That's already the case for people very far North/South. Summer/winter become their own day/night at the poles... according to the Sun. If you take a walk aroun

That's already the case for people very far North/South. Summer/winter become their own day/night at the poles... according to the Sun. If you take a walk around the pole, you can cross several timezones and end back where you started while having "lost an hour" every few steps. Of course, in one of those crossings you "gain a day" so, watch your step!