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The authors of  state that "it is interesting to speculate on the possibility that the origin of the anomalous signal is new physics." Even the title of their paper implies an "Anomalous, Weak, Long-Range Acceleration." From the above, it appears more likely that the result is "old physics," and requires a closer look at the equations used for comparing light-times, clock rates and Doppler frequency shifts.
To help validate his theory, Einstein made other predictions that could be tested. With his calculations he showed that light rays passing near the surface of the Sun should appear to be deflected from their straight-line paths because the space through which they are moving is curved. In other words, gravity would bend light rays, an effect not predicted by Newtonian mechanics because light has no mass.
Figure above shows a beam of light from a star passing by the Sun and continuing on to the Earth. Because the light ray is bent, the star appears to be shifted from its actual location. The largest deflection (a mere 1.75 arcsec) occurs for light rays grazing the Sun's surface.
This prediction was first tested in 1919 during a total solar eclipse. During the precious moments of totality, when the Moon blocked out the blinding solar disk, astronomers succeeded in photographing the stars around the Sun. Careful measurements afterward revealed that the stars were shifted from their usual positions by an amount consistent with Einstein's theory. General relativity had passed another important test.
Is Light Affected By Gravity?
Is light affected by gravity? If so, how can the speed of light be constant? Wouldn't the light coming off of the Sun be slower than the light we make here? If not, why doesn't light escape a black hole?
Yes, light is affected by gravity, but not in its speed. General Relativity (our best guess as to how the Universe works) gives two effects of gravity on light. It can bend light (which includes effects such as gravitational lensing), and it can change the energy of light. But it changes the energy by shifting the frequency of the light (gravitational redshift) not by changing light speed. Gravity bends light by warping space so that what the light beam sees as "straight" is not straight to an outside observer. The speed of light is still constant.
Dr. Eric Christian