Time is determined by the position of the sun. Originally clocks were adjusted locally to match daylight, so if you traveled east or west you would have to adjust your clock by a few minutes. Time zones were invented to make timekeeping easy for railroads to keep track of their trains over long distances.
On the poles this sort of time is irrelevant since the amount of sunlight is determined by the Earth's tilt, not its rotation. This means the solar day lasts an entire year: The sun shines during the hemisphere's summer but is completely obscured during the winter. Time zones for the poles are chosen to be convenience for working with the rest of the world.
People and supplies going to the Amundsen-Scott South Pole fly through a base in Christchurch in New Zealand, so New Zealand time is used there. Everyone there works one of three shifts, so no one is really working "late" or "early" as each shift has the same amount of daylight.
Since there's no permanent land on the North Pole there's no set time zone, either. People traveling there use whatever time zone is most convenient. For planes this is generally Greenwich Mean Time, also referred to as Coordinated Universal Time. Researchers and explorers use the time from whatever place they traveled from or the institution that is supporting them. For example, students and scientists from University of Washington's Polar Science Center set their watches for the Pacific Time Zone.
Posted 1883 day ago