Some parallel worlds have different time-flows, like the fabled dwelling-places of the elves: those who visit them under the hill for a night return to find that years have passed in this world. Perhaps it is the gate leading between the worlds which causes the alteration. If a gate were 'misaligned', the shift from '| |' to '| \' or '| /' as it were would lead to that difference, much as a light-beam split and bent by a prism ends up taking a longer path. There might even be a mathematical function linking degree of misalignment to alteration of time-rate.
A city the heroes visit is in a crisis, the king and queen are getting a divorce. Who shall rule? The inhabitants of the city take sides by tying a red or blue ribbon to their swords, sticks etc. Whose side will the Pcs take?