Paradoxes of the theory of relativity
Gravity Effects
Einstein's GRT has only a handful of testable results: light deflection, image distortion, redshift, signal slowing, clock slowing and planetary perihelion advance. While it is beyond the scope of the present paper to treat all of these effects, we can look briefly at the most unambiguously testable ones: light deflection and perihelion advance.
Let us consider first the deflection of star light traveling a path near a large mass such as the Sun. Two-step propagation means the light is always still attached to some "anchor" particle. The anchor particles are subject to gravity throughout the propagation process. Thus the anchor particles can drag the light around, which can affect the light.
Imagine the line from Earth to Sun to define a coordinate axis z. The Sun is at the origin, Earth is below, and a source star is above. Thus we have a deflecting mass at z=0 , an observer at z-->-infinity , and a light source at z-->infinity. Consider a ray passing the deflecting star at slightly positive y. During propagation down an incremental propagation path -dz , the anchor particles accelerate along y by incremental speed
And over the whole path, the anchor particles accumulate
where is the gravitational potential of the Sun, and subscript 'max' evaluates that potential at the minimum offset y. The minus sign and magnitude serve to make explicit the sign, as is always negative.
The situation created by the transverse motion of the anchor particles in the gravitational field is the same as if the Earth were moving at relative to the approaching light beam. The result of such motion has been known ever since 1728, when Bradley established the existence of a stellar aberration due to the orbital motion of the Earth: stars appear shifted slightly forward in the direction of Earth motion.
