Time travel is any movement through time that is not equivalent to the normal course of time, in particular a person or object moving from one time to another at a rate greater than the local entropic norm (i.e. moving forward in time faster than the normal "subjective second"-to-"objective second" ratio) leading to the "future," or in an reverse entropic vector (i.e. backwards in time) leading to the "past."
The Space-time Continuum
There are at least six accessible dimensions in the space-time continuum. For any space to remain finite but unbounded (as the universe is believed to be), it must possess at least one dimension beyond those that are generally discernible. Consider a two-dimensional piece of paper. In order to form a closed loop, the paper must pass through a third dimension. A two-dimensional "universe" effectively exists on the surface of the paper, but its theoretical inhabitants are unable to perceive the third dimension. A four-dimensional universe (three of space and one of linear time) must pass through two additional dimensions in order to form a finite but unbounded system.
These additional dimensions can be considered the "height" and "width" of time, while the linear temporal progression we can observe is time's "length." It is, of course, impossible to model these relationships accurately in three-dimensional terms. Still, for our purposes, consider the relationships of the temporal dimensions using a three-dimensional model.
If we describe the whole of the three-dimensional universe of space as a single point, then the first dimension of can be seen as a line, what we commonly refer to as a "timeline." This extends "forward" into the future and "backward" into the past. Any given point along this line is a moment in time as it progresses. Of course, a timeline is not nearly as fixed or absolute as a line displayed on a computer readout, as we shall see.
Adding an additional line, running perpendicular to the first, gives us time's "height." Adding a third, perpendicular to the first two, gives us its "width." This creates a plane of time, intersecting with the timeline, which contains a potentially infinite probability field.
Quantum theory tells us that, at any given moment, there is a vast range of possible outcomes. Do you go out to visit a friend or stay in and watch the baseball game? Do you speak to an attractive stranger or leave him alone? Billions upon billions of individual actions take place every moment. These choices are said to exist in a state of "quantum flux" before they take place, which is to say that the possibility of your going out is just as "real" as the possibility of your staying in to watch the baseball game—before you make the choice.
Of course, some outcomes are more likely than others. If you dislike baseball, and your friend is waiting for you at the door, it's highly unlikely you'll stay at home. Certain outcomes are said to carry a stronger "quantum charge" than others, making them more likely to take place. Some events have a particularly strong quantum charge, making them magnets for certain kinds of temporal phenomena.
Of course, our timeline is not the only one. The three dimensions of time actually contain a potentially infinite number of timelines, all coexisting parallel to each other throughout the probability field. To use the three-dimensional analogy once again, the continuum can be thought of as a bundle of fiber-optic cables: millions of strands, running parallel to each other.
Those strands or timelines "closest" together tend to exhibit the greatest similarities; their events and histories do not differ greatly, if at all. Those lines farthest apart (in terms of the Y and Z axes of time) show the greatest differences. Each strand vibrates with its own unique quantum frequency, like a string on a violin. The space "around" these individual strands of time, their "insulation," if you will, is called "subspace." Subspace is an expression of the multi-dimensional nature of the continuum.
Past and Future History
Now consider a single timeline, our own. It extends "behind" us into the past and "ahead" of us into the future. As far as we know, a timeline stretches out infinitely in both "directions," although the effective "pastward" limit of all timelines is believed to be the origin of our present universe, the "Big Bang" event.
While it is possible to pick out any single point along a line in a three-dimensional model, the progression of time is not so precise and linear. The dimension we call time is a series of progressions through the quantum probability field, of events occurring, then passing. However, these events are not fixed once they have occurred. It is common to think of the past as immutable, while considering the future in flux. However, neither is entirely true. Both past and future (and, for that matter, the present) exist in a state of quantum flux. The past can be changed, and in many ways the future has already "happened."
Any given outcome has a certain "quantum charge," as mentioned before. This is true of events in the past as well as events in the future. The greater a moment's charge, the more likely it is to remain "in" a particular sequence of events with a similar charge, forming a chain of events we call a timeline. If the quantum charge of a moment in time is altered, then it causes that moment, that link in the chain, to "attract" different events to connect to it, leading to a reorganization of the timeline as different moments in time attach to it.
The past can be changed and more importantly, changes to the past affect our present, and anyone "futureward" of the change is completely unaware any change even occurred. From their perspective, things have "always" been that way.
Given that the past can be altered, it is difficult to determine how any given change will affect the future. Highly advanced computers can calculate the impact of a particular alteration in a quantum charge over a very short time period, but the altered probabilities accumulate so rapidly that predictions become meaningless when projected more than a matter of days into the future. There are simply too many variables. Keep in mind this "plastic" nature of time does not extend only into "the past" as we know it, but also into the present and future.
The limitations on the understanding of time and our own linear perception of it often leads to situations considered logically impossible. Many of these "paradoxes" are not actually paradoxes, at least as far as the universe is concerned.
The Grandfather Paradox
The "grandfather paradox" refers to violations in causation, where an event cancels out its own cause. The classic "grandfather paradox" involves going back in time to kill your own grandfather before your father is born (or otherwise prevent your own birth). By doing so you should no longer exist, since the entire history leading up to your birth no longer "happened."
However, this is not the case. If you undo the circumstances of your own birth, you are not affected, since you are present when the change takes place. When the quantum charge of the moment you are in is altered by your intervention and connects to a different moment, leading to a different future, you become part of it. So it is possible for an effect to exist independently of (and even to eliminate) its own cause! However, you cannot return to the present you originally came from, since it no longer exists. On the other hand, if someone else alters the past to prevent your father's birth, while you remain in the present, then you do cease to exist, and no one in the present recalls that you ever existed.
The Information Paradox
Related to the grandfather paradox, this refers to an event becoming its own cause. For example, the developer of a time machine travels back to meet his younger self and tells him how to build the time machine. So who invented the machine in the first place?
As with the grandfather paradox, information paradoxes are quite possible. An event can become its own cause, and information sent back in time can alter the timeline, even though such alterations mean the information was never "really" sent to begin with. Regardless of this "out," it is unwise to depend on an information paradox to prevent damage to history.
The Predestination Paradox
Scientists and scholars have debated the nature of free will for thousands of years. What do our theories on the nature of time tell us about free will? If the future already exists, is there any free will at all, or are we merely puppets of fate?
Interestingly enough, the existence of time travel and a knowable future appears to affirm the existence of free will rather than deny it. The vast majority of the time, the future remains unknown to us. We must act based entirely on our past experience and hope for the best outcome. It may be that these outcomes are predestined but, since we have no means of knowing either way, it at least appears we have free will in these cases.
When the future is known, either through the intervention of a time traveler or techniques such as precognition, it is clear that our choices can influence it. Just as time travelers in the past can alter it, so can we in the present alter the future. Thus, if a time traveler appears from the future and tells you not to board a bus because it will crash, you can choose not to board the bus and avoid the crash. It is possible you might not have boarded the shuttle anyway but, again, we have no means of knowing other than the word of the traveler from the future. If he returns to his "present," he discovers the change as a part of his history. No one other than he even recalls the difference.
This phenomenon leads to the idea that certain changes in history, or the presence of time travelers at certain moments, are "predestined" in some way. It is possible that not only are all the events of our timeline already "in place," but that every temporal intervention that has or will happen already has happened in the sense of being part of a larger "metatimeline." In this case, there is no free will whatsoever, and we are all merely pawns of fate. As there is no means to prove predestination, however, this remains merely a theory. From our perspective, it still appears we have the ability to make our own choices.