# Vistarini: Some reflections on a possible holographic description of time

### Abstract

String theory has deeply changed the traditional scientific understanding of spacetime and geometry. During the last twenty years the theory made significant progress in showing the emergent nature of spacetime, whether spacetime is the geometrodynamical structure usually associated to general relativity or it is a spacetime having compact extra dimensions (the theory gives two different, but related, accounts of these two types of emergence).

However, the theory composite account of spacetime emergence does not equally involve space and time. Indeed, the many extra dimensions required by the theory are all spatial and a lot of progress has been done in understanding the nature of their emergence from physical dynamics taking place in lower dimensional spacetimes. But does the theory deliver a notion of emergent time?

This paper aims to present a holographic model of time’s emergence developed by a group of theoretical physicists (around 2006). They explore this idea inside the context of non-perturbative string theory.

As far as I know the only non-perturbative formulation of string theory presently complete is that provided by the AdS/CFT correspondence, also called holographic correspondence. The latter is a duality between a string theory over an Anti-de Sitter spacetime (the bulk spacetime containing gravity) and a conformal field theory over its boundary. This correspondence is the most concrete scenario in which some spatial dimensions of a theory (the bulk theory) “emerge” from the dynamics of a different theory (boundary theory) that does not contain those spatial dimensions. The prototypical case is a duality between Type IIB string theory on $AdS_5 \times S^5$ and the conformal $SU(N)$ Yang-Mills theory defined over the boundary of this spacetime.

The research program I am analyzing here is motivated by an attempt of finding a similar duality between a boundary timeless field theory, equipped with Euclidean geometry, and a time-dependent de Sitter bulk theory where time would emerge from the boundary by mimicking the AdS/CFT logic that underlies the emergence of a radial dimension in the Anti-de Sitter bulk.

Although this program has not been taken to completion yet I think it deserves philosophical attention as its holographic model of time seems to instantiate a case of emergence in a truly genuine philosophical sense, namely some physics in time arising from some underlying timeless physics. This scenario of emergence seems to be a much stronger option than that concerning emergence of space in the AdS/CFT correspondence, where some physics in space does not arise from some spaceless physics, rather from physics taking place in a lower dimensional space.