Shape from Sound: Toward New Tools for Quantum Gravity
- Creators
- Aasen, David
- Bhamre, Tejal
- Kempf, Achim
Abstract
To unify general relativity and quantum theory is hard in part because they are formulated in two very different mathematical languages, differential geometry and functional analysis. A natural candidate for bridging this language gap, at least in the case of the Euclidean signature, is the discipline of spectral geometry. It aims at describing curved manifolds in terms of the spectra of their canonical differential operators. As an immediate benefit, this would offer a clean gauge-independent identification of the metric's degrees of freedom in terms of invariants that should be ready to quantize. However, spectral geometry is itself hard and has been plagued by ambiguities. Here, we regularize and break up spectral geometry into small, finite-dimensional and therefore manageable steps. We constructively demonstrate that this strategy works at least in two dimensions. We can now calculate the shapes of two-dimensional objects from their vibrational spectra.
Additional Information
© 2013 American Physical Society. Received 24 December 2012; published 18 March 2013. A. K. gratefully acknowledges the kind hospitality at the University of Queensland during his sabbatical visit, as well as support by the Canada Research Chairs and Discovery programs of NSERC. D. A. gratefully acknowledges the support of the NSERC-PGSM program. The authors gratefully acknowledge useful discussions in particular with William Donnelly, Mikhail Panine, Ingo Roth, and Laurel Stephenson-Haskins.Attached Files
Published - Aasen_2013p121301.pdf
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Additional details
- Eprint ID
- 38085
- Resolver ID
- CaltechAUTHORS:20130424-075415962
- NSERC Canada Research Chairs Program
- NSERC Discovery Program
- NSERC-PGSM Program
- Created
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2013-05-06Created from EPrint's datestamp field
- Updated
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2021-11-09Created from EPrint's last_modified field