If the Ferengi's sensor beam was operating at LS, a simple Warp 1.1 jump would suffice.
Too slow. The Ferengi would re-engage and they'd end up in a tail chase again.
If you're going FTL with LS sensors you're picking up the trail of light as it hits your sensors.
To be sure, you're picking up the light FROM the trail as it hits your sensors. That light is being emitted from the entire trail at once, and you can plainly see a point in space (moving with the trail) where no light is being emitted.
It is not necessary to fly THROUGH the trail in order to detect it; you can see the trail from a distance, as long as you're behind it.
Are you still on about using LS sensors in an FTL ship to follow another FTL ship? Because if you are, your analogy is way off. You are going FTL, faster than your LS sensors can look forward.
Special relativity again: even at FTL speed, a beam of light still moves away from you at the speed of light. The other FTL starship one light second ahead of you is perfectly visible, especially if he's moving at the same speed you are (for a relative velocity of exactly zero no matter what's happening outside of your respective warp bubbles).
Yet that could not explain for the Stargazer's warp engine flash that preceded the warp streaks.
It would if the FLASH propagated faster than light, which is a very real possibility considering what it represents.
As seen in the "The Undiscovered Country" screencap, warp streaks are also visible while a ship is still AT warp.
And yet in the TUC screencap, the Enterprise is not moving at FTL speed
relative to the camera.
You're also conflating the engine glow from the TMP era with the elongated blur we see from TNG onwards; those are very different phenomena, considering TNG vessels don't have a noticeable glowing trail.
Relevant; Data's plan focused on using the tractor beam to seize the Stargazer and restrict it's weapons fire which did not include use of weapons.
The reason it's not relevant is because we do not know whether or not the use of weapons would have been easier or harder than the use of a tractor beam. Data implies that it is HARDER, because only a very powerful ship like Enterprise could do so, however we do not know for sure, and therefore we cannot definitively say that a tractor beam requires a less precise targeting solution than a phaser beam (although, based on "Conundrum," probably more).
The camera wouldn't be able to see the ship if it couldn't capture it with FTL capabilities.
Special relativity: light always travels at the speed of light in all reference frames. The point I was making is that the perception would have to be FASTER than light for the streaky "drop out of warp" images to be representative of "FTL until we stop." In those cases, you wouldn't be able to visibly trace the movement of the ship; there'd be a flash of light and it suddenly appears out of nowhere.
The existence of the warp streak tells us it is at warp.
At most, it tells us the warp engines are active. As it stands, we have
at least one solid datapoint from TVH that suggests "traveling at warp" and "traveling at FTL" are not necessarily the same thing.
And the "Lower Decks" example showed that they also "worked out the target ship's exact position" but after the E-D turned the firing solution was no longer valid.
I can see where you're confused.
A "firing solution" is a term derived from the mathematical equations used to direct artillery batteries; literally, a solution to an equation that involves the speed and direction and distance of the target, the speed and direction of the shooter, the arc and velocity of the shell, wind direction and coriolis effect, all to work out a determination of which way the gun must be pointed to score a hit. It is used by analogy to refer to weapons guidance in, for example, sonar-guided torpedoes and guided missiles involving the calculations needed for a guided weapon to properly intercept its target given its own constraints. The commonality here is that a firing solution is a calculation based on the spotter's best estimate of those values; in artillery, the solution becomes more accurate after the first couple of shots as you can see where your shells actually landed and compare that with your calculations to adjust accordingly. Guided missiles, on the other hand, do this in real time, by constantly adjusting their course based on the radar signal they're getting back from their target and recomputing the optimal trajectory they need to take thousands of times a second. IOW, for a guided missile or a torpedo, a "firing solution" consists of a computer asking itself "Am I going to hit it? Am I going to hit it? Am I going to hit it?" over and over again.
A "phaser lock" apparently works the same way, considering it is possible to maintain a phaser lock against a maneuvering target. The "float" means the FCS is constantly re-runnning this calculation all the time so that the solution remains current and you're not firing on where the target was expected to be a couple of seconds ago.
From the sequence in the dialogue, the attacker fired on the wrong one after the Stargazer appeared to be in two places at once.
Which, again, does not specify whether that is before or after Stargazer
fired its weapons. Recall again that Picard immediately opened fire after reversing his engines; Stargazer being in two places at once is apparently concurrent with its opening fire.
And Picard doesn't speculate on WHY the Ferengi fired on the wrong target. He merely states that they did, because that's literally all the information he had available.
As far as the Ferengi were concerned, it was not the middle of a firefight
In the scenario where the Stargazer suddenly appeared and opened fire, IT WAS.
Special relativity talks about light is always light speed in the case of two objects that are traveling near the speed of light. It doesn't really talk about FTL issues, AFAIK.
Mathematically, it doesn't make any difference: even if you're going FTL relative to some other observer (which we ARE over cosmic distances), you're still stationary in your OWN reference frame, and that is the context to which special relativity actually applies.
