The World as a Hologram

TL;DR

The work examines whether spacetime and its degrees of freedom can be described holographically by a two-dimensional boundary, building on Bekenstein and 't Hooft's ideas. It develops the framework of light-front quantization to model partons and boosts, showing that high-energy boosts drive rapid growth in parton multiplicity and transverse extent, with the density capped by Planck-scale limits and connections to string theory. The paper then presents a lattice string theory as a potential explicit realization of this holographic world, analyzes information spreading in highly boosted systems, and discusses the implications for black hole horizons and horizon entropy. It concludes with a discussion of open questions, especially the role of the regulator ε and the need for nonperturbative, supersymmetric realizations to firmly establish a holographic, gravity-anchored world.

Abstract

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 I 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 phenomena 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 from causality. Finally we consider string theory as a possible realization of 't Hooft's idea. The light front lattice string model of Klebanov and Susskind is reviewed and its similarities with the holographic theory are demonstrated. The agreement between the two requires unproven but plausible assumptions about the nonperturbative behavior of string theory. Very similar ideas to those in this paper have been long held by Charles Thorn.