IF I TRAVELLED AT LIGHT SPEED, WOULD FAR AWAY OBJECTS DISAPPEAR?
On Earth we can still see deep-space objects which no longer exist because their light takes a finite time to reach us. If we begin travelling towards such an object, we will continue to see its light, but will see its demise earlier than if we had stayed stationary, simply because we are decreasing the distance the light has to travel. Similarly, if we begin moving away from the object, we will be able to see it for longer than if we remained stationary, because we are increasing that distance. So, some objects will indeed disappear from our sight because we are moving – this is true whatever speed we travel, but the effect obviously increases the faster you go.
However, there are other factors at play when travelling close to the speed of light. First, the Doppler Effect means objects behind us will become redder, while those ahead will become bluer. At a great enough speed, objects will disappear from sight because their light is shifted out of the visible part of the spectrum. Also, as your speed increases, your field of view becomes narrower and brighter in the direction of motion and objects appear smaller and further away. Eventually, even objects which are behind you rotate into view in front of you. At light speed you would see only an infinitely small, infinitely bright spot ahead of you, and darkness everywhere else! So, if you are travelling close to light speed, you will not be able to distinguish individual objects and notice whether they have disappeared or not!