody knows, once the cabin door closes, all personal electronic devices must be turned off until the plane reaches 10,000 feet; the use of cell phones is prohibited from the moment the plane starts taxing until landing. These restrictions are familiar to most travelers and have been enforced for 30 years, but why cell phones can't be used on planes?
As it turns out, there's more than one reason and they follow a fairly convoluted rationale.
In-flight safety
The most intuitive justification is that electronic devices emit radio frequencies which can, in turn, affect nearby equipment - such as the aircraft's avionics - making it a matter of flight safety: if radio communications or pilot's flight inputs were disrupted, that could result in a dangerous situation for passengers and crew. As flight regulations are under the purview of the Federal Aviation Administration (FAA), one would expect the agency to be responsible for these onboard restrictions; however, contrary to what most passengers think, the FAA does not actually prohibit the use of personal electronic devices (including cell phones) on aircraft. Paragraph (b)(5) of 14 Code of Federal Regulations 91.21 leaves it up to the airlines to determine if devices can be used in flight, allowing the use of "Any other portable electronic device that the operator of the aircraft has determined will not cause interference with the navigation or communication system of the aircraft on which it is to be used."
In other words, before an airline could allow cell phone use in-flight, it would have to prove to the FAA that wouldn't interfere with the airplane systems; and accurate investigations and testing must take place before such a clearance is provided.
Following the (admittedly scarce) reports of harmful effects logged during actual flights that could be attributed to personal devices, advisory committees which comprise regulators, airline representatives, and academics, have been examining electromagnetic interference from electronic devices since at least 2003. The general results of all these experiences is that virtually all of the reported evidence for banning electronics below 10,000 feet and cell phones during the entire flight is anecdotal; yet, committees still maintain that "caution" is key as not having definitive evidence of interference does not amount to scientific proof of safety. Moreover, the electronics industry (that is releasing new mobile devices every year) evolves much quicker than the aviation industry, where things progress very cautiously and an aircraft type has a service lifespan of several decades.
The result is that no one in a position of authority (be it in the FAA, the airlines, or politics) wants to change a policy that may be later implicated as a contributing factor toward an accident. Therefore, it's a whole lot easier to do nothing and leave the policy as it is, in the name of caution, which is also a safe attitude in the aviation domain.
Ground interference
Even if airlines were able to prove to the FAA that cell phones wouldn't interfere beyond any doubt with the airplane systems, that would not resolve the problem as both the FAA and the Federal Communications Commission oversee the use of cell phones on airplanes; and the final authority for wireless devices rests with the FCC which, since 1991, has banned the use of cell phones on airplanes because of potential interference with ground networks.
The technical reason is that cell phone systems depend on frequency reuse to increase the number of customers that can be served within a geographic area on a limited amount of radio spectrum. However, devices that are traveling at high speed and high altitude violate fundamental assumptions that allow frequency reuse to work and would break havoc in the network management system and cause harmful ground network interference resulting in widespread disruption to the mobile service.
Technical solution and additional challenges
To address both the onboard and ground interference issues, new technology has emerged which proposes the use of a picocell, a small cellular base station capable of covering a small area such as an aircraft cabin. Acting like a cellphone tower, the picocell would communicate with cellphones within the aircraft and relay the signals to either satellites or a terrestrial-based system. This would allow mobile phones to operate without directly connecting to ground base stations (hence avoiding ground interference) and, due to its proximity, allow mobile radios to operate at the lowest possible power (preventing interference with onboard devices).
While technically sound, this approach presents challenges related to the multitude of incompatible mobile phone systems worldwide: to be effective, a picocell transceiver operating on an aircraft would have to provide compatibility with all of the different major cell phone protocols (TDMA, GSM, CDMA, iDEN) and their respective providers.
An alternative solution is leveraging the widespread diffusion of voice-over-IP services, which rely on data routed through the internet to provide text and voice services; in this scenario, Wi-Fi connectivity (whose radios are way less powerful than mobile) is provided in the cabin through a satellite relay and allows passengers to use communication apps like WhatsApp, Facebook Messenger, Skype, and others.
Human factors of social resistance
Besides the safety and technical hurdles, an equally important factor has emerged as many passengers expressed a clear preference for mobile devices to remain banned on aircraft, as that allows for a quieter flight free from the nuisance of mobile phone chatter.
Up in the air nobody can call you (yet)
As a result of all the above, there still is no widespread or standardized solution that allows for airline passengers to communicate with the ground 30 years after the original FCC ban on mobile phones. Specific regions and individual airlines have tried their hand at different approaches; yet, besides a cautious opening to onboard Wi-Fi (often for a very limited time, and more than not for a fee), the skies are still a quiet zone out of reach for telephone calls.