Editing Holographic principle (section)

==Limit on information density==
[[File:Bekenstein-Hawking entropy of a black hole.svg|thumb|upright=1.2|The Bekenstein-Hawking entropy of a black hole is proportional to the surface area of the black hole as expressed in Planck units.]]
[[Information content]] is defined as the logarithm of the reciprocal of the probability that a system is in a specific microstate, and the [[information entropy]] of a system is the expected value of the system's information content. This definition of entropy is equivalent to the standard [[Gibbs entropy]] used in classical physics. Applying this definition to a physical system leads to the conclusion that, for a given energy in a given volume, there is an upper limit to the density of information (the Bekenstein bound) about the whereabouts of all the particles which compose matter in that volume. In particular, a given volume has an upper limit of information it can contain, at which it will collapse into a black hole.

This suggests that matter itself cannot be subdivided infinitely many times and there must be an ultimate level of [[elementary particle|fundamental particles]]. As the [[degrees of freedom (physics and chemistry)|degrees of freedom]] of a particle are the product of all the degrees of freedom of its sub-particles, were a particle to have infinite subdivisions into lower-level particles, the degrees of freedom of the original particle would be infinite, violating the maximal limit of entropy density. The holographic principle thus implies that the subdivisions must stop at some level.

The most rigorous realization of the holographic principle is the [[AdS/CFT correspondence]] by Juan Maldacena. However, J. David Brown and [[Marc Henneaux]] had rigorously proved in 1986, that the asymptotic symmetry of 2+1 dimensional gravity gives rise to a [[Virasoro algebra]], whose corresponding quantum theory is a 2-dimensional conformal field theory.<ref>{{Cite journal |first1=J. D. |last1=Brown |name-list-style=amp |first2=M. |last2=Henneaux |date=1986 |title=Central charges in the canonical realization of asymptotic symmetries: an example from three-dimensional gravity |journal=Communications in Mathematical Physics |volume=104 |issue=2 |pages=207–226 |doi=10.1007/BF01211590 |bibcode = 1986CMaPh.104..207B |s2cid=55421933 |url=http://projecteuclid.org/euclid.cmp/1104114999 }}.</ref>