Thoughts on duality and fundamental constants

Abstract

We consider some fundamental constants from the point of view of the duality symmetry. Our analysis of duality is focused on three issues: the maximum radiated power of gravitational waves, the cosmological constant, and the magnetic monopole mass. We show that the maximum radiated power of gravitational waves implies that the Planck time is a minimal time. Furthermore, we prove that duality implies a quantization of the cosmological constant. Finally, by using one of the Euler series for the number $\pi $, we show that the Dirac electric-magnetic charge quantization implies a mass for the magnetic monopole (or neutrino) of the order of $10^{-5}$ the mass of the electron.