Lorentzian Gromov Hausdorff Theory Applied to Quantum Gravity
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This book starts by generalizing Lorentzian geometry towards time distance bi-functions, just as a distance bi-function goes beyond the standard requirements set by Riemannian geometry. Causality properties are generalized as well as the notion of a geodesic. Later on, convergence criteria are set up and limit spaces are studied which break the original equivalence between the Alexandrov and some metric topology. That is, the former becomes too weak to address proper questions and even the notion of geodesy becomes a non-local one. This thesis opens the way to properly discuss holism versus individualism in physics and may lead to deeper thoughts regarding this and several other issues.
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This book starts by generalizing Lorentzian geometry towards time distance bi-functions, just as a distance bi-function goes beyond the standard requirements set by Riemannian geometry. Causality properties are generalized as well as the notion of a geodesic. Later on, convergence criteria are set up and limit spaces are studied which break the original equivalence between the Alexandrov and some metric topology. That is, the former becomes too weak to address proper questions and even the notion of geodesy becomes a non-local one. This thesis opens the way to properly discuss holism versus individualism in physics and may lead to deeper thoughts regarding this and several other issues.
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