Warp drive makes it weird because you no longer have to be in another galaxy on the other side of the universe to be moving away from someone at FTL speeds. But SR still applies in exactly the same way.
You are already in agreement that a ship at FTL will outrun it's own emitted photons.
From the perspective of the OBSERVER, yes. From your OWN perspective, your photons are still ahead of you, moving away at the speed of light (which is, as I said, the point where the scenario gets weird).
Classically, this would be explained by relativistic time dilation. Warp drive is described as precluding time dilation of any kind, but I'm reminded that in special relativity, time dilation is an
observation difference and doesn't actually occur (it literally does in general relativity, usually due to gravitationally distorted spacetime). That is, if you're moving at relativistic speeds, an observer looks at you and sees that time appears to have slowed down tremendously for you, and that distorted time explains why you don't realize the photons' relative velocity is reduced (you think it's C, he thinks it's <C). You look at the observer and record the same thing: HIS time is slowed down, which is why he doesn't realize that his photons are moving towards you slower than they should be (he thinks it's C, you think it's <C). At FTL velocity, the distortion effect is so great that the FTL starship appears to be moving BACKWARDS in time; you appear to arrive in a place before you actually left, you appear to finish sentences you haven't started yet, etc. This is because the observer may track a photon leaving your ship and calculate a NEGATIVE velocity while you still calculate the normal lightspeed; that is only possible if your clock is running backwards, skewing your measurements. And again, the same observation works in reverse: from the starship's perspective, EVERYONE ELSE is moving backwards in time, which explains why their photons appear to be moving TOWARDS THEM (that is, your forward speed minus the normal lightspeed at which you receive them).
Simultaneity is preserved, but cannot be observed. Though the speed of light remains constant in all reference frames, it means that observers moving at high speed relative to each other cannot make truthful observations about what's happening to one another; their observations are valid in their own reference frames, and ONLY their own reference frames.
That's assuming they had time to do so. From Picard's flashback, it didn't sound like he gave them time at all. And we've seen ships in Star Trek go kaboom immediately.
Well, there is
The Law of Conservation of Ninjutsu to consider. Remember, in television any particular party to a conflict has a fixed amount of badass; a single protagonist against fifty ninjas therefore turns out to be a pretty even fight, since the amount of badass on the opposing side is distributed among those fifty ninjas. If, however, you have a protagonist fighting a SINGLE ninja, it is still an even fight, as that one ninja just happens to be a 50x badass relative to all of his dead peers.
This seems to be the case in "Way of the Warrior." The Klingons hit DS9 with about thirty ships, which is unfortunate because it apparently means every single one of them has about 1/30th their normal hull and shield strength (and we got to see a couple of Vorchas blown to bits where earlier in the same episode they seemed to take a pretty heavy pummeling). I suspect the same is likely to be true of the Ferengi; if Bok Junior had been part of a fleet of twenty ships, then the Picard Maneuver would have been used to destroy every single one of them in a massive guns-blazing turkeyshoot (and a couple of those twenty ships would have gotten confused and fired on the wrong target). One on one, though, concentrates the Ferengi's supply of badass on a single ship and makes it harder to kill; instead of simply blowing apart, the Ferengi ship would have listed sickeningly for a few moments with fire and secondary explosions billowing out, etc etc.
Which begs another question, why would you run to the tactical officer to have a discussion in the middle of combat?
Good question is good.
Riker: "Worf..." <BOOM!> what can you tell me about that bird of prey? Any weaknesses?" <BOOM!>
Worf: "They're using an old D12 bird of prey... <BOOM!> They were retired from service because of defective plasma coils!"
Riker: "Any way we can use that to our advantage?" <BOOM!>
Worf: "Are you shitting me? We're in the middle of a battle! Shut up and give some damn orders!"
Perhaps a bit inexperienced? Or did the young, inexperienced Ferengi Captain just say, "Fire at the Stargazer, ignore the new ship!"
Or suppose he said "Fire at that ship!" and the weapons officer -- who
wasn't watching the viewscreen -- fired at the distant image he was already locked onto?
Regardless, though, the fact is Stargazer is depicted as being very quick on the draw after deceleration. I could buy that Bok fired at the same time, but firing FIRST doesn't fit the narrative.
It doesn't quite work for FTL situations. As you've pointed out, a FTL ship can outrun its own emitted photons so LS Sensors are useless for looking around when going FTL.
But that's only true from the OBSERVER's point of view. From YOUR point of view, your photons are still moving ahead of you at the speed of light.
More importantly, most of the things in the universe were already there long before you engaged your engines, so you won't have to worry about them appearing to be in multiple places. It gets more complicated with another FTL ship, but it's worth keeping in mind that since light takes a certain amount of time to travel, you can see where he was thirty seconds ago, then where he was twenty seconds ago, then where he was ten seconds ago, etc etc until you get close enough to match velocities. Matching velocities restores simultaneity; all those weird time-dilation effects disappear and you are free to lock your weapons onto the target as you normally would.