The gemara learns from the pasuk שררך אגן הסהר, that the Sanhedrin sat בטבורו של עולם. We consider Yerushalayim and more specifically the beis hamikdash to be the center of the world, as rashi explains. This is actually the primary source for R. Tuchechinsky's approach in establishing the international dateline. If we view Yerushalayim as the center of the world, it is logical to assume that the globe which is 360 degrees, begins by Yerushalayim and expands out in both directions 180 degrees. Therefore, 180 degrees from Yerushalayim would be the "end of the world", which would be the point that by traveling west you would jump ahead 24hrs, and by traveling east you would jump back 24hrs. This approach would place the dateline between california and hawaii, which is east of the standard secular dateline which is between hawaii and asia. It is also unlike the chazon ish who places the dateline on the coast of China (with the exception of Australia which is drawn west toward asia).
Obviously, the ramifications of the dateline is enormous, and would make a big difference when it comes to owning chometz on Pesach. In truth, the discussion of owning chometz on Pesach would be relevant even before discussing the dateline, because a person can easily be in a different time zone than the chometz which he owns. R. Moshe (Igros Moshe O.C. 4:94) holds that for owning chometz we follow the individual, not the location of the chometz since the prohibition is on the individual, not on the chometz. The Oneg Yom Tov disagrees and holds that we follow the location of the chometz, not the person. If one would be in NY and have chometz in CA, Pesach begins for them before it begins for their chometz - R. Moshe would holds that the sale must be done early, whereas the Oneg Y"T would hold that it can't be purchased back until Pesach ends in CA. R. Tzvi Pesach Frank (Mikraei Kodesh 55) cites the Chesed l'avraham who holds that it is dependent on the person, like R. Moshe. He cites an interesting proof from the gemara in Pesachim 7a that discusses someone who is learning and realizes that he has chometz at home, he can just be mevatel, "even on Yom Tov". The gemara asks, how can he be mevatel on yom tov, since the z'man of bitul has already arrived. Why doesn't the gemara say that it is speaking when the chometz is in a time zone that yom tov has not yet arrived, so he can be mevatel? From here we see that since Yom Tov arrived in the location where he is, he cannot be mevatel since it is all dependent on the person.
Now, the dateline makes things far more confusing because even if we assume that it is dependent on the individual, even if he is in the same location as his chometz, it is not clear when he would have to rid himself of chometz. The ambiguous locations are Hawaii, which according to C'I follows the secular day, but according to R. Tuchechinsky Pesach begins a day earlier. Similarly, in New Zealand, which according to R. Tuchechinsky would follow the secular day, but according to C"I pesach would begin a day later. Therefore, if someone from NY visits Hawaii for Pesach and leaves chometz behind in NY, aside from the issue of violating Shabbos and Yom Tov that would exist according to R. Tuchechinksy (which some people are machmir not to do d'oraysa violations on Friday and Erev Yom Tov), he would have to make sure that the chometz is sold a day earlier (according to R. Moshe who holds that it is dependent on the person).