The game "A slower speed of light" from MIT claims to simulate effects of special relativity:
Visual effects of special relativity gradually become apparent to the
player, increasing the challenge of gameplay. These effects, rendered
in realtime to vertex accuracy, include the Doppler effect (red- and
blue-shifting of visible light, and the shifting of infrared and
ultraviolet light into the visible spectrum); the searchlight effect
(increased brightness in the direction of travel); time dilation
(differences in the perceived passage of time from the player and the
outside world); Lorentz transformation (warping of space at near-light
speeds); and the runtime effect (the ability to see objects as they
were in the past, due to the travel time of light).
But does restricting the render engine to special relativity not miss out several effects that might happen close to the speed of light? Especially I'm thinking about effects related to inertia and acceleration/rotation of the observer. So are there any important effects missing which would make the game a even more realistic simulation of the movement close to the speed of light?
Best Answer
I've played the game, see my report:
and I join M. Buettner. I am confident that all relativistic effects are incorporated. It includes the length contraction in the direction of motion, time dilation, but those basic things are rapidly changed by the fact that it really shows what you "see" and not what "is there" at a fixed value of your instantaneous coordinate $t'$.
So the effects that are "purely optical" and depend on the propagation of light and relativistic effects changing it include the relativistic Doppler shift – things change the color immediately when you change the speed although the change of your location is negligible at the beginning – and the shrinking of transverse directions if you're moving forward (or their expansion if you move backwards) which makes object look "further" (optically smaller) if you're moving forward. Because of this shrinking, you may effectively see "behind your head". You also see things how they looked like some time ago.
Because of the transverse shrinking, you also see straight lines as curved ones if your speed is high enough. One should also verify that the streetcars moving in front of you from the left to the right are "rotated along a vertical axis". I couldn't verify this effect but I see no reason to think that their simulation should do it incorrectly.
Good game. See also Real Time Relativity and Velocity Raptor. You may get to those sources from my blog mentioned at the top.
However, I am confident that the "general relativistic" comments are straw men. If the spacetime is flat, and in the absence of strong gravitational fields, it is, there is no reason why the proper simulation should consider general relativity. Special relativity is enough, despite the fact that the child (and the other stars of the game) are accelerating. Of course, acceleration "tears" solid objects because the proper lengths change asymmetrically etc. but if the material is flexible enough, the objects survive.