This is a question we are often asked by passengers. The simple answer is possibly!
The first thing to remember is even if you tried using a mobile phone it is unlikely you will get a signal above 5000ft, however that does not stop the phone searching for one.
The reality is with modern GPS navigation systems on commercial aircraft is that a mobile phone that is being used on an aircraft is unlikely to cause any issues to onboard flight deck navigation equipment. That said there have been 2 incidents where some electromagnetic interference has been suspected but not proven. In recent times this was the Crossair flight 498 which crashed 2 mins after take off from Zurich on 10th January 2000.
Investigators conducted various tests on the same aircraft type – a SAAB 340B to see if they could replicate electromagnetic interference through the use of mobile phones, however they were unable to demonstrate mobile phones had any effect on the aircraft systems so the incident was mainly put down to pilot error.
On 6th June 2003 an Air Adventures Piper Chieftain crashed in fog on approach to Christchurch Airport in New Zealand. There were 8 casualties including the sole pilot, but there were 2 survivors. It was reported that the pilot made a phone call whilst on the approach and this contributed to the crash as he descended below the minimum descent altitude.
There is of course the suspicion that there may have been electromagnetic interference from making this call, but this was again not proven and it was more likely the distraction of the pilot making the call was the reason for the crash.
So it appears electromagnetic interference with aircraft systems is unlikely, however the team at FDF including myself have experienced distractions through our radio headsets when a mobile phone is looking for a signal.
It is the same noise you get when a phone sends out signals and you stand next to a large speaker. It can be very distracting and make ATC radio calls hard to make out.
Some airlines already authorise the use of mobile phones in the air but that is through the aircrafts network system, most airlines now allow mobile phones to be switched on and used during ground operations but most airlines believe most of their customers would rather not have everyone onboard in their immediate surroundings talking on mobile phones so many do not approve voice calls but of course many airlines now have wifi onboard so texts, emails etc can be used.
EASA who is the European Aviation regulator does allow mobile phones to be used in flight including voice calls but it is up to individual airlines to allow and make the safety case to the regulator to allow their use.