Besides, what you're claiming here has nothing whatsoever to do with what you claimed before, that a ship could "get up to several times the speed of light" simply by accelerating at impulse. It's a total non sequitur.
I think
newtype is working from the "impulse is a non-Newtonian, warp field-like propulsion" hypothesis. That may also be the genesis of
Myasishchev's "low warp" comment that you objected to.
I think Newtype and I are on the same page as far as "FTL impulse" goes. I doubt very much that he needs to "read up on Einstein," particurly when you realize that most of what people think of as Einsteinian is only a SIMPLIFIED version of those equations (the E=mc^2 equation only holds when certain terms are dropped out... as they do at speeds wherein we're accustomed to seeing).
Christopher, I know you've heard this one before... so I'm not at all sure why you consistently act as though you've never heard it. But anyone who has never heard it:
"Impulse" is a classical, newtonian term. It as absolutely, undeniably Newtonian. You can no more redefine that term than you can redefine "mass" or "velocity" or "acceleration."
Still, we know (without ANY room for debate) that in TOS, and at least a few cases in TNG-era shows, that "impulse" can be FTL.
How can that be?
Simple... and there's plenty of in-universe backup for this (both in TOS and in TNG-era times).
We know two things about "subspace fields," both 100% canonical.
1) Subspace fields reduce the "apparent mass" of an object (that is, the amount of an objects "real" mass which is seen by the "real" universe). This was used several times in TNG, and in the pilot to DS9, and probably a few other times as well.
2) Static subspace fields are NOT "warp fields," but allow the local speed-of-light to be increased to a speed greater than that seen in the "real" universe. This, again, is repeatedly and consistently seen in TNG-era "treknology." The most common application of this is in the TNG-era "ftl computers."
We also know the following:
1) The Romulan War was fought with "impulse only" craft... pretty ludicrous unless you're willing to accept decades between engagements, isn't it? Of course, if you have "FTL impulse" you can get around that.
2) TOS shuttlecraft have both a central "impulse engine" and nacelles. Why both? We're also led to understand that these ships aren't "warp capable" but we know that they're capable of doing things that are 100% clear as being impossible (or at least utterly impractical) if they're sublight-only. Every time we saw one in TOS we see it doing something that would be ludicrous to try with a sublight-only craft, except for when they were being used to search for a craft which couldn't have been lost as it was if it were sublight-only.
3) The Enterprise tried to cross the "barrier" and lost its warp drive, and yet was able to travel to another star system, not years later or decades later, but just a matter of DAYS away. There are no star systems anywhere outside of the galactic core where they are mere "light days" away. In our local neighborhood, we're talking about light-YEARS between star systems. As you get further from the center, they're spaced further apart, as well. In other words... IT HAD TO TRAVEL FTL to get to Delta-Vega.
4) We know that sometime between the crash of Vina's transport and the "rescue" by the Enterprise (under Pike), there was a breakthrough in FTL transportation which was a "quantum leap" in technology.
5) We know that the Bonaventure was the "first ship with Warp drive" but it's clearly not the first FTL ship (you can disregard this point if you're inclined to reject TAS, but I don't do so, personally).
(Now, the series "Enterprise" sort of contradicts a lot of this... but where two series contradict each other, I choose to accept the SOURCE material (aka the earlier work) as being "more true." The later stuff needs to be fixed, to match the original, not the other way around, in other words.)
Okay... so, put this all together, and what do you get?
"Static-subspace-bubble Impulse Drive."
Generate a static (non-"warped") bubble of subspace around your ship. This allows you to accelerate much faster, and to a speed much higher, than you can in "real" space/time, but you're still using Newtonian techniques. Just "modified" Newtonian calculations, with the modifiers associated with C and with m.
