"12 hours POST MERIDIAN. Meridian is MID DAY, when the sun is directly overhead.
12 hours ANTE MERIDIAN is 12 hours BEFORE midday, so it HAS to be midnight."
Except ANTE means BEFORE while POST means AFTER. One problem. Midnight is BOTH 12 hours BEFORE AND 12 hours AFTER noon. Meaning 12AM and 12PM should really be identical, much as 0000 and 2400 are in military time (they DO use 2400 hours when referring to events that started before midnight but end right on it).