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A model of the holographic principle: Randomness and additional dimension


A model of the holographic principle: Randomness and additional dimension

Boyarsky, Abraham, GÓRA, PAWEŁ and Proppe, Harald (2010) A model of the holographic principle: Randomness and additional dimension. Physics Letters A, 374 (3). pp. 435-438. ISSN 03759601

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Official URL: http://dx.doi.org/10.1016/j.physleta.2009.11.005


In recent years an idea has emerged that a system in a 3-dimensional space can be described from an information point of view by a system on its 2-dimensional boundary. This mysterious correspondence is called the Holographic Principle and has had profound effects in string theory and our perception of space–time. In this note we describe a purely mathematical model of the Holographic Principle using ideas from nonlinear dynamical systems theory. We show that a random map on the surface S2 of a 3-dimensional open ball B has a natural counterpart in B, and the two maps acting in different dimensional spaces have the same entropy. We can reverse this construction if we start with a special 3-dimensional map in B called a skew product. The key idea is to use the randomness, as imbedded in the parameter of the 2-dimensional random map, to define a third dimension. The main result shows that if we start with an arbitrary dynamical system in B with entropy E we can construct a random map on S2 whose entropy is arbitrarily close to E.

Divisions:Concordia University > Faculty of Arts and Science > Mathematics and Statistics
Item Type:Article
Authors:Boyarsky, Abraham and GÓRA, PAWEŁ and Proppe, Harald
Journal or Publication:Physics Letters A
Digital Object Identifier (DOI):10.1016/j.physleta.2009.11.005
Keywords:Holographic principle; Random maps; Skew products; Entropy
ID Code:976829
Deposited By: Danielle Dennie
Deposited On:29 Jan 2013 14:21
Last Modified:18 Jan 2018 17:43


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