After explaining the importance of the debate on the tenability of Humeanism in light of LQG, and having presented the Humean doctrine, I review two cases which present serious threats to Humeanism, one concerning the fundamentality of vectorial quantities and the other concerning quantum entanglement.

Motivated by the idea that, in the background-independent framework of a Quantum Theory of Gravity, entanglement is expected to play a key role in the reconstruction of spacetime geometry, we investigate the possibility of using the formalism of Geometric Quantum Mechanics (GQM) to give a tensorial characterization of entanglement on spin network states. Employing the concept of a quantized spacetime, our theory demonstrates that the zero-point energy of the vacuum alone is sufficient to create all the fields, including gravity, the static electromagnetic field, and the weak and strong interactions. The approach taken by the authors is heuristic and uses simplifying examples in many places. Its application to general relativity, as well as to other theories of gravity, based on the socalled ADM formalism [1], has set up the basis for several approaches to a quantum theory of gravity, ... is recovered (For details, see [6]). RIS. A non-minimally coupled Nieh--Yan term alone cannot give successful inflation.

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After explaining the importance of the debate on the tenability of Humeanism in light of LQG, and having presented the Humean doctrine, I review two cases which present serious threats to Humeanism, one concerning the fundamentality of vectorial quantities and the other concerning quantum entanglement.

Motivated by the idea that, in the background-independent framework of a Quantum Theory of Gravity, entanglement is expected to play a key role in the reconstruction of spacetime geometry, we investigate the possibility of using the formalism of Geometric Quantum Mechanics (GQM) to give a tensorial characterization of entanglement on spin network states. Employing the concept of a quantized spacetime, our theory demonstrates that the zero-point energy of the vacuum alone is sufficient to create all the fields, including gravity, the static electromagnetic field, and the weak and strong interactions. The approach taken by the authors is heuristic and uses simplifying examples in many places. Its application to general relativity, as well as to other theories of gravity, based on the socalled ADM formalism [1], has set up the basis for several approaches to a quantum theory of gravity, ... is recovered (For details, see [6]). RIS. A non-minimally coupled Nieh--Yan term alone cannot give successful inflation.

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After explaining the importance of the debate on the tenability of Humeanism in light of LQG, and having presented the Humean doctrine, I review two cases which present serious threats to Humeanism, one concerning the fundamentality of vectorial quantities and the other concerning quantum entanglement.

Motivated by the idea that, in the background-independent framework of a Quantum Theory of Gravity, entanglement is expected to play a key role in the reconstruction of spacetime geometry, we investigate the possibility of using the formalism of Geometric Quantum Mechanics (GQM) to give a tensorial characterization of entanglement on spin network states. Employing the concept of a quantized spacetime, our theory demonstrates that the zero-point energy of the vacuum alone is sufficient to create all the fields, including gravity, the static electromagnetic field, and the weak and strong interactions. The approach taken by the authors is heuristic and uses simplifying examples in many places. Its application to general relativity, as well as to other theories of gravity, based on the socalled ADM formalism [1], has set up the basis for several approaches to a quantum theory of gravity, ... is recovered (For details, see [6]). RIS. A non-minimally coupled Nieh--Yan term alone cannot give successful inflation.

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