Derivation of the Planck Mass from Gravitational Polarization of the Quantum Vacuum

Abstract

The Planck units were originally derived from a dimensional analysis without a deeper understanding of their meaning. It was later believed that these units may provide a link between quantum theory and gravity in a yet to be developed theory of quantum gravity. I propose a model where the Planck units appear naturally by assuming that the quantum vacuum can be gravitationally polarized based on recent work on the gravitational properties of anti-particles. In order to match the observed values, we arrive at Planck particle/anti-particle pairs (micro black holes) with Planck masses that define the gravitational constant in vacuum through gravitational polarization. This gives the Planck mass a new important interpretation as indeed linking quantum fluctuations to gravity by defining the gravitational constant. In addition, a better understanding of why the Planck length is usually associated as the smallest length in nature can be illustrated from another perspective.