2000/03/08 by Lee Smolin
Physics and Astronomy · #Assertion #Black Holes and Theoretical Physics #Bounded function #Conditional entropy #Cosmology and Gravitation Theories #Counterexample #Entropy (arrow of time) #Gravitation #Holographic principle #Noncommutative and Quantum Gravity Theories #Semiclassical physics #Upper and lower bounds #gr-qc #hep-th
paper · pdf · doi:10.1016/s0550-3213(01)00049-9
published as Nucl.Phys. B601 (2001) 209-247 · Latex, 53 pages, no figures
arxiv created 2000/03/08 · openalex publication_date 2001/05/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.