(Phys.org) —Mathematics is, in essence, an artificial language for precisely articulating theories about the physical world. Unlike natural language, however, translating different classes of mathematics can be difficult at best. Such is the case encountered in the attempt to unify general relativity and quantum theory, since they are expressed in differential geometry and functional analysis, respectively. That being said, spectral geometry – a field in mathematics which concerns relationships between geometric structures of manifolds and spectra of canonically defined differential operators – may resolve this long-standing quandary by allowing spacetime to be treated as simultaneously continuous and discrete, essentially relating the frequency-based ringing of the fabric of spacetime to its manifold-based shape. Recently, scientists at California Institute of Technology, Princeton University, University of Waterloo, and University of Queensland normalized and segmented spectral geometry into small, finite-dimensional steps. They then demonstrated their approach of calculating the shapes of two-dimensional objects from their vibrational spectra as being viable in two, and possibly more, dimensions.
via Phys.org: Physics News http://phys.org/news/2013-04-gravity-lingua-franca-relativity-quantum.html
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