General Covariance and Background Independence in Quantum Gravity

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Part III Mathematics Essay

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Bärenz, Manuel
University of Cambridge
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The history of general relativity suggests that in absence of experi- mental data, constructing a theory on philosophical first principles can lead to a very useful theory as well as to ground-breaking insights about physical reality. The two related concepts of general covariance and back- ground independence are some of these principles and play a central role in general relativity. A definition for them will be proposed and discussed. Constructing a theory of quantum gravity – the sought-after unifica- tion of general relativity and quantum mechanics – could profit from the same approach. Two popular research areas of quantum gravity, string theory and loop quantum gravity together with spin foams, are being examined whether they comply with these principles.