If you travel VERY fast and look behind you, is it darker then in front of you?

Question

Very fast like 0.5 times the speed of light.

Answer 1

The light would stay the same but you may find it shifted towards the red.

Answer 2

No.  The basis of relativity is that regardless of how fast you are going you would measure the speed of the light the same.  Therefore, the light from behind you and light from in front you will arrive at the same time.  You would notice absolutely nothing different.

Answer 3

Yes it is, due to an effect called relativistic abberation.

When you are standing still in the rain, it appears that the rain is arriving from directly overhead, and your entire body gets soaked. But if you run through the rain, then it appears that the rain is coming from a direction in front of you, and the front of your body receives more water than the back of it. A similar thing happens with light. If you move quickly through a radiation field, more radiation hits the front of you than the back: objects moving towards you are brighter than objects moving away.

Answer 4

depends on where the light is coming from