Planck Scale from Vibrating Proto-Particles of a Dynamic Quantum Vacuum

A derivation of Planck scale and its link with the existence of a minimal length are explored in the context of a model of a dynamic quantum vacuum defined by elementary proto-particles associated to elementary energy fluctuations. The emergent nature of Planck scale is investigated and a new re-reading of the existence of a minimal length is provided in the picture of a generalized Compton wavelength intended as universal scale that determines the activity of the lattice of proto-particles of the vacuum and generates the actualization of black holes or elementary particles when opportune constraints are satisfied. Then, perspectives about the link with other current emergent approaches of the Planck scale are analyzed. In particular, the connection of the emergence of the Planck scale with the spontaneous symmetry breaking of a fundamental gauge symmetry of a pre-geometry from \(\:SO(1,\:4)\) to \(\:SO(1,\:3)\) is analyzed in terms of the activity of the fundamental lattice of proto-particles of the dynamic quantum vacuum at the generalized Compton wavelength. Finally, some considerations about the emergence of the cosmological constant and the existence of black hole remnants in this framework are investigated.