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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 than 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 Richard 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 calculate 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 trajectory around a star or using the Bajoran Orb of Time. (TOS episodes: "Tomorrow is Yesterday", "Assignment: Earth"; TOS movie: Star Trek IV: The Voyage Home; DS9 episode: "Trials and Tribble-ations")

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 of 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. (DS9 novel: The War of the Prophets)

A person cannot go back in time and create a "new" timeline. That's because there is no "new", no "before", or "after." Past and future are merely points on a curve. Change is merely the shape of that curve. All processes, all interactions, are in fact instantaneous. Relative time is an illusory concept. In physics, there is no preferred direction of time or causality. There is only the progression of cause and effect within the wave equation. As long as an interaction is logically consistent, the directionality of time is irrelevant.

Because all timelines exist side by side, a person can't simply go back and unmake a history once it's happened. A retrocausality generated history would coexist with the the original 'seed' timeline. It's a logical absurdity for a timeline to be erased. Anything that's happened has happened. A person can't change the shape of time as a whole because change is just part of the shape itself. So the only way one timeline could replace another is if they coexisted side by side from the moment of their divergence but then merged together again once they both reached a later point in the timeline.

Timelines diverge when they shift sufficiently out of phase to become non-interacting, but it's not impossible for them to interfere again at a later point in time. And if they did become entangled as a single system, then quantum information theory would demand that only one of the two conflicting sets of information would survive because a given quantum history has to be self-consistent. It would be as if one timeline suddenly transformed into another. The previous events would still have occurred, but they would no longer be remembered. The information would have been destroyed.

The catch is, for two timelines that have drifted apart to come back into phase would violate entropy. There'd need to be some kind of force acting to merge them back together. (DTI novel: Watching the Clock)

The conditions and equations defining time travel are very selective and highly complex.

Side effects

The side effects caused by time travel on different types of lifeforms can be varied and depend on the method of time-travel. When Centurion Karon commandeered the timeship Phoenix in an alternate timeline, Julian Bashir expressed a medical concern regarding the experimental time travel apparatus, in that the transition could cause unpredictable effects in the crew's physiology including gas problems, indigestion, bloating and diarrhea. Karon forbade Bashir to examine any of the Romulan crew, but gave him free contact with the captured Humans and Bajorans onboard if Bashir wished to take medical readings of such effects. (DS9 - Millennium novel: The War of the Prophets)

When Jonathan Archer was sent by Daniels ten months into his subjective past, his body was physically native to 2151. The Captain was confused how he could have the (future) memories of 2152 and not be a displaced duplicate of himself. (ENT episode: "Shockwave")

This is not always necessarily the case, when James T. Kirk encountered a very different 24th century than was shaped by the "natural" flow of history. (TOS novel: Timetrap)

In the 29th century, subjects undergo "temporal integration" when too many multiples are the outcome from their time travel activity. This results in a unified individual, capable of being accountable to all consequences that have- and haven't yet-taken place. (VOY episode: "Relativity")