It was suggested by dimensional analysis that there exists a limit called the Planck energy scale coming close to which the gravitational effects of physical processes would inflate and struggle for equal rights so as to spoil the validity of pure nongravitational physical theories that governed well below the Planck energy. Near the Planck scale, the Planck charges, Planck currents, or Planck parameters can be defined and assigned to physical quantities such as the single particle electric charge and magnetic charge as the ceiling value obeyed by the low energy ordinary physics. The Dirac electric-magnetic charge quantization relation as one form of electric-magnetic duality dictates that, the present low value electric charge corresponds to a huge magnetic charge value already passed the Planck limit so as to render theories of magnetic monopoles into the strong coupling regime, and vice versa, that small and tractable magnetic charge values correspond to huge electric charge values. It suggests that for theoretic models in which the renormalization group equation provides rapid growth for the running electric coupling constant, it is easier for the dual magnetic monopoles to emerge at lower energy scales. Allowing charges to vary with the Dirac electric-magnetic charge quantization relation while keeping values under the Planck limit informs that the magnetic charge value drops below the Planck ceiling value into the manageable region when the electric coupling constant grows to one fourth at a model dependent energy scale, and continues dropping toward half the value of the Planck magnetic charge as the electric coupling constant continues growing at the model dependent rate toward one near Planck energy scale.
Constraining the existence of magnetic monopoles by Dirac-dual electric charge renormalization effect under the Planck scale limit
