Time Travel in Star Trek: Deep Space Nine (DS9)
"I hate temporal mechanics!" (O'Brien, DS9: "Visionary")
DS9: Past Tense
Sisko, Bashir and Dax beam down to Earth, and they arrive at the right place, but in the year 2024. This transporter accident is attributed to chroniton particles from the Defiant's cloaking device, which misdirect the transporter beam. In the past, Sisko and Bashir meet Gabriel Bell, who is supposed to be an important man in history: To Sisko's knowledge, he is the man who avoids a massacre when homeless people take government employees as hostages. Bell, however, is killed prior to this incident when he tries to protect Sisko and Bashir. His premature death changes history, and the Federation ceases to exist in the future.
The Defiant is not affected by the timeline change thanks to the chroniton particles on the ship's hull. Dax, Sisko and Bashir are obviously protected as well, since they continue to exist in the past and have memories about their future. There is a difference to similar previous incidents, however, as the changes do not take place immediately. The Defiant is in contact with Starfleet Command for quite some time after the three officers have arrived in the past. In TOS: "The City on the Edge of Forever", in contrast, the timeline changed immediately after McCoy had crossed the Guardian of Forever.
A paradox does not occur in this episode. However, predestination does not apply, since the timeline was definitely temporarily changed. Sisko finally corrects the timeline by pretending he is Gabriel Bell, so it is not astonishing that his portrait will be depicted in history books (see also DS9: "Little Green Men").
Classification: past incursion, corrected with one visible consequence (Bell is now Sisko)
"Visionary" Miles O'Brien suffers from a radiation damage caused by delta type isotopes. In connection with the tetryon emissions from a Romulan Warbird's quantum singularity this is the cause for O'Brien's frequent time leaps.
Side note It is rather frustrating that highly qualified Starfleet personnel (namely Jadzia Dax) is not able to identify a "quantum singularity orbiting the station" as a cloaked Warbird. At latest since TNG: "Timescape" it should be a commonly known fact that the Romulans employ a quantum singularity as their power source.
This is the sequence of events in the order as shown in the episode:
1. While playing darts, O'Brien travels about 5 hours to the future, where he watches himself talking with Quark about a damaged holosuite on the upper level of the promenade deck. This situation causes the first (probably minor) paradox, since vice versa, while actually talking to Quark, he remembers his time travel and is aware of the other (time traveling) O'Brien who was not recognized in the first timeline. The fact that a temporal anomaly was found at the time of his departure and his arrival confirms that he actually traveled through time and did not hallucinate.
2. O'Brien travels to a turmoil in Quark's Bar, again about 5 hours in the future. An obvious paradox does not occur, since the turmoil takes place anyway, despite the improved security measures. The two O'Briens help each other struggling against the furious Klingons and Romulans. Still, the scene is slightly different in the second timeline.
3. O'Brien witnesses his own death when he is hit by a laser beam in front of the Romulan quarters 5 hours later. This time the timeline is definitely and significantly changed, since the accident is avoided.
4. Once again poor O'Brien travels to a time when he is dead, this time because of an irreversible brain damage. The future Bashir tells him that his basilar arteries should have been scanned in time. Back in his present, Bashir does so, and O'Brien's life is saved in the new timeline.
5. Things get even worse when DS9 has to be evacuated and finally explodes, and the wormhole is sealed. O'Brien witnesses these events in the future, but he fails to find a clue. Although it might endanger his life, he decides to attempt an intentional time travel in order to prevent or at least find the reason for the disaster. This is accomplished by flooding his body with delta isotopes and calibrating their time constant in a way that this time travel leads only 3 hours to the future.
6. The calibration being very inaccurate (at least for Star Trek standards), O'Brien arrives 3.5 hours later, just an instant prior to the evacuation of the station. Still, it is enough time left to find out that a Warbird destroyed the station along with the wormhole in order to prevent a Dominion invasion. Since the time traveling O'Brien suffers from severe radiation damage, he gives the time travel device to his future self.
This episode implies multiple paradoxes, unless we assume that the timelines in different times are isolated from each other. Only in this way it is possible that O'Brien repeatedly prevents his own death, which would have occurred anyway in a predestined timeline, and the prevention of which would have lead to a causality loop or paradox in other theories. Most obviously, the O'Brien who remains in the present, is an O'Brien that has memories of a timeline which is supposed not to exist any more.
