I found the relevant Summer Update
Three pieces of information there, and the discussion about the Magic Kingdom, lead me to need to overhaul my Theory of Erfworld Relativity:
1.)"A second was "one-thousand-one." A minute was sixty of those. An hour was sixty minutes, and a day was twenty-four hours. At least, within a given hex."
2.)"Only the order of our actions is important. Time isn't."
3.)"It [the sun] jumps backwards when I enter the hex?!" "Of course! To you," said Sizemore. "Because you traveled and were observed from that hex. If you weren't observed, you would find the sun in the same position as the previous hex."
I find statement 3.) from the summer update to be inconsistent with statement 2.) Both statements were made by Sizemore. To be consistent with statement 2.) Parson should observe the sun shifting backwards as he returns from scouting depending on what order events are happening in the Hex he returns to, rather than observation. To be consistent with statement 3.) Parson's scouting mission would return later in the day simply because no one was watching him.
If statement 3.) is amended to say (or understood to mean) "waited for" rather than "observed," I would find it far more consistent with the rest of the description of relativity in that update.
So, what of the sequential turns vs. simultaneous turns debate?
I find sequential turns make it easier to avoid paradoxes like the ones presented in this thread, with the exception of mid-turn communication between otherwise non-interactive sides. (Both via Thinkagrams and the Magic Kingdom.)
Simultaneous turns neatly solve the Thinkagram and Magic Kingdom issues, but leave possible weirdness when determining Battlespaces.
I propose a dual solution. Battlespaces are Predicted as if Sides always took Turns sequentially. Then Turns outside of Battlespaces are played simultaneously.
Here's how I use relativity to explain the paradox presented earlier:
Alberta and Borneo are at war. Alberta takes their turn first.
On Alberta's turn: Scouts from Alberta are sent to find the remnant of a routed army from Borneo. They scout through Hex 7, then return to Hex 3 having not found the army they sought.
Then on Borneo's turn: Borneo's army camped in Hex 8, and passes through Hex 7 as they flee.
No Battlespace is formed, so the turns play simultaneously:
Alberta and Borneo both have units in Hex 7 during the simultaneous turn.
Battlespace should be formed, so turns play sequentially (and we return to the first situation.)
My solution is quite simple. From the rabbit in Hex 7's perspective the scouts from Alberta enter and exit the Hex first, then Borneo's army passes through. Suppose Alberta's scouts search Hex 7 thoroughly, until the sun moves most of the way to Dusk. Borneo probably thinks it's weird that the sun jumps to dusk when they enter the Hex, but they'll explain it away by saying that something else must have happened there earlier this Turn. They might even guess that Alberta's scouts were there. The question is whether that information causes any further problems.