Electromagnetic properties of the quantum vacuum calculated from its structure

Abstract

Maxwell’s equations and quantum electrodynamics are valid for any value of the permittivity ϵ0 of the vacuum; therefore, something additional is required to establish the value of ϵ0. A fundamental postulate of physics is that the properties of a physical system are determined by its structure. Since ϵ0 is an electromagnetic property of the vacuum, it should be possible to calculate ϵ0 using Maxwell’s equations and quantum electrodynamics to describe the interaction of photons with the quantum vacuum. The feature of the quantum vacuum that allows for such interactions is the presence of vacuum fluctuations that appear as particle-antiparticle pairs. To minimize the violation of energy conservation and conserve angular momentum, the pair appears with zero center-of-mass momentum in the most tightly bound state that has zero angular momentum. Because vacuum fluctuations each appear as a bound state, the permittivity of the vacuum can be calculated somewhat similarly to the way that the permittivity of a dielectric is calculated, yielding ϵ0 ≃ (6μ o/π)(8e 2/ħ)2 = 9.10 × 10−12C/(Vm), which is 2.8% larger than the experimental value. Formulas for the speed of light in the vacuum and the fine-structure constant follow immediately from the formula for ϵ0.