Perhaps generating an appropriately-sized Subspace bubble reduces your "projected mass" on the real fabric of space-time to 1/100 of a percent of your "real mass... or 1/10,000. This means that, for a given thrust output, you'd accelerate 10,000 times faster than you would without that "subspace" boost, then your inertial effects (as seen by you, from inside the "bubble" would be similarly affected... meaning that you wouldn't see F=ma effects as though it were in "real" space/time at that acceleration, but only as seen within your "pocket universe" bubble.
So, you produce propulsive acceleration at 700m/s^2. Apply that in "real" space/time over ten seconds, and you accelerate to 7,000m/sec. But apply it in the "static subspace bubble" (assuming that 1/10,000 ratio, which I'm sure wouldn't be the REAL number, just one I chose for ease-of-understandint)....
... and you see (internally) the equivalent of 700m/s^2 acceleration, but (externally) something more like 7,000,000m/s^2 acceleration.
Furthermore, since the "local speed of light" inside this little pocket universe you're inside of (the "static subspace bubble" isn't REAL space/time, though it's very nearly "colocated" with "real" space/time) is higher (relative to real space/time)... well... it's almost as though the outside universe "looks smaller" from inside the bubble.
You're still seeing the speed of light as a constant... but whereas the moon is about eight light-seconds from earth in "real" space/time, if you're inside this bubble, it might be 1/8 of a second away... not because you're (locally) going faster, but simply because the SCALE is different viewed from these two different perspectives.
It's commonly accepted that (due to our current understanding of relativistic physics) about 0.75c is the "speed limit" before you start to see unacceptable effects due to time-dilation. Well, I've kind of arbitrarily (based less upon hard-science and more upon fictional "trek history") determined that the "FTL impulse" speed limit... where you start to see relativistic effects within this subspace-bubble "pocket universe"... is 75c.
Why 75c?
Well, several reasons... first off, it's consistent with a relatively small range of reachable systems, but allows for interstellar travel easily enough.
Second... using the old (WF^3)*C = V formula (nearly universally accepted before TNG came along and "redefined" the scale), this is the equivalent of WF4.2, which is what was defined about the time of TMP by Sternback and Co in the Starflight Chronology as the "speed limit." So I'm paying homage to that.
Third... it allows you to keep 99% of what we see, on-screen, in "Enterprise" without having to "redefine" any of the real storytelling. "WF4.2" is certainly the range that our hero's ship tends to travel at most of the time. If you can "retcon" away the "warp speed" nomenclature, everything else from "Enterprise" can be kept. (If you don't do that, you have to toss away a lot of TOS/TAS stories, however)
Finally, it seems to fit well with all the other on-screen evidence (including the shuttlecraft pursuit in "The Menagerie") from TOS. And still leaves Jose Tyler's "you won't believe how fast we can get back" making a certain amount of sense!
The one final piece of evidence comes from the change in terminology from the time of Pike to the time of TOS... Pike was using far more formalized language ("Time Warp Factor" and so forth) than was in use a short time later. This infers that when Pike was using it, the technology was still reasonably new, and hadn't fallen into slang-usage yet. Sort of like how when the Army replaced it's jeeps and pickups, the vehicle they did this with was the High-Mobility Multi-Wheeled Vehicle, and that's what we called it. The abbreviation was HMMWV. Over time, this became to be "slang-i-fied" into "Hummvee." And then "Hummer."
We know that there was an FTL propulsion breakthrough not long before "The Cage." We know that impulse is a newtonian term. We know the effect of static subspace fields. We know that "impulse" must be able to drive a vehicle FTL in the Trek universe.
The only solution I've ever seen that really matches EVERY requirement... both real-physics and "trek historical" in nature... is the "FTL impulse as real newtonian propulsion inside of a static subspace bubble" explanation.
It's all make-believe, of course, so there is no "right" answer. But unless you're willing to toss aside either our understanding of real-world physics, or a major portion of Trek-universe fiction, I don't think you can accept any other solution.
You're welcome to disagree, of course. But please at least stop pretending you've never heard the argument before, K?
