Physically motivated uncertainty relations at the Planck length for an emergent non-commutative spacetime

Luca Tomassini (1) , Stefano Viaggiu (2)

1 CRC - Courant Research Centre "Higher Order Structures"
2 Dipartimento di Matematica

We derive new space-time uncertainty relations (STUR) at the fundamental Planck length L P from Quantum Mechanics and General Relativity (GR), both in flat and curved backgrounds. Contrary to claims present in the literature, our approach suggests that no minimal uncertainty appears for lengths, but instead for minimal space and four-volumes. Moreover, we derive a maximal absolute value for the energy density. Finally, some considerations on possible commutators among quantum operators implying our STUR are done.

Mots clés: 04.20.-q; 02.40.Gh; 04.60.-m; 03.65.-w

Domaines: Relativité Générale et Cosmologie Quantique [gr-qc]

Luca Tomassini, Stefano Viaggiu. Physically motivated uncertainty relations at the Planck length for an emergent non-commutative spacetime. Classical and Quantum Gravity, 2011, 28 (7), pp.75001. ⟨10.1088/0264-9381/28/7/075001⟩. ⟨hal-00686088⟩