M.G. Ivanov^1,2 and I.V. Volovich³

¹ Moscow Institute of Physics and Technology; Institutsky Per.9, Dolgoprudny, Moscow Reg., Russia.
² Department of Physics; University of California; 94720-7300, Berkeley, CA , USA.
E-mail: [email protected]
³ Steklov Mathematical Institute; Gubkin St.8, 117966, Moscow, Russia.
E-mail: [email protected]

Received: 23 May 2000 / Accepted: 29 July 2000 / Published: 20 June 2001

Abstract: A simple derivation of the bound on entropy is given and the holographic principle is discussed. We estimate the number of quantum states inside space region on the base of uncertainty relation. The result is compared with the Bekenstein formula for entropy bound, which was initially derived from the generalized second law of thermodynamics for black holes. The holographic principle states that the entropy inside a region is bounded by the area of the boundary of that region. This principle can be called the kinematical holographic principle. We argue that it can be derived from the dynamical holographic principle which states that the dynamics of a system in a region should be described by a system which lives on the boundary of the region. This last principle can be valid in general relativity because the ADM hamiltonian reduces to the surface term.

Keywords: entropy; uncertainty; holography; black hole.