No, 12:00:01 AM being a second after noon (i.e. 12:00:01 after the start of the before-noon) is the only one that makes sense. You can't just swap out the refer

No, 12:00:01 AM being a second after noon (i.e. 12:00:01 after the start of the before-noon) is the only one that makes sense. You can't just swap out the reference point and keep counting, that's just as moronic as claiming 1/500 of a dollar is 0.002 cents, because it's in the cents territory. If you want to switch the reference point, you also have to reset the counting to the correct value: 00:00:01 PM = 12:00:01 AM.