The strong and weak holographic principles

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. * smolin@phys.psu.edu 1

Outer Boundary of the Expanding Cosmos: Discrete Fields and Implications for the Holographic Principle

“…It involves Pair Production (1) to produce electrons, Asymmetrical baryogenesis (2) to produce protons, Beta+ decay (3) to produce neutrons. Hence provision of all the subcomponents for the assembly to simple atoms (4). This represents the sequence as it is commonly accepted, and is not in contention.…”

“…Extending this to the universe as a whole, the principle suggests that the two-dimensional (2-D) information on the outside surface of the universe, the cosmological boundary, encodes for the whole threedimensional (3-D) content of the universe within [2,3]. The concept is typically identified with string theory [2] and information theory [4]. The holographic principle implies that everything that we perceive as physical and real in the universe, even life, is merely a hologram projected in from the cosmological boundary.…”

TASI Lectures on Black Holes in String Theory

“…See also a different discussion of holography in [15]. While the Bousso bound is a statement that makes sense only in a semiclassical regime, it may well be more fundamental, in that the consistent quantum theory of gravity obeys it.…”

“…So, let us consider the near-horizon geometry of the 0 ≤ p < 5-branes. Abbreviate 15) and look at the geometry for r ≪ r p , i.e. let us ignore the 1 in the harmonic function for the Dp-brane geometry.…”

Holographic Weyl entropy bounds

“…Much study has been devoted to the related topics of black holes, entropy bounds, and holography, and we will not be able to do justice to the bulk of prior work in the field. For reviews see, for example, [3,4,5,6] and references therein.…”