Create effect where light takes time to reach camera I would like to reproduce the effects of light's finite speeds.  So an object that is far away will be rendered as if it were still in a position that it was in previously.

For example, to create a realistic scene in space, the light from some objects will take a few seconds to reach the camera.  A given object should therefore appear as it appeared in the scene (fps)*(Z/c) frames ago, where c is the speed of light and Z is the distance from the camera.

Some examples of what I mean:

Visual: VSauce Distortions
I don't have a Blender related answer but if you are comfortable coding you can have a look at the OpenRelativity opensource toolkit created at MIT.  There is a demo program available their gamelab website called A Slower Speed of Light.  

Here's the current link.  If the link goes down in the future you are all free to edit this answer.  http://gamelab.mit.edu/games/a-slower-speed-of-light/