Dates are set against calendar which in turn is set against hourly increments that are offset by local time zones. There is the infamous AoE or "Anywhere on Earth" time zone which can be used to say things like "we won't start until after the 16th Anywhere on Earth", meaning it will at least be the 17th in all timezones before the work gets started, but even in that case, you're referring to an implicit time zone.

What do you mean? In Auckland _right now_ it's Wednesday, 30th of June, while in Los Angeles it's Tuesday, 29th of June.