Introduction
We exist in a universe described by mathematics. But which math? Although it is interesting to consider that the universe may be the physical instantiation of all mathematics, there is a classic principle for restricting the possibilities: The mathematics of the universe should be beautiful. A successful description of nature should be a concise, elegant, unified mathematical structure consistent with experience.
Hundreds of years of theoretical and experimental work have produced an extremely successful pair of mathematical theories describing our world. The standard model of particles and interactions described by quantum field theory is a paragon of predictive excellence.
General relativity, a theory of gravity built from pure geometry, is exceedingly elegant and effective in its domain of applicability. Any attempt to describe nature at the foundational level must reproduce these successful theories, and the most sensible course towards unification is to extend them with as little new mathematical machinery as necessary. The further we drift from these experimentally verified foundations, the less likely our mathematics is to correspond with reality. In the absence of new experimental data, we should be very careful, accepting sophisticated mathematical constructions only when they provide a clear simplification. And we should pare and unite existing structures whenever possible.
The standard model and general relativity are the best mathematical descriptions wehave of our universe. By considering these two theories and following our guiding principles, we will be led to a beautiful unification.
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Submitted on 6 Nov 2007 by A. Garrett Lisi
http://www.arxiv.org/abs/0711.0770v1
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