A compelling piece of evidence of the effect of gravity on the velocity of light comes from recent knowledge about neutrinos! These elusive, nearly massless particles can pass through the earth without interacting with anything, and yet they exist in enormous numbers. A recent experiment seems to show that they travel faster than the speed of light!† Scientists at CERN, in an extremely accurate test, sent beams of neutrinos 454 miles through the earth to a highly sensitive neutrino detector in Italy. They repeated this experiment more than 16,000 times.† When all the possible errors had been accounted for, they found that the neutrinos had traveled 60 nanoseconds faster than the speed of light, considered impossible according to Einsteinís theory of relativity. Needless to say, this has rocked the scientific world.
The CERN experiment sent neutrinos 732 Km through the earth to a sensitive neutrino detector.† The measured travel time was faster than the speed of light.
More recently, CERN has claimed to have found experimental errors that invalidate these results.† This in spite of the fact that the team had spent four months verifying their results prior to publication of their findings! Some believe that the reporting of these errors is a face-saving attempt by CERN to regain public confidence after reporting unpopular findings.† You be the judge.
But the speed of light has been measured in an imperfect environmentóone permeated by the gravitational fields of the Earth, Sun and the Universe. The effect of gravity on these results has not previously been considered. But if the speed of light measurements are slightly too low because of the effects of gravity, then the results of this experiment are reasonable.
With our knowledge of gravityís effect on the speed of light, a simple explanation of the CERN experiments emerges. Neutrinos are not affected by gravity and travel at the true speed of light. The measurement of the speed of light in the presence of the earth and sunís gravitational fields is slightly underestimated. To confirm this, neutrinos from the supernova SN 1987a were detected three hours before visible light was recordedóstrong evidence both for the gravityís effect on the speed of light, and that neutrinos are not affect by gravity.
In a fortuitous set of circumstances, a supernova (SN 1987A) was detected by telescopes just hours after it apparently exploded. What makes this so important is that a large influx of neutrinos were detected just two to three hours before visible photons arrived to earth, presumably from that same supernova. †While some astronomers attribute the delay to local delays of photons during the eruption, I would argue that this is clear evidence that neutrinos and photons travel through space at different velocities.† This occurs because photons are slowed by the gravitational fields in space, and neutrinos are not affected by these gravitational forces.†
This is not the same velocity difference found in the CERN experiment.† Such a difference would have resulted in a 3-4-year delay between neutrinos and photons for SN 1987A. †The 2-3 hour delay for SN 1987A is the result of very weak, but significant, gravitational fields in space, while the CERN delays are a direct result of an understated velocity of light due to light velocity measurements being carried out within the gravitational fields of the earth and sun.
Another piece of evidence that the sunís gravitational field reduces the velocity of light is found in the anomalous motion of the satellites Pioneer 10 and Pioneer 11.† The Pioneer 10 and 11 satellites were launched in January 1987, and were the first spacecraft to exit the solar system.† Their trajectories were followed for many years with extreme precision until their transponders were too weak to respond.† Detailed analysis showed a strange anomaly in their positions.† It appears they were drawn very slowly toward the Sun beyond anything predicted by the Theory of Gravity.
A large team of astronomers and scientists conducted a very detailed analysis of every possible cause of this effect.† In the end they published an extensive 55-page report (http://arxiv.org/PS_cache/gr-qc/pdf/0104/0104064v5.pdf) with the conclusion that no cause could be found.† One of the researchers did, however, make the suggestion (in a separate paper) that the anomaly could be explained if the velocity of light in the vicinity of the Sun was less than thought (i.e. as if the radio signals to and from the satellites were slowed very slightly due to the sunís gravitational force). †
This then leads to the conclusion that the Sunís gravitational field has slowed the velocity of light in its vicinity by an extremely small, but significant, amount.
∑ Neutrinos travel at the speed of light (c), unaffected by gravity.
∑ The measurement of the velocity of light is too small (i.e. <c) due to the fact that the gravitational fields of the sun and earth reduce this velocity by a small amount.
∑ This answer to the OPERA result is so simple and plausible, why hasnít someone else thought of it?
∑ The denial of their experimental results by CERN suggests to me that CERN will readily falsify experimental results to maintain credibility.
 For an example of political interference by CERN, see http://www.theregister.co.uk/2011/07/18/cern_cosmic_ray_gag/