Classification: multiple travels to the future, accidental and to avert future disaster
DS9: The Visitor
Some time in the 25th century, a young woman visits old Jake Sisko and asks him why he stopped writing a long time ago. Jake tells her that he lost his father in an accident on the Defiant many decades ago. At that time, Ben Sisko disappeared to subspace, and since then reappeared on rare occasions, always in the vicinity of his son. The title of the episode is ambiguous and may refer to the young woman as well as to Ben. While Jake first tried to cope with this situation and became an author, he later turned to science and took any effort to get his father back, but without success. Finally, the dilemma is resolved when old Jake dies and the bond between him and his father is torn. Back on the Defiant, Ben is aware of what would happen, and he can avoid the accident this time.
Obviously there is a biological effect involved, a connection that keeps Ben in subspace as long as Jake is alive, and always in his son's vicinity. This is odd because traveling from one space-time to another is a purely physical process for which neither the presence of a certain DNA should matter, nor the fact whether the other person is alive or dead.
If we accept the biological component, the resolution is still not consistent. Firstly, there is a clear grandfather paradox when the accident does not occur again at the end of the episode, because by avoiding the accident Ben Sisko erases the whole timeline in which he and Jake are bonded together. Secondly, why does Jake's death not only cut the bond but even send Benjamin Sisko back through time? It is mentioned in the episode that the captain who has emerged from subspace for a few minutes is out of temporal sync. But quite obviously this statement only means that, while in subspace, his time is halted relative to everyone else much as if he had been in suspended animation. Finally, there is no clue why Ben is thrown back to an instant just a second prior to the accident, and not exactly to that instant. This does not seem to be a coincidence, although old Jake anticipated just that. It almost appears to be some kind of divine intervention.
Classification: alternate timeline that ceases to exist, unresolved grandfather paradox, with biological impact of time travel
DS9: Little Green Men
Quark and Rom accompany Nog on his way to Starfleet Academy, when their shuttle "Quark's Treasure" is thrown back to the year 1947 and crashes near Roswell, New Mexico. In this odd story the three Ferengi are responsible for the so-called Roswell Incident, which some people in our time still believe to be authentic. This Star Trek plot can be regarded as the third one based on a predestined timeline after TOS: "Assignment: Earth" and TNG: "Time's Arrow".
As if he knew that the future would not be endangered because everything is predestined, Quark seizes the chance to sell 24th century technology to the "Australians", which could dramatically change Earth's history. In contrast, his nephew Nog tries to avoid any damage to the timeline. His threat that Ferengi Marauders would attack Earth is a good idea in this respect, since he tells the 20th century humans exactly what they expect to hear. Besides, at the beginning of the episode Nog holds a PADD in his hands where "Gabriel Bell" Sisko is depicted, which reflects the timeline change in DS9: "Past Tense".
Classification: past incursion, with minor consequences (Roswell Incident), possible causality loop
The injured Akorem Laan stumbles across the Bajoran Wormhole with his sailing ship around 2172. His wounds are healed by the Prophets. Akorem emerges from there 200 years later, possibly because of a "mistake" by the Prophets, who are not aware of the linear nature of time. In the 24th century, Sisko and Akorem struggle for the position of the Emissary, and they enter the wormhole to let the Prophets decide. When Akorem learns that he is not supposed to be the Emissary, he agrees to be sent back to the time when he first encountered the wormhole.
The Prophets promise to send him back healthy, but without a memory of anything that happened. The timeline would have been changed at any rate, because Akorem travels to a past in which he was believed to be dead. He finishes a poem that Kira remembers to be incomplete. While we may suppose that he didn't finish the poem the first time simply because he was stuck in the wormhole, the question occurs why of all people Kira should not be aware of the now different history. But as Sisko himself suggested, the Prophets may have intentionally left this little conundrum.
Classification: past incursion with minor consequences
DS9: Trials and Tribble-ations
The time travel is enabled by the Orb of Time, and this could be a sign that the protagonists are actually guided and protected by the Prophets, such as in DS9: "Wrongs Darker than Death or Night", where it is explicitly mentioned. In fact, the mission to prevent a change in the timeline is successful, and Kirk is saved without even noticing it. Amazingly the episode seems to be completely consistent with the events as shown in TOS: "The Trouble with Tribbles".
