The date line is a time traveling four letter word.
Where I'm sitting right now, it is Friday December 30th. But in the Independent State of Samoa, it is Saturday December 31st. In fact, they never had a Friday December 30th 2011, they skipped right from the 29th to the 31st by declaring themselves to be on the western side of the International Date Line effective at midnight, instead of on the eastern side, where they had been since they moved in the other direction in 1892. Why the move? Most of their interaction was with countries such as New Zealand, Australia, and China which were on the western side, so it made more sense to only be 3 hours off instead of 21 hours off.
The date line takes some thinking to get used to. After all, does it really make sense that crossing this line would automatically send you one day backwards, no matter what time you crossed the line? We think about the date changing if we cross a time zone around midnight... but this happens no matter when. The line is a necessary consequence when traveling west to east (and east to west, but it is more difficult to grasp that way). Every time zone east you go, you will have "lost" an hour from the previous time zone - so if it was just 6 o'clock, going east a time zone it will now be 7 o'clock. If you keep doing this going around the globe, you will have lost 24 hours total when you get back to your starting point. If you hadn't adjusted your date/time watch, you will discover that everyone else thinks it is one day later than you do. The date line "forces" you to catch up and make this adjustment. (I don't mean to spill a plot point, but this becomes crucial in the Jules Verne book Around the World in 80 Days. Which you should read if you haven't.)
This isn't the first time a country has fiddled with its calendar. Over the years, countries who have moved from the Julian calendar to the Gregorian calendar have had to lose days or weeks, never mind strange calendar systems that have been adopted briefly by revolutionary countries at one point or another. Countries have shifted one way or the other over the date line before - as noted, Samoa did it in 1892. And standardizing time zones didn't really come about until the railroads forced the issue - before then cities operated on "local time", setting noon for when the sun was directly overhead in their location.
Not quite the time traveling you were hoping for, I bet.