A sun dial will only ever show you solar time, not whatever political abstraction passes for "time" wherever you happen to be.

Fun fact: Only with the advent of railroads did time begin to be synchronized in larger areas. Until then, each city and town set it's own time, based on the local solar time.

https://en.wikipedia.org/wiki/Railway_time

There exists public clocks that track both local and standard time: https://en.wikipedia.org/wiki/The_Exchange,_Bristol#Clock