"space may be the final frontier, but it's made in a Hollywood basement"
Red Hot Chili Peppers

Hi,
The students didn't actually say anything about faster than light travel. They assumed the MF travelled just under light speed and then blue shifted everything and which would (maybe) cause a different EM radiation source to dominate the visible spectrum.
I would be interested to know how light would work going though a warp bubble.

FTL is NOT happening - but *effective* FTL is. Huge difference. Moving mass takes enormous amounts of energy, warping space does not. What does warping space look like? You literally see your destination zoom up to you as the space in front of you does a very wierd lensing effect. You step through this distortion onto the ground of your destination. You turn, look back at where you came from, and see that you are now surrounded by your destination - your point of origin is a very long way away, not even in sight. No streaks or large fuzzy glows. Cool, but very much less impressive than movie special effects...

A friend of mine and I were discussing what, if anything, you might see as you approached the speed of light and then went beyond it. Or what you might see from outside of it if an object was to do that in front of you. Before I go any further, kudos to those students on factoring the upward shift of the ENTIRE EM spectrum into the equation! I had completely forgot about that part of it; light energy would shift upwards to UV and beyond due to the Doppler Effect. But now, as opposed to Early Greek times (it was thought by them at one time that our eyes created light which bounced off of things, thus making them visible to us), we know that we cannot see objects unless light from an energy source is bouncing off of them. Light is invisible to us, unless it is bouncing off of things be they small like molecules, or smoke or relatively large things like planets, or is coming straight at us from its source. Sound cannot travel upstream against a flow that is moving faster than the speed of sound, so how could we see with our eyes rays of light coming towards us, if we are traveling at or beyond light speed?? Imagine light from a star shining on a planet that we are approaching at light speed, and that reflected light has to reach our eyes, how could it possibly register as anything at all? It would be gone faster than the blink of an eye! You can't even see clearly the blades of a ceiling fan when it is on high speed! So therefore, even though there may be energy all around us, I posit that we wouldn't be able to tune into it because our body just isn't set up for that kind of an experience. You wouldn't see a star ship growing in length like a rubber band being stretched as in STTNG and you wouldn't see dots of light stretching out into long lines (recall where in Hot Rod Lincoln he says "Slow down, I see spots, the lines in the road just look like dots"), it would all just disappear from your sight, you'd be completely blind unless you somehow had a way of shifting the spectrum back down into your normal band of perception. If you could find a transparent substance that could slow the speed of light down enough, you might be able to see something again. But I don't know of anything short of transparent aluminum that can do that!! ;-P

This has already been calculated/theorized by other astrophysicists who've essentially said looking out the window at lightspeed would look exactly as it does before the jump. Primarily because even at lightspeed the distances are so great that you would not appear to be moving any faster.
I'm no physicist so I don't know but, I'll take their word for it over that of the students until the answer is proven to be otherwise.

Looks just the same way Spider Robinson described it a decade ago

If it were possible to travel faster than C, you would see NOTHING. Every spectum visible and otherwise would be doppler-shifted past cosmic ray frequencies.

The "Hollywood" depiction is accurate, showing the earliest moment(s) approaching the speed of light. Then the disc of light.

So, what would you see behind you? A reddish black, black, or your place of origin?

Nice try; but the Observer in this scenario isn't traveling faster than the Speed of Light.
The SPACE the Observer is in, is what's moving, not the Starship.
Trek Explanation:
Your Starship is merely coasting on impulse thrusters; the Warp Drive decompresses Space in front of your ship, making the distance to the destination shorter, and compresses Space behind your ship.
You ride forward in that Reference Frame.
For you, it's as if the stars ahead are rushing TOWARD you.
So you might see visual effects, as, after all, light is going to be altered as it passes through the decompression stage.
A star directly ahead of you might not look odd, but stars off to the sides certainly would.
Remember that "Blue Shift" happens in normal space when you are accelerating and the wavelength of incoming light gets compressed into higher frequencies.
But in the "Warp Drive" scenario, you aren't accelerating.
Here's an analogy; imagine that your Star Drive worked with tiny, instantaneous Jumps.
It's called "Trans-Cilial Drive".
You'd Jump; the duration would be so short you couldn't perceive it, but you'd be a light-day closer to your destination.
Then you'd Jump again, with only microseconds between Jumps.
Three Hundred and Sixty-Five quick Jumps equals one Light Year, and we're at Alpha Centauri Prime for breakfast.
The light from stars ahead of you would be unaffected because you aren't accelerating. You're skipping in and out of normal space and avoiding the whole "Blue Shift" issue.
Now consider that this is what is happening with Warp Drive.
You aren't accelerating there, either. So the wavelength of incoming light doesn't get compressed, doesn't Blue Shift, and you don't get X-Rayed to death.
Is there a likelihood that incoming light will be affected by the Decompression Field?
Sure. And I'm sticking with the "streaks of light" image until I see proof to the contrary.