Mathematician Alain Connes cites a French legal rule that explicitly accounts for propagation of information at finite speeds substantially below the speed of light:
There was a legal rule according to which a law decreed in Paris on day J was applicable in Paris on day J, but it was valid at distance n km of the capital only on day J + 1, at distance 2 n km on day J + 2, and so forth, where n is the number of kilometers covered by a stagecoach in one day.
Large ancient empires, such as the Roman Empire, must have seen similar situations very often. (E.g. the emperor makes decision X in Rome on day J, but it's yet unbeknown to the governor of a remote province when he partially counters it with decision Y on day J + 1).
How did the Romans and others deal with these situations? Was it completely ad-hoc or did they also have special applicable rules in their legal codes? (Although I'm referring to an emperor in my specific example and emperors may not have been constrained by legal codes, relevant situations must have also occurred e.g. in private business across the Mediterranean.)
UPDATE This week´s Economist carries an article about the economics of interstellar flight which makes for interesting related reading. It cites an early (perhaps tongue-in-cheek) paper by Paul Krugman who even came up with two fundamental theorems of interstellar trade :-)
Such trade will be affected by relativity theory, which shows that beings on Earth (or Trantor) will see time pass at a different speed from those who are on board cargo ships moving between the two. This could make it hard to calculate the net present value of a shipment. And the fact that messages can move at best at the speed of light (and cargoes more slowly still) might do odd things to the ability to arbitrage between the economies of the two worlds.
As I thought more about the question I was also reminded of George Nashes biography of Herbert Hoover: Hoover was sent to Australia in 1897 as a young mining engineer. A visit to headquarters for a thorough briefing was a then especially important part of his preparation because instant world-wide communication was impossible and relatively junior persons had to make independent decisions on the spot. Presumably this was even more the case e.g. for say imperial generals in ancient times and is less the case today.