This article is from the Star Trek Tech FAQ, by Joshua Bell inexorabletash@hotmail.com with numerous contributions by others.
And then there's "Threshold" [VOY] in which Voyager - a ship running
low on supplies, with half its crew dead, stranded away from repair or
research facilities, on the other side of the Galaxy from the
Federation - manages to upgrade one of its never-ending supply of
shuttles to make a Transwarp flight, something that has defied the
best minds in the Federation for a century. There are a lot of things
in this episode that many people wish had never seen the light of
television, so we'll just focus on technobabble as it relates to warp
travel.
The [TECH] isn't too bad, however. Warp 10 is identified clearly as
infinite speed, but the pesky Warp 10 barrier is mentioned.
Presumably, this is meant as the barrier to going at an arbitrarily
large speed without draining the antimatter tanks and/or dilithium
crystals and/or other ship components. When the shuttle does achieve
Transwarp, it registers as Warp 10 and is everywhere at once for a
brief time. Now that is the way to travel! Sensors also lose track of
the shuttle, indicating that things in Transwarp do not interact with
things in normal space, unlike warp travel. (Thanks to Vikash R. Goel
for pointing that out.)
You can probably just ignore any parts of that episode that don't make
any sense - various members of the Star Trek production crew have
indicated that they plan to.
 
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