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Is it possible to travel in time, by technological and planned meaning? Or does it happens across all the episodes purely as an effect of some coincidence, defect, error etc.

I know (from one of ST:VOY episodes), that planned time travels are possible in 29th century and (from another ST:VOY episode), that there are species capable of changing timelines and even erasing entire histories, but what about 24th century, when most of TOS, TNG, DS9 and VOY episodes happens, and that-time Federation technology? Does it allows to travel whenever anyone wants to any point of time?

Is this case ever addressed in-universe?

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This isn't an answer as it doesn't fit the question, but you can use the theory of relativity to prove that Constant C + FTL == Time Travel anyway. The science doesn't fit the canon though, so lets just ignore that... – Joe Bloggs Jan 4 at 12:25
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TOS is actually 23rd century. (Also, the standard abbreviation for The Next Generation is TNG.) – jwodder Jan 4 at 13:52
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Thank you all for all the enlightening answers. If -- as it turns out -- traveling through time is so easy in Star Trek universe, then it is a bit surprising, that there are any laws created / addressed about not changing timelines etc. I recall the only connection to Temporal Prime Directive in 29th century. – trejder Jan 4 at 15:00
    
    
It seems, that we have an interesting situation here. Answers to this question are all (or most of) written in mood of "yeah, time travelling is not a problem in Star Trek universe". While this Richard's answer seems to be in direct contra-point to all those. It seems, that he is claiming there, what I was always assuming -- that time travelling in 24th century, in Star Trek universe, using Federation technology is not possible and always is an effect of some accident or usage of other species technology (like Borg). – trejder Jan 4 at 21:32
up vote 35 down vote accepted

In Star Trek IV The crew of the Enterprise under Kirk do a planned and (mostly) calculated travel back in time, the only necessary parts being a ship, a star and the necessary speed.

So, it is possible with the right calculations. The technology from the 29th century only makes it more convenient.

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Yep - we can only assume that the process is classified/restricted in the TNG era due to The Prime Directive. The events of Star Trek IV would be a matter of history, however. – Omegacron Jan 5 at 15:36

In Assignment Earth, Kirk takes the Enterprise to 1968 for routine historical research.

Captain's log. Using the light-speed breakaway factor, the Enterprise has moved back through time to the 20th century. We are now in extended orbit around Earth, using our ship's deflector shields to remain unobserved. Our mission – historical research. We are monitoring Earth communications to find out how our planet survived desperate problems in the year 1968.

If it was that easy and unremarkable for Kirk to travel through time in the 23rd century, it was probably just as easy in the 24th century.

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I just watched "The Alternative Factor" (S1 E26) and Lazarus being a time- traveler seemed like it was surprising to Kirk & co. Is it plausible that time travel was invented between seasons? – ssdecontrol Jan 4 at 22:34
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@ssdecontrol: Could be. Might explain why they suddenly decided to go check out 1968. "Hey, Starfleet just sent us a new time travel procedure. What's say we give it a try?" – Lightness Races in Orbit Jan 5 at 9:26
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Personally I prefer to pretend that episode didn't exist (as entertaining as it was). – PointlessSpike Jan 5 at 15:22
    
1968? I guess he just wanted to watch first-run episodes of Star Trek on TV then? That would be weird... – Darrel Hoffman Jan 5 at 15:26
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@DarrelHoffman They wanted to watch the pilot of the Gary Seven show. That didn't pan out in our time line. – jejorda2 Jan 5 at 15:35

In Star Trek: First Contact (TNG crew), the Enterprise travels into a temporal wake created by the Borg sphere to earlier in Earth's history, but at the end of the film the Entrprise travels "back to the future" without assistance from the Borg.

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Yeah, this is the most solid example to show that the Enterprise had Time Travelling capability. – Evil Angel Jan 4 at 14:51
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This is almost the most solid example of time travel. However, they were following a Borg Sphere that initiated time travel. On the way back, they were exactly reversing the source and destination. There is no indication that they got to choose the times involved. They might have been following a "road" of Chroniton particles left behind by the Borg sphere (perhaps remnants of that road even existed days later, allowing the return trip). So the Federation figured out how to use what the Borg left, but that incident isn't proving that the Federation had fully independent capabilities then. – TOOGAM Jan 4 at 15:07

In Star Trek (TOS) season 1 episode 4: The Naked Time, an incident involving an antimatter explosion propels the Enterprise three days back in time. Although this situation was very dangerous, Spock claims in the episode that they could use this method for controlled time travel.

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In the TOS episode The City on the Edge of Forever, they found an object named Guardian of Forever, which functioned essentially as a time portal.

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The guardian of forever can hardly be called "federation technology" – Gerald Schneider Jan 4 at 11:28
    
@GeraldSchneider The question says "Star Trek technology", not "Federation technology" – Rick Sanchez Jan 4 at 11:31
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The question does say "that-time Federation technology". – armb Jan 4 at 12:49
    
@armb Yeah you're right, my brain skipped that part. Though my answer isn't really invalid, since though not created by the Federation, GoF is in their possession. – Rick Sanchez Jan 4 at 13:09
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The planet that the Guardian of Forever is on may (or may not) be within Federation space, but the GoF itself would probably deny any claims of ownership. – Xantec Jan 4 at 14:35

While there are several examples of time travel in unusual conditions using either accidental circumstances or technologies of other races, there were two examples of intentional time travel. Star Trek IV's is well-known but an emergency situation conducted under less than ideal circumstances. There was another situation, the TOS episode Assignment: Earth, where the Enterprise journeyed back to 1968 as part of an assigned, historical research mission. There, they met Gary Seven, who claimed to be trying to stop a nuclear war from breaking out, and ran into an issue trying to decide if the proper timeline was to stop him or let him proceed. It seems clear that Star Fleet intentionally used time travel at least once, though given the risks of even a purely observational mission, they may have stopped using it afterward.

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While others have already pointed out that it is clearly within the technology level of multiple Star Trek crews to successfully travel in time, I feel the need to address the question from a slightly different angle.

Yes, Federation vessels clearly have the ability to time travel, but it is important to remember that the Temporal Prime Directive is a fundamental principal of the Federation and plays an important factor in why planned time travel is not a commonplace occurrence.

I don't believe that there is a clear point when this Directive was officially put into place, but it is discussed first in TNG and then numerous times during VOY and again during the DS9 Trials and Tribble-ations episode. As such, Starfleet has clearly taken the idea of changing the future to heart and even stresses the idea of non-interference to students at the Academy

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As was said already, if the Enterprise-E can return from the 21st century, as the events of 'Star Trek: First Contact' showed, then yes, the Federation has the power to travel in time in the 24th century. That said, and if I may be indulged (since the question has been answered), I took up this question because I want to expand on this a bit further. If the JJ Abrams-helmed reboot of Star Trek in 2009 is to be considered canon (and I believe it is), then Star Trek's usual time travel guidelines were changed by Abrams and the writers (Orci, et al.). I believe that in the official Star Trek TV shows and films prior to 2009, the timeline was always considered to be 'sacred'. Things were always returned to "what should happen". There was, in fact, a savage alternate universe, shown across a few TV series, but as Kirk said in 'Mirror, Mirror' - it co-existed with his native universe - but the origin was unclear. Perhaps it just always existed - as the actual theory of the 'mulitiverse' postulates. But Abrams and his writers took another part of the multiverse theory and expanded on it. That is, that a disturbance in the time line might "spin off" an alternate universe which would then also co-exist with the "prime" universe, as it's being called. That, I think, is a big departure from Star Trek's usual modus operandi when it comes to time travel. It opens up a can of worms, I think.

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