Well, scifi writers have used a wide variety of different ideas and concepts of time travel over the years. But ultimately all time travel formulas are based around two core theories of time from regular science. The first is linear time. IE, time flows in a single, straight line, and every action has a corresponding effect that changes the future ever so slightly in a different direction. This is where a lot of paradox stories come from. It is believed that the moment you arrive in a given point in the past, you're already changing history, thus creating what is called by some the "Grandfather Paradox". IE, any interaction with the past changes it, thus creating a situation where you never went to the past and thus didn't change history. Kind of a did, and yet really didn't kind of thing. The only known exception I can think of for this paradox is the "Insertion Paradox", which is a situation where you arrive in the past, but don't actually change anything. Instead you become a functioning part of history, rather than a driving force of change.
The other is parallel time. This theory states that a new branch in the timeline is created for each and every decision a person could make. So for example, if you walked into an icecream shop and there were five flavors of ice cream, you might ultimately have anywhere from five possible choices, to as many as thirty, depending on if you want to mix and match the flavors, get extra toppings, etc. Thus the timeline fractures, allowing each of those potential decisions to happen, resulting in the formation of multiple branches in the timeline.
The problem with this theory is that, according to the 2nd law of thermodynamics, it's impossible, as you'd need an infinite amount of energy in order for it to occur, as each individual branch of the timeline would have its own unique and massive energy requirements equal to all the others. So each time the timeline branched, the power requirements to support and sustain such a change would be a factor of the number of divisions in the timeline. So if there were seven possible decisions, the power requirements would increase seven times what they had been before. That would require so much energy that the galactic reserves of energy (whatever insane amount those might be) the universe needs to function would be quickly depleted and everything would come to a grinding halt. And if all of the energy of the universe is contained within the timeline, it wouldn't be long before the timeline split so much that it ran out of energy.
That's where "Collapse Theory" comes into play. Applying the 2nd rule of thermodynamics, the theory states that no all branches of a given timeline survive. Some branches are stronger than others, and as they progress farther down the timeline, the stronger ones feed off the weaker ones, thus causing them to collapse and cease to exist. Their energy is then folded into the parent trunk and used to feed the branches further down the timeline.
Yeah, I know that's a bit of a nerdy description, but it's actually such a fun pair of theories that I've been working with them for some time trying out all kinds of different ideas. Interestingly too, is the fact that a lot of writers mix and match various elements from the two theories together as needed and where they prove most convenient. The problem is, the theories are mutually exclusive. IE, They can't both exist. You either have linear time, or parallel time. You can't have both. Now there is a way around this however, as parallel time can be observed as linear time to the time traveler simply because they're immersed in the flow of time, and thus all events appear linear to them.
Thus if you change the past, the future appears to change accordingly with the alterations you made. However, no change has actually occurred. You have simply traveled down a different branch of the timeline from what the current version of you knows. It's being high up in a tree, climbing down one branch to the trunk, and then climbing up another. To you it appears as though you're still on the same branch, but in reality you're on a different one. This also opens up a rather interesting plot element that can be tons of fun to play with. Since time is branching, finding alternate timelines involves simply stepping from one timeline and into another.
Stargate SGI and Atlantis did this exact thing in several of their episodes. SG1 followed the idea of going back in time and traveling up a different branch of the past, whereas Atlantis merely remained in the present and hopped between various branches of time. So each of these ideas have been explored in the past, and will likely continue to be explored in the future as well. So they're pretty much free for anyone to use if done right. Now, one other thing that can be used as a plot element, and this has been used as well, is the enormous energy requirements necessary to break out of one branch of the timeline and head to another, or to travel up and down the branches. By moving through time, you're essentially jumping between temporal snapshots which would require considerable energy by the time traveler to overcome in order to travel through time.
The Back to the Future trilogy tinkered with this idea a little, what with needing plutonium in order to provide the incredible amounts of energy required to make the jump through time. Anywho, that's my blurb on time travel.
