Uncertainty Relation from Holography Principle

We propose that the information and entropy of an isolated system are two sides of one coin in the sense that they can convert into each other by measurement and evolution of the system while the sum of them is identically conserved. The holographic principle is reformulated in the way that this conserved sum is bounded by a quarter of the area A of system boundary. Uncertainty relation is derived from the holographic principle. PACS number(s): 03.65.Ta,04.60.-m,03.67.-a The concepts of information and entropy [1, 2] play more and more important roles in physics both in technical and theoretical aspects [3]. It seems that information is more fundamental than space as well as matter since each physical law must be written in terms of a certain type of information such as coordinate, curvature, energy, mass, etc.. Hence, in order to construct the unified law of all interactions in nature, one should inquire what are the informational contexts of space and matter and how to measure these physical quantities in a unified framework of information. Ever since the holographic principle was proposed [4, 5] the information and entropy manifest themselves as key concepts as a guide for constructing successful theory of quantum gravity (for recent review, see [6]). The information, known as how much uncertainty can be eliminated in light of an observer, can be defined as the deviation of the actual entropy of a system from the maximal entropy that the system may contain [7]. The feature of information is that an observer’s E-mail: [email protected] E-mail: [email protected]