Oh, what's that? Local spacetime is distorted so that photons cant travel at the same speed?
I am the first to admit I'm not a quantum physicist, nor did I especially enjoy my quantum-adjacent courses, but I've read through the paper and I'm pretty sure that's never claimed. What
is claimed is that strong magnetic fields polarise quantum fluctuations (not new), that polarisation causes an effect on protons similar to that of a dielectric medium (i.e. reduction of phase velocity) (not new), and that as a result it seems reasonable to claim that a charged particle in a vacuum can, supposing it is within a powerful enough magnetic field, emit Cherenkov radiation the way one would expect in a dielectric medium (a completely logical follow-on to the previous statements).
Nowhere does it posit that
c is exceeded, nor that this really changes anything other than presenting a potential explanation for some currently murky astronomical gamma ray emissions. Especially, the result you seem to be taking particular offense to (light in a vacuum behaving as though in a dielectric medium) seems, although I could be wrong here because I'm reading papers I barely understand, to be decades old:
It has been suggested that the nontrivial refractive index due to photon–photon scattering could induce a lensing effect in the neighbourhood of a magnetar (Shaviv et al., 1999).
The general interactions between photons and nonlinear QED effects in vacuums have been researched since the 70s or before, too.
I'm sure if I hunted more I could find older results or understand the topic better, but like I said, I don't particularly care for quantum.
Oh, and as for
How? What?
The paper is
on arxiv and presumably, to a physicist in the field, explains those quite adequately.