Stephen Hawking said that time travel to the past is probably impossible, but travel to
the future is possible. One way is to travel at near the speed of light. Einstein's theory
of relativity predicts that on your return, time would have passed everywhere but for you
it would have slowed down.

If the ancient Mayan civilization were sufficiently advanced, perhaps they left Earth to
avoid the diseases of the Spanish invaders. They have been traveling at near light speed
on a trajectory that would return them to Earth in 2012. That's why their calendar stops
in 2012, not because it's the end of the world. It's because that's how long it will take
them to return.

I'm writing about this in a sequel to my short story "The Flats." It seems the Flats
turned out to be true. But they were merely placeholders until the Mayans returned.