Causality in philosophy already is logically incoherent, so not big loss here.
Causality isn't incoherent, it's a set of dependencies of more minute details on grander information that they modify- outside the context of the past, the future is incoherent. In the context of MWI (which is the only coherent interpretation of quantum physics in terms of relativity), it's easy to understand.
Violations of causality within the context of a causal relationship create contradictions; they provide a genesis of information.
Time-symmetry in simplified Newtonian physics poses no problems for legitimate causality, nor does it negate it; causality is about accumulation of information on the quantum side of things (which is erroneously ignored in Newtonian systems), and segregation into discrete realities. Quantum physics is not non-deterministic in the context of legitimate interpretations.
If none of that convinces you, I don't think I'll have time to explain more. Although discussion of causality can be fun, this could be a much more lengthy philosophical discussion than I was bargaining for (I was hoping to stick to light conversation topics like relativity and quantum physics), so I think I'll (try) to leave it at that.
So in conclusion: I'm right and you're wrong.
Probably. I simply do not know enough to exclude any entanglement-like setups, where we can post-factum establish, that neutrinos in CERN and Italy "appeared" within certain time interval but not have enough control in CERN to "set" the starting point of given time interval with enough precision.
That is at least part of what they were investigating as the possible cause over the past couple years. Experimental controls have to be pretty tight to prevent noise from giving false positives.
There always remains the possibility that there was something wrong with the experimental set up- which is why I prefaced everything with a gigantic "IF".
Why is gravity "the only thing" that could have slowed down light?
How about our theory of light is completely wrong and it never moves with speed C but always slightly slower depending on other factors than gravity? Thus both special and general relativity can still hold (as C being constant in all reference frames but not the speed of light).
"Slowing down" is admittedly a bad way to phrase it, but there is little else available in the English vocabulary (As Discount_Flunky pointed out, the relationship is complicated).
Anyway, that's why I gave a definitive 'no' to the other explanations, but only said that this one is 'very unlikely'.
Our observations of light have been extensive, and there's nothing I'm aware of to suggest additional forces coming into play here. Most of those aren't so much theories as hypotheses- when they propose a means of being tested and falsified, they can become theories (in which case, they'd be tested and disproved or proved pretty quickly).
The speed of light in vacuum on Earth is consistent with that expected from time dilation predicted by relativity.
Maybe vacuum fluctuations are slowing down light everywhere (and effectively slowing down out perception of time everywhere, light being the principle means of measuring time), but not slowing down neutrinos because of a weaker reaction with electron-positron pairs (for as long as they exist). But along with that would have to come an explanation for our observations that, on astronomical scales, light moves a bit faster than neutrinos. Maybe there's dark matter in between here and the observed supernovas that slows down neutrinos, but not light?
Eh... yeah, we could test part of that.
Set up some electron beams in a vacuum and shoot light through them to measure the speed of light through a haze of dispersed electrons with density of variable X to plot a curve of light speed through dispersed electrons at variable densities. Assuming positrons to be identical to electrons (which is a very fair assumption), we could estimate the speed of light from that curve given the average density of positrons & electrons in the vacuum. Then we could compare that to the speed of the neutrinos and see if that accounts for the difference.
Then we'd have to assume some other exotic matter in space is slowing down neutrinos there, but not on Earth.
For all I know they already tested that (or it has already been tested elsewhere) and ruled it out, but maybe not. I'm not read on every experiment that's ever been done regarding light speed (it's pretty extensive).
OK, you win that one. I'll change my "very unlikely" to just regular "unlikely". I'd have to do some research to see if there are any experiments along this line.