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Hobart and William Smith Colleges

Project Title

Set Theoretic Forcing and Information Theory

Project Summary

Physics uses numbers that can in principle be specified to infinite precision. There is a well developed theory of information that incorporates key ideas from physics, and there are arguments suggesting that, at a fundamental level, the theories of physics should be theories of information, yet the existing mathematical correspondence of physics and information breaks down when we consider numbers specified to infinite precision. Mathematicians, in dealing with the surprising finding that there are different sizes of infinities, have developed a technique known as forcing. In my research, I will demonstrate that the mathematical technique of forcing provides the tools necessary to characterize how much information is encoded in arbitrarily well specified numbers. The techniques of forcing will provide a way to understand how experiments can squeeze out more information by going to every higher precision, how theoretical physics can track the information flow from input to output, and how a theory of information can be developed that works whether we have a finite or an infinite number of possible outcomes. The resulting, more powerful theory of the relationship between physics and information would also represent the first real-world application of the abstract mathematical technique of forcing.

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