I'm on an international flight to LAX (now waiting in heathrow) and that question popped to my mind
Hipparchus of Nicaea (c. ~190-120 BCE) seems to have been the first person to propose using a grid system to find the position of cities (and other places) on a globe, which implies an understanding of longitude. He built on earlier work by Eratosthenes of Cyrene (c. 276-194 BCE), who had mapped the known Earth, including finding its circumference. Hipparchus' method of finding the longitude of places was to use the differences in timing of lunar eclipses at different points on the globe to calculate the difference between local time of those points; the drawback is that there was no accurate-enough method of timekeeping to lead to useful calculations. Edit to clarify: The difference in local time between observed beginning and end of the eclipses would serve, essentially, as a way to understand the longitude between places.
The knowledge that local time would be different at different points on the globe is what led eventually to what's called "the discovery of the longitude" in around 1760 or so, when two methods of reliably finding longitude using time were discovered and implemented. To quote myself from an old answer:
Longitude is more tricky. The most straightforward way of determining longitude is comparing local time to time elsewhere on the globe (usually, Greenwich Mean Time) and figuring out the time difference; if it's 1 p.m. at Greenwich at your local noon, you're 15 degrees west of Greenwich. Once marine chronometers became widespread, the longitude problem was easier to solve; but, chronometers were only provided to British naval ships traveling in far distant waters starting in the 1790s, and did not become standard issue until the 1840s. (Captains or masters could buy chronometers, although they were horribly expensive -- 60 to 100 guineas new, plus 5 or 10 per year for cleaning/resetting, and ships needed three to correct for errors.) So our theoretical 1785 captain had three options for dealing with the question of his longitude:
- Running down a line of latitude -- widely used before the "invention of the longitude" around 1760, this implied that you'd sail to an easily-found point of latitude and turn dead east or west, steering for a landmark. This could be very risky -- there's only something like 1.75 degrees of latitude between the Scillies and Ushant, the entrances to the English Channel, so you better be darn sure of your latitude to enter the Channel that way.
- calculate your time, and thus position, based on "lunar distances" -- either finding the degrees between the moon and another celestial body, or by measuring the positions of the moons of Jupiter, to compare it to tables and find Greenwich mean time. I am way in over my head on the math on these, but Wiki has what I am told is a perfectly cromulent summary.
So while that doesn't answer the question about time zones per se, because standardized time zones didn't exist until the railways made them necessary, it will hopefully show how early we understood that time is different in different parts of the globe.
On a related note, I'd like to know what Pliny the Elder meant, writing in the 1st Century, in his "Natural History".
Natural History, 2.2 (my emphasis):
That [the Earth] has the form of a perfect globe we learn from the name which has been uniformly given to it, as well as from numerous natural arguments. For not only does a figure of this kind return everywhere into itself and sustain itself, also including itself, requiring no adjustments, not sensible of either end or beginning in any of its parts, and is best fitted for that motion, with which, as will appear hereafter, it is continually turning round; but still more, because we perceive it, by the evidence of the sight, to be, in every part, convex and central, which could not be the case were it of any other figure.
The rising and the setting of the sun clearly prove, that this globe is carried round in the space of twenty-four hours, in an eternal and never-ceasing circuit, and with incredible swiftness. I am not able to say, whether the sound caused by the whirling about of so great a mass be excessive, and, therefore, far beyond what our ears can perceive..
He assumes, though, that the stars are all revolving as well, so he's not quite got the correct idea:
...nor, indeed, whether the resounding of so many stars, all carried along at the same time and revolving in their orbits, may not produce a kind of delightful harmony of incredible sweetness. To us, who are in the interior, the world appears to glide silently along, both by day and by night.
It seems to me that Pliny believes the Earth to be being "carried round" the sun every 24 hours, which appears to us as the sun rising and setting. He's got all the ingredients for being able to know about time zones (spherical earth, night caused by rotation) even if he's got it a bit wrong.
If you're wondering about proper timezones , those became a necessity with railroad travel in the us. Before that, each city used to establish its own time standard (for example New York and Newark were 15mn apart). The railroad situation became so crazy, it prompted Sanford Fleming to propose a world time conference in 1880 and a standard for timezones. The book Time Lord http://www.goodreads.com/book/show/1374860.Time_Lord_ has a good biography of Fleming as well as some timetables from before the timezones era.