No. A single time zone can span thousands of kilometres from East to West. This means that when the time is Noon at the reference location, the sun's position can be anything from 11 am to 1 pm at the extremes of the time zone.
local noon (not noon according to the clock)
You would expect to find the shortest shadows around noon when the sun is at its highest point in the sky. This is because the angle of the sun's rays are more directly overhead, resulting in shorter shadows.
Yes the sun is always highest in the sky at noon
At "local apparent noon", when the Sun is highest in the sky. This will be noon on your watch only if you are at the middle meridian in your time zone and if you are not on daylight savings time.
At "local apparent noon", when the Sun is highest in the sky. This will be noon on your watch only if you are at the middle meridian in your time zone and if you are not on daylight savings time.
Shadows made by the sun are shortest at solar noon, when the sun is directly overhead. At this time, the angle of the sun's rays hitting objects is at its steepest, resulting in shorter shadows.
NOON When the sun is at it's highest point in the sky
local noon (not noon according to the clock)
The shadow of a tree is shortest when the sun is at its highest point in the sky, typically around noon. This occurs when the sun is directly overhead or at its zenith, resulting in minimal angular displacement of the shadows. The length of the shadow can also vary depending on the time of year and the geographic location, but generally, midday shadows are the shortest.
Your shadow would be shortest at noon because the sun would be directly overhead.
noon
noon