Time travel

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Time travel is any movement through time that is not equivalent to the normal course of time, in particular a person or object's travel leading either to the "past" or faster as usual to the "future".

Any given time traveller 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), or in an reverse entropic vector (i.e. backwards in time), has to move outside of normal space-time. This movement was mathematically calculated by a scientist named Feynman to be a predictable curve.

Thus, people displaced in time can use the data points of the "start" and "end" points of their journey to caclulate their return trajectory along their circumstance-specific Feynman Curve to return to their own time. It can also be used to calculate a path to initiate a controlled time displacement.

The return journey along that Feynman Curve is entirely dependent on the actions (or more accurately, the non-actions) of the displaced personnel. If their interaction is kept to a minimum and the integrity of the timestream is maintained, their Feynman Curve also retains its integrity and the displaced personnel can return to their own time in the same manner they were initially displaced, be that a slingshot trajectory around a star or using the Bajoran Orb of Time.

However, if the actions (or non-actions) of the displaced personnel cause a major disruption in the timestream, a new future is created from that point and the Feynman Curve of the displaced personnel collapses. This is because the Curve's end point--the traveller's start point--no longer exists, except in a now parallel reality completely disconnected from the timestream the traveller currently inhabits. An analogy of this is the severing one end of a rope bridge: The other side of the chasm is still there, but the traveller's connection to it is now lost, and they have to consider another means to get there--such as interdimensional travel.

The difference between what the Einsteinian-era physicists thought and what is known in the 24th century, from actual experimental demonstrations, is that no paradox results from time travel.

As to how that is possible, two solutions are suggested, but neither is testable—so both have equal validity. One solution is that if you, say went back and killed your grandfather, a temporal feedback loop would be established that would collapse into a hyperdimensional black hole, cutting the loop off from any interaction with the rest of the universe. The end result would be as if the events leading to that feedback loop never happened. The second solution states that the instant you killed your grandfather, you'd create a branching timeline. That is, two universes would now exist—one in which your grandfather lived, and one in which he died.

If he died, you can't come back and kill him. Not from the new timeline. But since you came from the old one, there's no paradox. However, because the Feynman curve you followed no longer exists, you are trapped in the new timeline you created, with no way to get back. In effect, you're a large virtual particle that has tunneled out of the quantum foam.

The conditions and equations defining time travel are very selective and highly complex. (DS9 - Millennium novel: The War of the Prophets)