I recently spent some time working on exactly this, in 2D:<p><a href="https:&#x2F;&#x2F;github.com&#x2F;blevinstein&#x2F;SRAsteroids" rel="nofollow">https:&#x2F;&#x2F;github.com&#x2F;blevinstein&#x2F;SRAsteroids</a><p>To see what it looks like, you can check out this youtube video:<p><a href="https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=_hSCz7tRl1s" rel="nofollow">https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=_hSCz7tRl1s</a><p>I wrote an engine that modeled object positions as &quot;timelines&quot;, where position varies with time, and demonstrated the basic relativistic effects (length contraction, time dilation, and frequency shifting).
Unfortunately, I never really figured out how to turn these into actual game mechanics.