Someone remarked on the obvious, that there are relatively few reasons to go back to the past, other than:
1) Attempting to change the future. However, the drawbacks to this are so blatant that the assumption has to be that it would be avoided. The one exception being to cause an *indeterminate* statistical aberration, that *could* have happened naturally.
This can be subdivided into three things in time: a probability, a possibility, and an alternative.
A probability is like flipping a coin, which would typically be heads or tails. Probabilities end when they “normalize”, say you put the coin back in your pocket, assuming the coin flip was not used to change something that “mattered”.
A possibility is typically more complex. There must be multiple instances that fit the Standard Distribution, aka “bell shaped” Curve (SDC) in their outcome. Like ball bearings on a peg board.
http://i.imgur.com/3CbdeM7.png
To demonstrate temporal interference, you have to show that the distribution is *even*, that is, a “flat line” distribution; or to really nail things, an *inverted* bell shaped curve, which should not happen in nature.
However, like a probability, a possibility still normalizes after the event is over. In the real world, people regard such things as phenomena, and promptly forget them in other than “how about that?” or anecdotal terms. So unless people *act* on such information, it is lost.
An alternative actually causes a temporal rift. That is when a probability or possibility actually causes a split in time with two distinct alternatives that even when they reach the same conclusion, they have caused a “butterfly effect” far outside repair for the foreseeable future.
This happens naturally all the time when people choose irrevocable outcomes in their lives. Such as “Should I become a Marine, or a ballet dancer?” Whichever one they choose, their future is split in half. However, there is “overlap”, such as becoming a Marine who really loves to watch ballet, or does ballet as a hobby rather than a career; or a ballet dancer who fantasizes a lot about being a Marine, and goes camping a lot.
Alternatives matter a lot to time travelers, because if they influence them, they may migrate from one alternative future to another. Some have even theorized that there is no way a time traveler from the future could *return* to the same future from where he left. A lot of debate about this theory, however.
2) (Back to the reasons for time travel) The second reason is the gathering of accurate historical data. As was pointed out by Asimov, this one is extremely problematic, because, as we might say today, the National Security Agency (NSA) would *love* such a capability, to spy on people in the unchanging past, of perhaps an hour ago. It creates a “fish bowl” world of zero privacy. And a scoundrel, like Obama, would absolutely love the ability to use secrets for political gain; or even to change the past to make America the disaster he wants it to be.
3) The third rationale is “wasted resource recovery”, which is the ‘Star Trek IV’ idea of bringing extinct whales to the future to repopulate the Earth. Other things would include recovering brilliant people who died young, like Mozart, while substituting a replacement to take the place of their body, putting the real one in a suitable place adapted for them, so that they can continue to be creative.
You could travel back to buy rare coins (or book, painting, etc) and bury them, or some resource like gold when it was $35/oz, or get some disease bacterium before it mutated.