That gives me so many questions: Should there be a non-Earth timezone? How do you define a "day" in space? Is there a day light saving in space?

At least they are not travelling near the speed of light. That's a whole different can of worms.

At least the proposal let's time-zones go away, since "day" is completely artificial:

https://en.wikipedia.org/wiki/Timekeeping_on_the_Moon#Coordi...