I've heard the saying "time has no meaning", but it looks like we might be living it on this trip.
From the Abercrombie and Kent itinerary booklet:
In Antarctica, technically you can choose your time since at the South Pole itself there is only one “day” and one “night,” each 6 months long; however, when cruising in the Antarctic Peninsula, the ship operates on Argentine time.
I think I will choose 9 am.
And for those playing the home game, Argentina operates on Greenwich Mean Time minus 3 hours. So when it's noon on the Prime Meridien, it's 9 am in Argentina.