<p>There are numerous research groups using relativistic codes, for all sorts of physics problems; from <a href="http://arxiv.org/abs/astro-ph/0202447" rel="nofollow noreferrer">Relativistic Electrodynamics</a>, <a href="http://arxiv.org/abs/0907.3647" rel="nofollow noreferrer">Relativistic Fluid Dynamics/Magnetohydrodynamics</a> and for gravitational based simulations etc. Astrophysical applications are the main place you would meet relativistic codes. </p>

<p>A 4D game engine is what you already have in games like FIFA and COD. This is just a 3 + 1 implementation, which incedently is what many relativistic codes are (they use the 3 + 1 formulation of space-time). This splitting of space-time is much easier to handle computationally for many different reasons. Of course as you go from 1D to 2D etc. you complexity increases inline with the simulated physics.</p>

<p>To me it makes no sense to have a physics engine in n-dimensions. We do not experience physical processes in n-diemensions, but four. To ask about hypercubes etc. is not physics but geometrical/mathematical constructs. These are separate from what you would traditionally associate with a physics engine.</p>
4d and n-dimensional physics engine
<p>Was somebody trying to implement 4d or n-dimension physics realtime (or not) engine?</p>

<p>What difficulties in this implementation, compare to 3d and 2d physics engines? Of course, one of which is presentation problem. Is's an interesting to look at and to find out more about 4d hyperspheres, hypercubes, springs, joints, liquids and other objects.</p>

<p>I am just curious, and not have a real application using it.</p>

<p>Generalization of my idea is physics in lobachevskian or riemann geometries, distortion spaces (you can go through the needle's eye), looped spaces (returning to the same place), physics paradoxes and other amazing things.</p>