Classification: past incursion to change history, corrected
DS9: Children of Time
The Defiant crew members are surprised when they discover a planet which is inhabited by their own descendants from a changed past. These "Children of Time" know that when the crew tries to leave the planet the Defiant will cross a temporal barrier. The ship will be thrown back in time and crash land on the planet, leaving no possibility to escape. The question arises whether it is right to allow the time travel in order to preserve the people on the planet, or to take countermeasures to get home. Sisko eventually decides to let things happen and orders a course towards the temporal field. However, the older version of Odo, who has spent the whole time on the planet mourning for Kira who died without medical treatment after having suffered a plasma shock, prevents the time travel. History is corrected, and the small colony on the planet ceases to exist. Still, the crew remembers them.
The Defiant crew descendants are there without actually a time travel to the past occurring. This should be a clear sign for predestination, and in this case it would have been the last DS9 episode, leaving the Defiant crew trapped in the past. Yet, the timeline is altered when the Defiant finally escapes. So this episode features a strange and inconsistent mixture of causality concepts. The odd phenomenon of breaking an existing causality loop is similar as in VOY: "Time and Again", and cannot be resolved. Yet, here the original timeline in which the "Children of Time" live on the planet is not just erased, since they are still remembered after they have disappeared. Everything on the planet did actually happen and, most importantly, Kira learns that Odo loves her.
By the way, Sisko's decision to let the time travel happen is highly doubtful in three respects. Firstly, from an ethical viewpoint it is equivalent to abandoning his duty and family intentionally and condemn his first officer to death. Moreover he more or less orders his crewmates to do the same. Secondly, the fact that the crew have learned about their future in the past will almost certainly change the history of the planet, considering various possibilities of female/male relationships that cannot be controlled and would develop in a completely different way. In this case the known descendants might never come to existence and the sacrifice of the Defiant crew in favor of them would be useless. Thirdly, even if we accept that the timeline with the Defiant crashed on the planet is the original one (because it is "predestined"), it is created involving a time travel, and this is not possible in the natural course of time. In this regard, if it is possible to break the causality loop, it would be generally the right decision to alter history in a way that the time travel and its effects are avoided or compensated.
Classification: broken predestined timeline ("causality loop")
DS9: Wrongs Darker than Death or Night
Kira's time travel is guided by the Orb of Time and therefore by the Prophets. It is not mentioned how the Prophets manage to protect the timeline or at least reduce the possible damage to a minimum. Kira would have enough chances to alter history, since she encounters her mother and also herself as a child. Finally, she even tries to kill Dukat and her mother, and it is not clear if the Prophets would have avoided the bomb explosion, if Kira had not done it herself. It is possible that Kira's time travel lead to an isolated past which had no impact on the present. Still, it is not very fruitful to discuss the capabilities of supernatural beings who exist out of time and can manipulate time as they like it.
Classification: intentional travel to the past, without visible consequences
DS9: Time's Orphan
Eight-year-old Molly O'Brien travels 300 years to the past after falling into a time portal. The DS9 crew manages to reactivate the destabilized portal and get her back. However, due to an instability in the temporal field Molly comes home 10 years too late. She is now an 18-year-old girl, who has spent the past 10 years of her life alone on an uninhabited planet and is run wild. Nevertheless, the O'Briens decide not to alter the timeline again, since the existence of their older daughter would be extinguished once they tried to get her back at the age of eight. When Miles and Keiko finally decide to send her back to her home in the past, the time portal works properly again and she arrives at a time 300 years ago instead of the intended 290 years. So Molly meets herself as a little girl who has just arrived there, and persuades her to cross the time portal towards the future. At the same instant, the 18-year-old Molly vanishes, since she has never existed. Still, Keiko and Miles do remember her, as does the young Molly from her trip to the past.
The net time travel is that of 18-year-old Molly ten years into her past. In this respect it didn't matter whether the time the portal sent Molly to in the first place was in the future or in the past, as long as no interaction with the present was possible. The obvious paradox in this story can be solved, if we postulate that the time portal has an isolating effect, allowing that different timelines exist on its two sides.
Classification: past incursion, with change of history
DS9: The Sound of Her Voice
The crew communicate with Captain Lisa Cusak, whose ship has crashed on a remote Class-L planet. When they arrive, it turns out that she died three years ago. An energy barrier around the planet caused a time shift of the signals going in and out. While basically communicating with the past may have the same consequences as going there in person, the time travel of the signal remains without consequences here.
Classification: communication with the past, without visible consequences
Some screen caps from TrekCore.