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So, what is the tractor beam actually locking on to? (Parallax)

at Quark's

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Just viewing Parallax.

In this episode, the ship is caught in the event horizon of a quantum singularity. When the crew first sees the singularity, they see a distorted ship at the edge, which they try to pull out using a tractor beam. Later, we learn that Voyager itself has been within the event horizon from the first shock and that the ship we see is nothing but a 'time-delayed reflection' of themselves. This is later reinforced by the notion B'elanna and Janeway have on the shuttle that only one of two very real-looking images of the ship will have any substance to it.

OK, fine so far (ignoring the question of (lack of) realism of physics, of course). But, if there is nothing there, what is the tractor beam they point at the beginning of the episode at this reflection actually locking on to, and why does it have such a serious effect on the ship? Is it simply locking onto the singularity itself?
 
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I assume it was the interaction of their tractor beam (which is a gravity beam) with the gravimetric distortion of the singularity/event horizon itself. They never said they locked onto anything; they just said the beam was penetrating the event horizon, then that they were being pulled toward it.
 
^They say that, yes. However (as I understand it at least), unknown to them, they themselves are already within the event horizon at that moment, so what is it really doing? (I don't suppose it is penetrating the event horizon in outward direction).
 
^As I said, it was an interaction of the tractor beam (a gravitational effect) with the space warp of the singularity (also a gravitational effect). I assume it was some sort of gravitational feedback or disruption. Maybe the ship was even locking onto itself, as Holly Day suggested.

It doesn't really hold up to detailed scientific analysis; in reality, an event horizon isn't a "force field" or a barrier, it's just the distance from a singularity at which the escape velocity equals the speed of light, so that no matter or information from inside can reach the outside universe (not at sublight speeds, anyway). But the science consultants handwaved that by calling it "a type 4 quantum singularity," so that it could be some novel kind of singularity that had whatever arbitrary sci-fi properties the script needed. After all, Voyager could've escaped a regular black hole just by using warp drive, but even at warp speed, they were still trapped.

Although there is some merit to the idea that light just within an event horizon could be trapped in a loop that could circle back on its source, creating an effect similar but not identical to the "reflection" they saw in the episode. Ultimately, all lightspeed or sublight paths within an event horizon would spiral down into the singularity, but something near the edge could follow a nearly circular path.
 
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