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Relativity already has the inability to distinguish between past and future states built in: https://en.wikipedia.org/wiki/Relativity_of_simultaneity

I have no idea how 2D time would work, though.

It's possible to distinguish between past in future states if they exist in the same light cone. It says this in the wiki you linked to

> However, if the events are causally connected, precedence order is preserved in all frames of reference.