Yes, the value of the vacuum permittivity, ε₀, can be derived from Quantum Electrodynamics (QED) in combination with experimental measurements.
In QED, the vacuum permittivity arises as a fundamental constant related to the behavior of the electromagnetic field. The value of ε₀ is determined by the coupling constant of QED, which is known as the fine-structure constant, denoted by α (alpha). The fine-structure constant represents the strength of the electromagnetic interaction and is approximately equal to 1/137.
The vacuum permittivity ε₀ is related to the speed of light in vacuum, c, and the Planck constant, h, through the equation:
ε₀ = (1 / (μ₀c²)) = (αh / (4πc)),
where μ₀ is the vacuum permeability. This equation provides a relationship between the electromagnetic properties of vacuum (ε₀ and μ₀) and fundamental constants (c and h), including the fine-structure constant (α).
While QED provides the theoretical framework for understanding the electromagnetic interactions, the precise value of ε₀ is determined experimentally. Measurements of the speed of light and other electromagnetic phenomena help establish the value of ε₀ with high precision.
Therefore, QED establishes the theoretical underpinnings of ε₀ through its connection to fundamental constants, but experimental measurements are necessary to determine its precise value.