Noon-Midnight Red Shift

A terrestrial atomic clock at noon can be some 10^g cm nearer the sun than an antipodal clock at midnight. The difference in gravitational potential due to the sun corresponds to a difference of time rates corresponding to a red shift =810^-13. But this red shift is almost exactly cancelled by a violet shift arising from the relativistic Doppler effect, so that the resultant shift is essentially zero. If the earth shielded or focussed the solar gravitational field, the gravitational contribution to the red shift would be altered and one might expect a resultant shift. But the motional contribution to the shift is also altered and, except for unrealistically large shielding or focussing, the resultant shift would still be zero. However, all this is true only if the principle of equivalence is valid. The Pound-Rebka experiment confirms its local validity with a 10% accuracy. A 10% discrepancy could imply a noon-midnight red shift =810^-14, compared with 510^-16 in the Pound-Rebka experiment. Moreover, since the solar gravitational contribution to the value of g is only 510^-4g, the Pound-Rebka experiment is insensitive to solar effects and would not detect possible anomalies arising from shielding or focussing by the earth of the locally almost uniform solar gravitational field which might nevertheless affect the noon-midnight shift. Detection of a significant noon-midnight shift would be a disproof of the general theory of relativity.