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As to my knowledge, from many sources (including real Wikipedia), trans-warp (or warp 10) mean the infinite speed and that someone or something is everywhere in the same time. And hard part about using trans-warp is to exactly calculate and predict, where one would actually appear. Is that true?

How can then Voyager actually travel in trans-warp? In many episodes we see animation of some sort of corridor and -- what is the most important -- we clearly see, that such travel does take some time. In the end of Dark Frontier episode, captains log says even about traveling for some time and passing few thousands light years before trans-warp coil has given up the ghost.

If speed is infinite and an object is in every place in the universe in the same time, that means (at least to me -- correct me, if I'm wrong), that time part stops playing anything in this equation. For me, traveling in trans-warp doesn't actually mean to travel as in time aspect. You are here, when you initiate trans-warp coil and then, immediately, you are there. Wherever this is.

  • Hm... many of my questions gets downvoted, though it generate many, good quality or even perfect answers. This is strange for me. I don't know, how does this works in SF&F, but in other SE sites, that I participate, it is rather uncommon to have a question with many good-quality answers to get downvoted. Either question is poor (so it gets downvoted) or it is good enough to bring enough attention (so it gets many good answers). Strange... – trejder Mar 24 '14 at 7:21
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    I didn't DV this (I don't believe I've voted on any of your questions), but "good" questions that generate "good" answers don't mean that they're a good fit for the site. Nor does it mean it was researched well before being asked, or that the premise of the question was valid to begin with (which may have been the reason for the DVs here). – phantom42 Mar 24 '14 at 13:05
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In the TNG Episode "Descent, Part I" Geordi LaForge makes it clear that the term "Transwarp" specifically refers to any technology that would allow a ship to exceed the "normal subspace limitations" that prevent Starfleet vessels from travelling beyond Warp 9.999

GEORDI : Our current theory is that the Borg have established several transwarp conduits through subspace. A ship entering a conduit is immediately accelerated to an extremely high warp velocity. It's like falling into a fast-moving river and getting swept away by the current.

PICARD : How fast would a ship travel through one of these conduits?

GEORDI : We don't know... normal subspace limitations don't apply to transwarp variables. Based on the distance we covered in our trip through the conduit, I'd say the speed is at least twenty times faster than our maximum warp.

In the Voyager episode "Threshold", Tom Paris manages to exceed the Warp 10 barrier and achieves 'transwarp speeds' (albeit with some additional mumbo-jumbo that's never spoken about again).

KIM: Nothing in the universe can go warp ten. It's a theoretical impossibility. In principle, if you were ever to reach warp ten, you'd be travelling at infinite velocity.

NEELIX: Infinite velocity. Got it. So that means very fast.

PARIS: It means that you would occupy every point in the universe simultaneously. In theory, you could go any place in the wink of an eye. Time and distance would have no meaning.

In the final episode of TNG an alternative future version of the Enterprise-D is able to reach transwarp speeds in excess of "Warp 13"

In answer to your specific question, 'how can Voyager travel in Transwarp?', the answer is that they've stolen a "transwarp coil" from the Borg. The actual technical details are never described.

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    @izkata - set scanners to 'retcon' Mr. Sulu. – Valorum Mar 22 '14 at 16:35
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    Thank you for your enlightening answer. My question come from the misunderstanding (as I was pointed out), that Warp 10 = Transwarp = infinite speed. I thought, that Transwarp means infinite speed and according to Tom Paris' words, you cited, "Time and distance would have no meaning". Since I was wrong, and Transwarp isn't an infinite speed, this question is a little bit off-topic. But thank you for a great answer once again. – trejder Mar 22 '14 at 20:44
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Your understanding is wrong. Transwarp is a means of bypassing the limitations of warp technology. Warp 10 is what you think it is, and that is a nut that Voyager fails to crack.

  • If Warp 10 is an infinite speed, is there anything left to pass? What limitations can an infinite speed have? – trejder Mar 22 '14 at 10:25
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    As seen in Threshold, simply achieving infinite speed isn't enough. You need to know what to do once you've achieved that speed. Since even species as advanced as the Borg and the Voth use transwarp instead, this indicates that the infinite speed problem is far beyond the Federation's technology; it may not be solvable at all. – James Sheridan Mar 22 '14 at 10:27
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    I already told you that transwarp wasn't infinite speed. – James Sheridan Mar 22 '14 at 10:33
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    @trejder - Don't get too hung up on "threshold". Even the writers have agreed that it's weapons grade balonium. ex-astris-scientia.org/treknology/treknology-e.htm – Valorum Mar 22 '14 at 11:02
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    I think @trejder's confusion lies with the fact that warp technology and warp factors share a name even though they're not completely related. The warp in "trans-warp" refers to the technology, not to the velocity units. Imagine if MPH were called "automobile factors". – Plutor Mar 22 '14 at 20:30
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The term 'transwarp' essentially means 'beyond warp'... or logically, any speeds greatly surpassing regular warp speeds.

In Voyager 'Threshold'... Warp 10 was specifically termed 'infinite velocity'. However, there are other forms of transwarp, such as versions used by the Borg and Voth for example... those are obviously slower than Warp 10 (inifinite speed)... but faster than conventional Warp speeds as used by Starfleet.

In the final episode of TNG, the warp scale seems to have been redefined again to allow numbering of Warp factors beyond Warp 10 so as to avoid going into the extreme decimals past Warp 9.9. Essentially, Warp 10 (or 'infinite velocity') in that timeline might have been pushed to say Warp 20 or higher.

But it's also possible that particular restructuring of Warp scale might also mean that the future which Picard experienced was never part of his reality... or basically an alternate future reality (and probably why making changes in the past or present never affected that future... all 3 time periods seem to have been distinct realities). So, that future from final TNG episode could be using TOS Warp scale for all we know.

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