Will we need to update Electrodynamics? A contradiction to the Electrodynamics by the experiment. The author has said that, accordning to the experiment, photon is no more gauge invariant? Why is that? 
An important thing is that Although the assumption contradicts the gauge invariance but the predicted correction has a reasonable agreement with the experimental observations from Supernova 1987a. 
If he is true then will we need to update Electrodynamics? 
 A: When supernovae go bang they emit light (obviously) but they also emit neutrinos. Since neutrinos are massive (well, at least two out of the three types of neutrinos) we would expect them to travel slower than light, so at a first glance you might expect the light from the supernova to arrive before the neutrinos. However the neutrinos from 1987a were detected two to three hours before the light.
But this doesn't mean the neutrinos travelled faster than light. When a supernova goes bang the EM radiation and neutrinos are generated deep in the star. Neutrinos interact very weakly with matter so they escape quickly, but light is scattered very strongly in the star's interior and the light takes longer to escape. So the reason we observed the neutrinos first is that they were emitted first, not because they travelled more quickly.
Calculating exactly what the difference in the arrival times should be is hard, because we don't understand core collapse supernovae well enough to do really accurate calculations. However it's generally accepted that the difference in the neutrino and light arrival times is not at odds with what we know about supernovae.
Now to Franson's paper. Incidentally this isn't a new paper - it was published on the Arxiv in 2011. Franson points out the well known fact that as measured by a distant observer the speed of light is reduced in gravitational potentials. This isn't controversial. It's the basis of gravitational lensing and was pointed out by Einstein himself. You'll find several questions related to this on this site.
However Franson suggests that the virtual particles associated with a photon can produce a gravitational field, and this gravitational field can slow light and reduce it's speed as viewed by us distant observers. In effect he's saying vacuum has a refractive index very slightly greater than one. He suggests the magnitude of this effect could be about the right size to account for the difference in the neutrino and light arrival times.
I can't comment on Franson's calculation as it's far outside my area of expertise. All I can say is that it seems superfluous as an explanation for the arrival time difference as we already (think) we understand that. I'd also point out that if we start considering the contribution of virtual particles to gravity we'd then have to explain why zero point energy doesn't contribute to gravity. The fact that the paper is three years old and physics hasn't been overturned yet suggests the physics mainstream holds similar views.
