would it make you happier if they said 12:00.001 am instead?
[quote=] Midnight marks the beginning and ending of each day in civil time throughout the world. It is the dividing point between one day and another. With 12-hour time notation, authorities recommend avoiding confusion between noon and midnight by using "midnight", "12 midnight", "12 mi", or "12:00 midnight."[1]

In the United States and Canada, digital clocks and computers commonly display 12 a.m. right after midnight. While that phrase may be used practically, it helps to understand that any particular time is actually an instant. The "a.m." shown on clock displays refers to the 12-hour period following the instant of midnight, not to the instant itself, because at that time you are looking at clocks midnight has already passed and the period before noon (a.m.) of a new day has begun. In other words, 11:59 p.m. shows until midnight; at the instant of midnight it changes to 12:00. Simultaneously, the p.m. changes to a.m., though, strictly speaking, a.m. does not apply to the instant of midnight which separates p.m. and a.m. In 24-hour time notation, "0:00" and "0:00:00" refer to midnight at the start of a given date. Some styles, such as ISO 8601, allow 24:00 to refer to the end of a day. Noon is 12:00:00.
One way for a digital clock to show midnight

While computers and digital clocks display "12:00 a.m." and "12:00 p.m.", those notations provide no clear and unambiguous way to distinguish between midnight and noon. Strictly speaking, it is actually incorrect to use "a.m." and "p.m." when referring to noon or midnight (12:00). The abbreviation a.m. stands for ante meridiem or before noon and p.m. stands for post meridiem or after noon. Since noon is neither after noon nor before noon, and midnight can equally be twelve hours before and after noon, neither abbreviation is correct (although the length of the error is determined by the smallest unit of time — 12:00:01 p.m. would be correctly notated, however it can't be read as "12 hours and 1 second has passed after noon"). [/quote]

this is from wiki.