Cell phones dont work underwater. Radio waves don't penetrate water except at extreme low frequency and even that wont at this depth. Undersate communication is by acoustics not radio waves mostly, and that is very limited.
I'm not sure what kind of signal was sent from the mother ship to the Titan, which received it via transponder (see below). So it likely wasn't cellular. However, it has been reported that way several times (I did find a good article on the situation - it's the last one below).
The first article below does not state how deep they were usually able to use this method, but I would assume since they had used it before, they knew something about it worked. Newsweek doesn't have as much detail as Scientific American - but the Scientific American article states that
the Titan could only receive and not send messages. Via sonar transponder, if I'm reading correctly.
This article describes the use of texts
as long as the Titan was directly under the mother ship. The idea was supposed to be that the mother ship could keep track and send texts as long as the two vessels worked in unison and the mother ship stayed in column with the submersible.
The small submersible, operated by OceanGate Expeditions, disappeared just 1 hour and 45 minutes into its dive to the famed wreckage of the Titanic on June 18.
www.newsweek.com
From the article:
The vessels can send short messages back and forth, however the data shared between the two is extremely limited, Stefan Williams, a professor at the School of Aerospace, Mechanical and Mechatronic Engineering Australian Centre for Field Robotics at the University of Sydney, reported on The Conversation.
The means of sending the messages was, according to this article, text messages. Is there something else that sends texts besides cellular service? GPS doesn't work under water, but apparently, if the mother ship was directly over the submersible, text messages did work.
However, articles where the writer has more expertise (IMO) state that the communication was not "back and forth."
Many articles (including the one above) mention that an electrical outage/power failure would have meant that the pings no longer got sent. Texts would have been only incoming (the Titan wasn't texting back, from what I understand).
This has lead several experts who are opining in the media to ask whether, in fact, the Titan had a back-up battery. The illustration posted by
@imstilla.grandma (which is the best I've seen) on the construction of the sub, with no mention of a back-up battery (I figure someone will report more on these aspects in coming days, possibly in online versions of magazines).
And, so I did go search some more and found this excellent article:
A submersible called Titan has gone missing on a dive to the remains of of the Titanic
www.scientificamerican.com
However, details missing from all articles include whatever mechanisms they had for jettisoning ballast, which is supposed to happen automatically (according to various experts) in certain scenarios (without power, for example). I suppose that's why the "they're caught in something down below" is a popular theory, since theoretically, the Titan should have surfaced on its own right now.
The Scientific American article expresses confidence that the Titan did have some automatic way of jettisoning and therefore, surfacing.
IMO.