I may be off-base here, but isn't the length contraction backward? Things should appear closer as you approach the speed of light, not farther away. And, it should not matter if you move backward or forward to observe that effect, yet it does (try moving backwards).Also, relativistic motion doesn't appear to affect the movements of the other actors, though it's kind of hard to tell for certain.

 With my very limited understanding, my impression is this:As you move in relativistic speeds, your eye hits more photos, even those going sideways (or backwards), because the photons at an angle are slower than your eye (imagine a car moving fast through the rain, even drops that go in the other direction will hit your windshield).Therefore, your field of vision grows (you can see things behind you), but only when walking forward.I haven't read anything about going backwards, but I imagine that your field of vision would shrink, as you are now faster than photons that would previously hit your eye. My guess is that you would only see photons coming directly to you from your front, until you reached the speed of light and went blind (or could see 360 degrees, moving forward).
 Photons always travel at the speed of light in every frame of reference. Only the medium matters, not the observer's speed.The observable change is the separation between photons (wavelength) caused by a moving source.
 Photons traveling along an X axis are traveling along a Y axis at 0 m/s. If you're traveling along the Y axis, you're going faster.
 Except that's not what we measure. Instead we find the speed of a photon depends only on the medium, not on the motion of the source or receiver.
 You aren't listening to me. The speed of the photon is c in the direction it's traveling, a photon traveling due west is going north with no speed at all.
 I don't think it makes sense to say that the speed of a photon is c "in a direction", since speed is a scalar quantity.(correct me if I'm wrong, I'm terrible at physics!)
 Here, speed is a measure of the magnitude of velocity. It's perfectly acceptable to describe velocity (or a component thereof) as speed in a particular direction.
 I think I got it. Lengths will contract, but when you're moving toward something very quickly, the speed of light remaining constant, it will seem farther away. And the reverse is true when you're moving away from it.It actually helps to just forget about relativity for a moment, and think about the angles light from distant objects will have to take to intercept you. Then it becomes more clear.
 Yes, exactly. Your eye intercepts photons from a wider angle the faster you're moving, therefore you get a wider field of view, even seeing things behind you.I'm not sure I'm missing a step going from "wider fov" to "things seem farther away", maybe I am...
 We don't have some magic sensor that tells us how far away an object is -- it's all gleaned from the light, and distorting the angles, in particular, will throw off this perception of distance.It would be nice to see a write up of exactly what effects they considered, though.
 Right, very true, thank you.
 There are two separate effects at relativistic speeds.One is that the actual size of things changes. That's length contraction.But the other is that, because you are moving at such high speeds, how you observe objects is also affected. That's what StavrosK discusses in the adjacent post.
 I think it might be time dilation. You intercept photons that were transmitted a bit back in time?

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