Reddit mentions of Advanced Global Illumination

Ray tracing very much uses these laws to render photorealistic images, but our hardware is only just approaching the point where we can do it at interactive speeds.

Your solution would require tracing rays from all points (or a stochastic approximation of all points) on the player to the mirror- which by definition is ray tracing. The quantity of your "particles" that need to be emitted by the player needs to be a lot higher than you expect in order to converge to a quality image. Especially an image better than the lowest LOD offscreen rendering technique we use now for mirrors.

For more information on the theory behind this kind of thing, check out Advanced Global illumination