Solar noon is the instant the sun stands highest in your sky, due south or due north — and rarely at twelve on the clock.

The clock says twelve at solar noon only at the centre of a time zone on four days a year. The rest of the time your longitude within the zone shifts it by four minutes per degree, and the Earth's tilted, elliptical orbit adds the equation of time — up to sixteen minutes either way — on top.

Time zones and the equation of time push it as much as an hour either way; shadows are shortest then.