Unless it hasn't been invented yet, in which case...
No, really, according to Stephen Hawking, other very smart people, and that Nova TV show on PBS, it would be impossible to change history due some sort of distribution of energy and the space time continuum. That is, there is literally no way you could change things, some equalizing factor would limit your ability to make changes in a scope of any magnitude (see: independent and dependent variables).
Another explanation, is that we did invent time travel, sometime around 1992. You, Kubla Khan, stole the technology and went back to 5000 BCE, to bestow upon the first civilized humans the benefits of modern technology. However, this changes the course of history so radically that you, Kubla Khan, are never born, because everything is so different, that your parents are different people, and they never meet, so you're never born. That, of course, would mean that no one is there to give the technology to the primitive humans, so history reverts to how it currently is, with no technology being given to the primitive humans.
Or, current technology is so destructive to the planet, that 5000 nonstop years of using it causes humans to become extinct before we even reach the current time period, meaning that, of course, no one ever was there to give technology to the primitive humans, so history reverts...
Someone should make a really esoteric independent film about this.
DataJunkie: As I've heard it, assuming we could create a stable
wormhole (which itself is very theoretical, and supposedly takes a sustained
fusion reaction the size of
Jupiter to create a stable, 1 meter
wormhole), we could then put it on our ship which can travel at near the
speed of light (also extremely theoretical) and send it out for, say, 100 years. A much smaller amount of time would pass for the wormhole ending on the ship than for the ending on
earth. When the one on the ship returns, it would be, say, 30 years behind its
counterpart (I have no idea how the
math works, that's just a random guess). Assuming you had pre-set the date of its return, you could then step through the 100-year
wormhole and arrive at the 70-year
wormhole, thus travelling back in time 30 years. The limitations are thus that you cannot travel further back than the invention of the time travel technology, and you have to basically invest a lot of time and money into your singular travel plan of choice, would take the amount of time you want to travel back to begin with to come to fruition. Given this, it would almost be more appropriate to call this method a "
time hack" instead of
time travel. And so, we have it
made in the shade for right now, but as soon as we
invent the technology, then we'll be
majorly screwed. I bet the governments of the
world would come up with some kind of collective
moratorium if there was even any serious possiblity of something like this being invented.
Of course, this all depends on two fantastically thoeretical, crazy technologies which themselves will probably never be invented.
Anyone interested in this sort of thing should be Arthur C. Clarke's The Light of Other Days, which, while not about exactly this topic, explores the idea of wormholes as timegates and their effect on society.