OK, we've got some discussion going on about issues affecting life within the gray zone of the Halachic Dateline and the International Dateline, but what is the original source of such a concept, if there is one? Can it not just be that whatever is deemed Saturday in some remote place in the world is Saturday (as in the minority opinion at the end of this article)?
I'm not sure I understand your question, but basically many rabbis feel that the Torah states where the dateline should be, so we don't really care what the local population thinks. (Though a frustrated Rabbi Yitzchak Zev Brisker, when asked about the dateline, exclaimed -- " I don't know. And I don't know why everyone else thinks they know!")
There are various Talmudic statements that could be read as placing the dateline either 90 or 180 degrees east of Jerusalem. If you feel the Talmud fixes the Halachic dateline, that's what we'd be bound to follow.
Some point to a Gemara in Rosh HaShanah (20b) which indicates that the Beis Din would not declare a day to be Rosh Chodesh unless the new moon was visible in Eretz Yisrael before noon on that day; if it appeared after noon, the next day would be Rosh Chodesh. Although certain Rishonim explain the Gemara (Ibid.) as referring only to details concerning the declaration of Rosh Chodesh, the interpretation of the Ba'al HaMaor (Ibid. 5a in Rif s.v. Ki) and others relates it directly to this issue of the date line. ...
This means that the area 90 degrees east (6 hours ahead) of Yerushalayim was then experiencing nightfall (sunset) and was already beginning the next day. That location, then, must be the date line because that was the first place on earth to go on to the next day; this indeed is where the Baal HaMaor (Ibid.) places the date line, as shown above.
This position about the date line is articulated as well in the Sefer HaKuzari (Maamar 2 Siman 20), and is clearly accepted by the Ran in Rosh HaShanah (Chidushai HaRan to Rosh HaShanah Ibid. s.v. Tzarich), and, apparently, by the Ritva there (Ibid. s.v. Ki).