Correct use of AM and PM
Noon is 12 PM or 12:00 hrs. Midnight is 12 AM or 00:00 hrs.
A.M. and P.M. start immediately upon Midnight and Noon respectively.
The universal convention is that 12:00 AM signifies midnight, and every moment afterward is also 'AM' until the precise moment of 12:00 PM which is midday.
Therefore every day starts precisely at midnight, and A.M. starts immediately so that 00:00:00 (24 hour format) is the first moment of A.M. (see also leap seconds )
When scheduling around midnight, some use 23:59 to mean "same-day" and 00:01 to mean "next day." But it is best to use the correct date, since 00:00 is always same-day, there is no option within the 24 hour notation of specifying tomorrow.
More on Time of Day
Under consideration for clock time is a notional Prime Meridian (or meridien for the more archaic Anglo-French spelling) this is a line of longitude that is measured rotating in view of the sun and makes practical world time possible. At midday, 12:00 PM GMT the sun is directly above this notional line in Greenwich, London and at midnight the sun is directly opposite on the other side of the earth. The interchange of the terms, Meridiem and Meridian is interesting, since the former refers to time and the latter to space.
The discovery of relativity in the early 20th century lead to the understanding of space and time as a combined dimension. Einstein referred to this dimension as "space-time." You cannot measure time without a spatial marker and constant velocity, and you cannot measure velocity without assessment of both space over a measured interval, leading to impossible, circular definitions.
Time is therefore a metaphysical quantity that we may only approach indirectly through spatial observation and cumulative effect. Over a period of time there is relentless energy dissipation, and increasing disorder on the one hand, versus entropy-defying growth (life), which is an accumulating order, on the other.
Life, of course, is another metaphysical quantity for which there is no adequate scientific definition.