The strong and weak holographic principles

TL;DR

This paper reviews various formulations of the holographic principle, analyzing their validity in quantum gravity, and concludes that only the weak form, which constrains boundary information, is likely to hold in the full theory.

Contribution

It classifies and critically assesses different holographic principles, highlighting the limitations of strong and null forms and emphasizing the robustness of the weak form in quantum gravity.

Findings

Only the weak holographic form is supported by generalized second law arguments.

Strong forms face counterexamples at semiclassical level.

Null forms are limited to matter entropy, with difficulties including gravitational degrees of freedom.

Abstract

We review the different proposals which have so far been made for the holographic principle and the related entropy bounds and classify them into the strong, null and weak forms. These are analyzed, with the aim of discovering which may hold at the level of the full quantum theory of gravity. We find that only the weak forms, which constrain the information available to observers on boundaries, are implied by arguments using the generalized second law. The strong forms, which go further and posit a bound on the entropy in spacelike regions bounded by surfaces, are found to suffer from serious problems, which give rise to counterexamples already at the semiclassical level. The null form, proposed by Fischler, Susskind, Bousso and others, in which the bound is on the entropy of certain null surfaces, appears adequate at the level of a bound on the entropy of matter in a single background spacetime, but attempts to include the gravitational degrees of freedom encounter serious difficulties. Only the weak form seems capable of holding in the full quantum theory. The conclusion is that the holographic principle is not a relationship between two independent sets of concepts: bulk theories and measures of geometry vrs boundary theories and measures of information. Instead, it is the assertion that in a fundamental theory the first set of concepts must be completely reduced to the second.