# Why is the speed of light in vacuum frequency-independent?

I recently came across this paper: Mainland & Mulligan, Foundations of Physics 50(5), 457–480, "Polarization of Vacuum Fluctuations: Source of the Vacuum Permittivity and Speed of Light" (2020). They calculate the speed of light in vacuum in the same way as it is calculated in polarizable matter – from its polarizability. Yes, vacuum has a polarizablilty, unlike truly empty space, because of vacuum fluctuations (VF). In the paper the example they use is positronium.

Like any normal atom positronium also has resonance frequencies [1, 2] around which its polarizablilty is strongly peaked. This is what made me sceptical about the theory. The paper says (page 467):

The electric field of a photon that interacts with a parapositronium VF is the electric field of the photon at the instant $$t_i$$ that the photon becomes part of the polarized VF state. The photon released in the decay of that state is identical to the incident photon. (See the “Appendix”.) The mathematical result is that the calculated expression for the permittivity $$\epsilon_0$$ of the vacuum does not depend on the frequency $$\omega$$ of the incident photon, implying that the behavior is not resonant.
This is rather confusing to me, because the absorption of a photon is not an instantaneous event, but a process happening on timescales of the inverse of the Rabi frequency associated with the field the photon was part of. With the same argument one could claim that any atom doesn't have resonance frequencies.
I guess what they mean is that VFs appear and disappear very fast. For parapositronium VFs the average lifetime is $$\Delta t_{p-Ps} \approx 3.2 \cdot 10^{-22} \, \text{s}$$. This doesn't leave much time for interaction and therefore broadens the transitions, but still not infinitely. If the resonance line is a Lorentzian of width $$1 / \Delta t_{p-Ps}$$ the refractive index for light of frequency $$3 \, \text{EHz}$$ would be $$1 \, \text{ppm}$$ lower than that of visible light, which should be measureable.

Even worse, when a parapositronium VF is excited by a photon its lifetime increases to $$6.2 \cdot 10^{-11} \, \text{s}$$. This should give plenty of time for a subsequent photon to perform a frequency-dependent excitation to a higher energy level.

I'm not familiar with VFs, so maybe I just lack knowledge of a single fact which is too trivial to be mentioned in the paper. If so, please be forbearing.