کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1861692 | 1037536 | 2010 | 4 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: A model of the holographic principle: Randomness and additional dimension A model of the holographic principle: Randomness and additional dimension](/preview/png/1861692.png)
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 S2S2 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 S2S2 whose entropy is arbitrarily close to E.
Journal: Physics Letters A - Volume 374, Issue 3, 4 January 2010, Pages 435–438