The theory of general relativity suggests that light travels at a constant speed of 299,792,458 meters per second in a vacuum.
That would be the Special Theory of Relativity NOT General Theory of Relativity.
If such splitting and rejoining occurred many times with many photons on a journey of 168,000 light years,
There's no IF. Quantum Field Theory unequivocally says this happens.
the distance between us and SN 1987A, it could easily add up to the 4.7 hour delay, he suggests.
And, although the journalist is breathlessly reporting this as an earth-shattering cataclysm, this represents a relative error of about 3 x 10-9. The error in the length of the meter is on the order of 10-10 so this is not that far from the error in absolute measurement. And as for consequences? Well, just for example, it would mean that the universe is potentially about 10 c-yr smaller than believed, which is ~45 bn c-yr in diameter. That number itself has only two significant digits, so an error in parts per billion represents NO CHANGE whatsoever.
Nearer at hand, the Sun is about 500 c-sec away. This order of correction would cause light to reach us all of 1.5 microseconds later [in vacuum.] Since the intervening space is not vacuum and is not even uniform, nor is the distance to the earth's surface, we could not measure this change in any meaningful way.
Finally, I'm a tad confused about the claim that this is "related" to the fine structure constant: on the one hand, of course it is, as are all relativistic electromagnetic corrections. On the other hand, the FSC [α] is ~1/137, which is many orders of magnitude larger than the error actually claimed...
1987a has been thoroughly studied and the difference in time between the arrival of neutrinos and photons is understood. It should be noted that the author of this new theory is not an astrophysicist.
Does the special theory actually cite a number like that, or does it leave everything in terms of c?