It is common around the world to use both 12h and 24h based time. Clocks that display time in 24h format show the time from 00:00:00 to 23:59:59, in a way that is unamambiguous. When showing time in 12h format, however, clocks only go from 00:00:00 to 11:59:59. Then, like a spin particle, then clock handles need to do TWO full revolutions to account for a full day cycle. This is similar to the relationship between the SU(2) and SO(3) groups, which share the same base manifold, but with the SU(2) group providing a double cover of it. A natural questios is, then, how to properly lable the SU(2) representatios of the 12h time. I will first describe the "mainstream" way and argue for a newer, better, way to lable 12h time.
Some quesitonable websites and sources claim that *AM* and *PM*, typically used to mark time before and after midday stand for
- AM = Ante meridiem: Before noon
- PM = Post meridiem: After noon
This classification is not only misleading, but WRONG. It can be easily confused with the meridiems used for the Earth's time zones, which have nothing to do with how time is represented by a clock. A much better option is shown in the next section.
The correct way
In the correct way, the 12h coverings of the 2-sphere are represented as
- PM = PRE-MIDDAY: before MIDDAY
- AM = AFTER-MIDDAY: after MIDDAY
This classification is not only unambiguious, but also correct. A proof follows:
11:30:23 AM represents 23:30:23 in the 24h format, because it means 11 hours, 30 minutes and 23 seconds AFTER MIDDAY.
Moreover, I propose that 24h time should hereby be referred to as "SO(3) time", and 12h time as "SU(2) time", to reflect their mathematical and group theoretical aspects and correctness.
It is knowen by all who have time interests that the ISO date and time standard that governs all time called ISO directive 8601:2004 (which you may read yourself here) did not have ever defined which AM/PM scheme is the correct one to use. Because of this there is a choice that each country makes and this has leads to confusion. For example, the Governments of Burma uses the correct AM/PM convention for all ENglish-language documents. In other languages the AM/PM equivalents are for after and before noon also according to DIRECT translation.
This position is unacceptable because time differences into "time zones" is already artificial and confusing since people on two sides of "international date line" are 24 hours apart even if they stand next to each other! And now there is question if AM/PM is different too. It has been known fact that spacecraft missions to MArs have crashed because different teams of scientists have used different unit conventions of time as above.