The idea that the Excelsior's engines failed never really made sense to me. Why would the first activation of experimental engines be performed in a unplanned pursuit, in a fully manned starship, from Earth orbit? [..] I could imagine the performance levels perhaps not reaching the levels hoped for but still being superior to existing designs.
Then again, it could well be that the the engine did work but was
inferior to existing designs. That's what happened with the early jet engines, after all, and against theoretical predictions and prototype work.
Such things might only be revealed when scaling up. I rather like the idea that warp in the 23rd century is much like aerodynamics in the 20th, with lots of nifty theoretical ideas and very little chance of applying them for accurate numerical modeling. There'd be lots of prototypes and testbeds, and many a great idea shot down by the harsh reality of physical application.
Which is also how a rudimentary understanding of low warp factors would translate into a fundamental misunderstanding of high warp factors, until one built an engine actually capable of high warp and discovered there was no Warp 11 where the old tachometers had it marked.
Sometime, less than eighteen years prior to "The Cage," the "time barrier" has been broken. Whatever that means.
We never hear of any improvement in space travel within that timeframe from any other source, though. So I'm tempted to say that this is something highly specific to the issue of reaching Talos IV from Earth or vice versa. Perhaps a physical barrier between the two, a nebula or something, that was too dangerous for the older ships to brave?
Also Pike calls for "time warp, factor seven."
Putting a twist to this would be tempting as well.
We hear Pike PA his crew: "This is the Captain. Our destination is the Talos star group, our time warp factor seven..."
Now, the first bit of information is actually informative - did Kirk ever bother to tell his crew where they were going? But what is the purpose of telling the crew the engine setting chosen?
It would make far more sense for Pike to give an ETA. And in that case, he would be saying "Our time - (at) warp factor seven - will be... Umm, fill me in here, Number One". The artistic cuts in the scene, including an artsy fade into a starfield, would result in us hearing many other bits of this exciting back-and-forth militarobabble, but miss the tail end of Pike's PA.
So the "time warp" of the 2240-2250's is the "warp" of the 2260's onward.
Or Pike's "elevator" is Kirk's "lift", and most skippers scoff at those who apply needlessly long forms of technobabble when colloquial abbreviations will do.
So we have four levels of warp development:
We really ought to take into account the warps of other Federation members, developed without Cochrane's input. If warp really comes in different styles, these should be manifest in the early Federation and its jargon. But probably no longer in the 23rd century where everybody uses nacelles already.
We miss out on evolving jargon when visiting the 22nd century in ENT, though. So instead of evolution, we'd do wisely to believe in a steady state, one that just happens to be diverse with odd parallel types of terminology.
Timo Saloniemi