An illustration of branching timelines:
This is our default timeline. The time traveler's present is point Y. Point X is where he intends to go. Point P is some event that happened prior to X.
To take an example: Point Y is the regular TNG universe on the day the events of Yesterday's Enterprise took place, just prior to when they encountered the temporal rift. Point X is the Battle of Narendra III. Point P is, oh, say, Kirk's encounter with the Gorn.
Our time traveler successfully goes back to point X and changes history, creating a branching timeline. His home timeline is unaffected. However, he can't return to it, because now he's on the new timeline he created. He returns to the future to find it changed to Y'.
To continue our example: Enterprise-C has been yanked forward in time through the temporal rift. She's saved, but unfortunately, there's no evidence a Federation starship responded to a Klingon outpost's distress call. Relations between the two states decay until war breaks out, a war which the Federation is losing. Point Y' is the day in which the events of "Yesterday's Enterprise" took place, immediately AFTER E-D encounters the rift. The history of the past 22 years is obviously very different. However, if for some reason Captain Garret decided to page through the E-D computer's history files, she'd find that it says Captain Kirk staved off a war with the Gorn by sparing the Gorn captain's life and establishing contact between the Gorn and the Federation.
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P-----X-----Y
|
|-----Y'
|
|-----YY
Our time traveler HATES the Y' present, and decides to do something about it. So he returns to point X and alters history again, either by preventing himself from changing history or correcting the results. A new timeline branches off the Y' timeline, and when he returns home, it will be to point YY, which isn't exactly like point Y, but it's close enough for him.
To return to our example: The Y' E-D sends E-C back through the rift, with refreshed torpedo stocks and some repairs, along with Tasha Yar. We don't see what happens to E-C once she returns, but it's quite possible she did better for herself than she did in the Y timeline, which is how there managed to be survivors for the Romulans to capture. At any rate, Tasha Yar, who was an infant on a dying Federation colony at the time of the Narendra incident, is now present as an adult in the battle, and later as the love-slave of some Romulan bigwig. Meanwhile, the Klingons see the Federation helped them, relations improve, war is avoided, and history in the new timeline unfolds about the same way it did before, bringing us to point YY, a future basically like point Y except that there's a Romulan-Human crossbreed with a chip on her shoulder named Sela Yar climbing the Romulan power structure. And history students can still read about how Captain Kirk avoided war with the Gorn by refusing to kill the Gorn captain.
Why do I bring up the Gorn? Because you, Admiral_K, have said several times that because of time travel and many worlds, continunity doesn't matter. You've whined that this thread isn't about Enterprise, but you've trotted out this theory several times in defense of that show, and since it DOES have continunity errors, it makes for a good illustration of what's wrong with your theory.
Basically, ENT is set in a parallel timeline that diverges from the "regular" Trek timeline at the point of first contact with the Vulcans. On this, we don't disagree. And because of that, perfect continunity can't be expected--or should be. The most blatant sign is the design of ENT herself. She bears little resembalance to any known "primitive" Starfleet design, is unseen on the rec room wall in TMP or in Captain Picard's model collection, and shares several design elements with later Starfleet vessels, notably the blue glowing nacelles, which aren't seen in the "real" Trek timeline until U.S.S.
Excelsior is launched. The rationalization seems fairly obvious: Cochrane got a look at E-E in orbit, and probably learned some things by talking to LaForge, and he refined his ideas. Thus we see a more advanced NX-01 (and for that matter, a Starfleet before we should have--again, Cochrane could have gotten the idea from the crew of E-E).
So, hooray. Why has this thread gone on this long? Because he's the one part of branching timelines you don't seem to understand or want to understand: events that happened before the divergence are unaffected. And therefore, the consequences of those events are unaffected. Anything not directly changed by the time traveler or the Butterfly Effect remains the same at point Y as it does at point Y' as it does at point YY, and so on
ad nauseum. Which means CONTINUNITY DOES MATTER. There is no possible way the events of First Contact could make telepathic Vulcans rare oddities who can catch a fatal brain disease by mind-melding, no more than the E-C jumping ahead 22 years could have made Captain Kirk kill the Gorn captain.
Now, straight up "many worlds" is different.
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P--------X--------Y
P'-------X'-------Y'
Q------XX------YY
Our time traveler isn't actually time traveling at all. He travels to a parallel universe where the timeline is at point X, does whatever he cares to, and when he goes to the future, it's point Y' (he could do so merely by accelerating to near lightspeed in realspace and thus conveniently solve any parallel universe problems for the trip back for us). Y' is different because X has been changed--but since this is a parallel universe with no connection to his home timeline, point P might have changed, too (Kirk killed the Gorn). When he goes back to fix the mess he's made, he might be travelling to a parallel universe where X happened but P didn't happen at all (Kirk and
Enterprise discovered the Planet of the Bimbos in Miniskirts two weeks before they were to be in Gorn space and haven't been heard from in months).
In this system, Vulcans who catch brain diseses by mind melding are perfectly possible in ENT, because we're not really on the real Trek timeline at all. Here's your first problem: what evidence there is one way or another points against you. Every single Trek incident where they recognized they were traveling to a parallel universe, they stayed on the same point on the timeline--jumped from Y to Y' directly, in other words. In fact, the DS9 mirror universe episodes showed that time in the Mirror Universe flows at the same rate as our universe. Not a single one of the E-D's seen in Parallels was visibly from the past or the future--no shots of crew in first season uniforms, no Galaxy-X modifications. Worf never randomly hopped to a universe further ahead or behind on the timeline. And Worf could be identified as being from another universe--his subatomic particles are out of line with the rest of the universe, something that's never been seen with time travelers, even though such a handy way to identify them would be useful, especially to the likes of Daniels.
Second problem for you, this one from a literary standpoint: if ENT is set in a parallel universe, than it isn't a prequel, even by your loose definition of it, any more than
The Lord of the Rings is a prequel for
The Hunt for Red October or a series set in the mirror universe in Kirk's time would be a prequel to TNG.
And finally, no, the differences we see in the mirror universe or parallels are NOT enormous. The same people live in them, for Christ's sake. There's nothing that says a parallel universe has to have the same
physical laws as ours. That's why it's more likely the parallel universes are actually split from the same timeline and have just started diverging.
In conclusion: the evidence for either is thin, because Trek writers obviously intend for there to be only ONE timeline, and changing events at point X caused point Y to BECOME point Y'. But writer's intent is trumped by visual evidence and simple logic, and logic says most Trek time travel cannot work like that. So we need to find a rationalization. Yours ignores what we know about parallel universes in Trek. It introduces unnecessary extra terms. It makes Enterprise not a prequel. All your insisting that your theory is right and appealing to Mike's authority (who, by the way, makes allowances for BOTH theories in that essay) won't change any of that.