Semi-classical estimation of the fine-structure constant

In the present work we propose a semi-classical model that links well-known phenomena of quantum field theory, such as the Casimir force and the vacuum polarization. We assume for the Casimir effect in dielectrics, that the virtual pairs statistically created in the vacuum near the plates induce image dipoles in the latter, interacting with each other. Taking the limit of the dielectric constants of the plates to the value corresponding to the vacuum, we arrive at an equality that provides, on the one hand, a framework of unconventional physical interpretation for the Casimir effect through vacuum polarization and, on the other hand, a possible way for a theoretical estimation of the fine-structure constant. Regarding the latter, an example result of a first approximation to the problem is shown, with which we find a numerical value for the aforementioned fundamental constant, with an error of 44 parts per million with respect to the 2018 CODATA experimental recommended value