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arXiv · 2012.03994

The Spacetime Picture in Quantum Gravity

Alejandro Ascárate
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Abstract

We propose an approach which, by combining insights from Loop Quantum Gravity (LQG), Topos theory, Non-commutative Geometry à la Connes, and spacetime relationalism, provides fertile ground for the search of an adequate spacetime picture in Quantum Gravity. With this approach, we obtain a novel way of deducing the quantization of the possible values for the area of a surface. One gets the same area values than those from the area operator in standard LQG, but our approach makes a further prediction: some smaller values and sub-divisions are also allowed. In addition, the area arises as a noncommutative distance between two noncommutative points, and thus they should be interpreted as irreducible string-like objects at the physical level (where the area interpretation for the noncommutative distance holds).

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Alejandro Ascárate. 2021-03-10. The Spacetime Picture in Quantum Gravity. https://doi.org/10.1088/1361-6382%2Fabcbde

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