The 20th Amendment moves the date of inauguration from March to "noon on the 20th day of January." Under the Constitution, the old president continues to hold full power through 11:59:59, and then power shifts at noon. Article II, Section 1 requires that the new president, before executing any duties, take a prescribed oath or affirmation. To avoid a constitutional power vacuum, the Inauguration Day program is certain to schedule the swearing in for as close as possible to noon. The Chief Justice of the United States typically administers the oath, although the Constitution does not require that the oath be performed by the Chief Justice
Cheers,
Scott.
(It won't keep the wingnuts from caterwauling about it, though.)