The world as a hologram

According to ’t Hooft the combination of quantum mechanics and gravity requires the three‐dimensional world to be an image of data that can be stored on a two‐dimensional projection much like a holographic image. The two‐dimensional description only requires one discrete degree of freedom per Planck area and yet it is rich enough to describe all three‐dimensional phenomena. After outlining ’t Hooft’s proposal we give a preliminary informal description of how it may be implemented. One finds a basic requirement that particles must grow in size as their momenta are increased far above the Planck scale. The consequences for high‐energy particle collisions are described. The phenomenon of particle growth with momentum was previously discussed in the context of string theory and was related to information spreading near black hole horizons. The considerations of this paper indicate that the effect is much more rapid at all but the earliest times. In fact the rate of spreading is found to saturate the bound fro...