If they knew the earth rotated, then they could assume that noon happened at different times at different locations. But did they have a way to prove this without being able to travel or communicate fast enough to observe the effects?
In: Mathematics
Ancient people had an inkling about time differences, but “time zones” as we know them? That’s a bit of a stretch.
The concept of the Earth rotating wasn’t widely accepted until much later, so the idea of synchronized time zones wasn’t really on their radar. However, they weren’t completely oblivious to the fact that the sun’s position changed depending on location.
Travelers and traders noticed that the sun’s position varied as they moved east or west. Sundials in different places showed different times. But this was more of an “huh, interesting” observation rather than a codified system.
Eratosthenes, a Greek mathematician, came close when he calculated the Earth’s circumference by measuring shadows in different cities during the summer solstice. But he wasn’t thinking about time zones specifically.
Proving it definitively? That was beyond their technological capabilities. You’d need near-instantaneous communication across vast distances to demonstrate it conclusively.
It wasn’t until the advent of long-distance, rapid communication (think telegraphs in the 19th century) that we could actually prove and implement the concept of standardized time zones.
So, did they know? Sort of. Could they prove it? Not really. They had observations that hinted at it, but lacked the means to confirm or standardize it in any meaningful way.
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