I have been giving much thought on how warp drive would look in real life, according to general relativity and
Alcubierre warp drive. If realism is the name of the game with STE, and assuming the warp drive principles in Star Trek are analogous to the Alcubierre metric theory, the I shall try to give a few tips on how warp should look.
When observing inside the ship or warp bubble in general, things should look normal. But when engaging the warp engines up to the light barrier, light coming in from the ship's front should become compressed and shifted blue (something like the Doppler effect), and light coming behind should be stretched and shifted to red. Once the light barrier is broken, a region of black should form when looking back, since light cannot reach the ship from behind, now that we are moving faster than light. If the field of vision is a sphere, it should be divided into two hemispherical regions: one facing forward, where light is coming in, and one facing behind, where no light is seen. It would almost appear like the ship is hovering over the event horizon of a black hole. The boundary between these areas may change with changes in warp speed, with the black region expanding and visible region contracting with faster warp speed, and vice versa, almost like the iris of an eye. This is because faster warp speeds will cause light moving in from stars to the left or right might "miss" the higher-velocity warp bubble, like a bullet trying to hit a faster target. In the visible zones, light should be highly blue shifted in the center of the region, and red shifted near the boundary (again for Doppler effect reasons). The visible region should also give an effect of gravitational lensing, since that if light rays coming in at right angles to the ship hit the front of the warp bubble, the contraction of space at front should bend the light toward the ship. The "warp stars" effect can still be valid, as particles may seem to move at high velocities past the ship, but the stars themselves should be a bit more static, with perhaps a tad of motion blur.
From observers outside the warp bubble, things may look like they do in the TMP era warp effects. Since the ship is moving faster than light, light emanating from the ship should make a "sonic boom" effect, except with light, appearing in a sudden streak and shifting from blue to red before then disappearing (once again I am saying this from a Doppler effect perspective). If course, this makes true sight-viewing of ships practically impossible, due to the delay caused by the speed of light, which may make a ship appear in one place where it actually far ahead. This can be compensated by moving the observer closer to the ship at warp, but then the ship won't be seen until it is directly upon the observer. If the observer is moving alongside the warp bubble but outside it, the observer must stay in the light "shockwave," or else the ship is effectively invisible, with perhaps the exception of gravitational lensing due to contraction of space before the ship.
Entering and exiting warp should be a cross between the TMP and TNG era effects. Entering warp should cause the ship to appear to stretch until it creates the TMP type warp streak, with light shifting from normal to red. Exiting from warp should cause a reversal in stretching back to normal, with light shifting from blue back to normal.
Most of this is just off the top of my head, trying to mentally simulate real warp drive according to Alcubierre theory, but I hope it is an accurate representation. Naturally, this could interfere with things like actually being able to detect ships and making combat at warp, but if a ship's subspace effects can be detected with sensors this problem might be circumvented. In any case, I think that the Alcubierre idea could be a good mathematical basis for actual warp in Star Trek.
