Actually, it's theorized that you and your changes would exist in another time-line independent from the one you departed. That way there's no paradoxes. Even just the disturbed atoms and photons from your arrival would create a very different time-line.
One of the potential ramifications of quantum theory, and all the weird "neither here nor there" stuff particles can do, is that reality, the universe, whatever you want to call it, "splits" every time a decision is made creating an ever expanding "tree" of universes that goes back to the big bang.
For every particle zig-zag outcome, universes are spawned for each possible outcome. The number of new univereses is not infinite, but it has been growing exponentially all the time. Essentially everything down to the smallest random sub-atomic changes that can happen does happen, but the options are narrower and narrower as you go back to the moment of creation where all time-lines merge, just like following branches down to the trunk of a tree.
That's why we don't see the results of "time travelers", the instant you do so, you create a new reality chain parallel to your own. The "past" that you visit is by default not your own by the very fact of your arrival.
Time travelers also better do so in a space ship, because the earth is moving in orbit around the sun, and the sun is moving in orbit around the Galaxy, and the Galaxy is moving in relation to the other galaxies from the expansion of the Universe. Now granted, there's no such thing as a absolute or "privileged" frame of reference in Einstineian space, but if you could time-travel, it's an almost certainty you'd wind up very, very, far from Earth when you "popped out".
Some of the latest thinking I've read is that time travel is "possible" in the sci-fi sense, but you'd need near infinite amounts of energy to force one of the sub-atomic wormholes that comprise the "quantum foam" at the smallest level of existence open into a useable size, then you'd have to drag the mouth of the wormhole around a near relativistic speeds, then figure out a way to survive the trip through the incredible tidal forces that want to turn you and your ship into spaghetti.
Of course the easiest method to "time travel" is to go forward. All you need for that is a spacecraft capable of traveling near the speed of light, and take a round trip ending back at Earth the number of light years you want to be in the future. If you maintain close to light speed for the majority of the trip, you'll arrive years, if not centuries in the future, while only a few weeks or months have passed as measured from the spaceship's frame of reference. Of course, time wise, it's only a one-way trip.
It's still a difficult engineering challenge, but orders of magnitude easier than coming up with entire galaxies worth of energy to force wormholes to do your bidding.
- Get them TWICE!!
Colored smoke would be helpful too The gentry back then knew about "Greek Fire", but had lost the recipe
