Q. If one missed zman krias shema in the place where he is, but in a different place (time zone) it is still before the zman, is he mechuyev to take a plane to the second place and say Shema there?
One has to spend up to 1/5 of his wealth for a chiyuv d'oraisa.
How about if one is just close do a dateline, such as living in Australia and he can go back one day?
A. It is very unlikely that one can find nowadays readily available transportation to supersede the speed of rotation of the planet and go back on the geographical clock.
In regards to crossing the dateline, even if one is in the right location (See questions; 982, 983, 986, 987, 1035, 1036 and 1040), Horav Shlomo Miller's opinion is, that once the mitzva that is time dependent was not kept, there is no obligation to travel to a prior date zone, and comply with the already missed mitzva, as you cannot travel back in time. Thus if you were to indeed cross to an earlier date, it would be considered a new mitzva.
Similarly, in regards to changing signed documents by crossing the dateline, it would not have an effect, since they are not only time sensitive but also place sensitive.
On question 1151 in regards to traveling back on time, we wrote: "It is common to find in regards to the Yom Tov of Shavuos the notion of being present at the time of the reading of the Torah as if we are back on the day of receiving of the Torah at Har Sinai. A similar notion is mentioned in regards to Pesach in the hagada. However, the key word “keilu” is used, meaning that it is only as if it were, a spiritual notion but not a physical reality.
Horav Shlomo Miller's Shlit'a opinion is that we find in Halacha some sort of minimal travel back and forth in time when crossing the dateline. Real traveling back in time would seem an impossibility as you would be able to change true facts already recorded in the Torah."
Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit'a