Information Physics: The New Frontier

Abstract

At this point in time, two major areas of physics, statistical mechanics and quantum mechanics, rest on the foundations of probability and entropy. The last century saw several significant fundamental advances in our understanding of the process of inference, which make it clear that these are inferential theories. That is, rather than being a description of the behavior of the universe, these theories describe how observers can make optimal predictions about the universe. In such a picture, information plays a critical role. What is more is that little clues, such as the fact that black holes have entropy, continue to suggest that information is fundamental to physics in general. In the last decade, our fundamental understanding of probability theory has led to a Bayesian revolution. In addition, we have come to recognize that the foundations go far deeper and that Cox's approach of generalizing a Boolean algebra to a probability calculus is the first specific example of the more fundamental idea of assigning valuations to partially-ordered sets. By considering this as a natural way to introduce quantification to the more fundamental notion of ordering, one obtains an entirely new way of deriving physical laws. I will introduce this new way of thinking by demonstrating how one can quantify partially-ordered sets and, in the process, derive physical laws. The implication is that physical law does not reflect the order in the universe, instead it is derived from the order imposed by our description of the universe. Information physics, which is based on understanding the ways in which we both quantify and process information about the world around us, is a fundamentally new approach to science.

17 pages, 6 figures. Knuth K.H. 2010. Information physics: The new frontier. J.-F. Bercher, P. Bessière, and A. Mohammad-Djafari (eds.) Bayesian Inference and Maximum Entropy Methods in Science and Engineering (MaxEnt 2010), Chamonix, France, July 2010

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