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Be not so arbitrary, John. It is a matter of convention as to whether
"mass" means restmass or it means the energy of a system divided by c^2.
Using the latter definition, and delta E = mgh, one gets the correct
answer for the Pound-Rebka experiment and 1/2 the correct answer for the
bending of light by the sun (the other half we can ascribe to the
curvature of space).
Convention is like religion, you know. Whatever gives you your jollies is
fine with me.