http://bogpaper.com/2013/10/06/science-sundays-with-john-duffield-speed-of-light/ "Einstein started with the constant speed of light in 1905 when he was doing special relativity. But check this out: 1911: "If we call the velocity of light at the origin of coordinates co, then the velocity of light c at a place with the gravitation potential phi will be given by the relation c = co(1 + phi/c^2)". 1912: "On the other hand I am of the view that the principle of the constancy of the velocity of light can be maintained only insofar as one restricts oneself to spatio-temporal regions of constant gravitational potential". 1913: "I arrived at the result that the velocity of light is not to be regarded as independent of the gravitational potential. Thus the principle of the constancy of the velocity of light is incompatible with the equivalence hypothesis". 1915: "the writer of these lines is of the opinion that the theory of relativity is still in need of generalization, in the sense that the principle of the constancy of the velocity of light is to be abandoned". 1916: "In the second place our result shows that, according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity and to which we have already frequently referred, cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity of propagation of light varies with position". (...) Light doesn't curve because it curves, and it doesn't curve because spacetime is curved. Einstein never said that. It curves because the speed of light varies with position."
http://www.einstein-online.info/spotlights/redshift_white_dwarfs Albert Einstein Institute: "One of the three classical tests for general relativity is the gravitational redshift of light or other forms of electromagnetic radiation. However, in contrast to the other two tests - the gravitational deflection of light and the relativistic perihelion shift -, you do not need general relativity to derive the correct prediction for the gravitational redshift. A combination of Newtonian gravity, a particle theory of light, and the weak equivalence principle (gravitating mass equals inertial mass) suffices. (...) The gravitational redshift was first measured on earth in 1960-65 by Pound, Rebka, and Snider at Harvard University..."
And now something awful: If, in a gravitational field, the speed of light varies like the speed of material bodies, then, in gravitation-free space, it varies with the speed of the observer as predicted by Newton's emission theory of light and in violation of special relativity:
http://www.youtube.com/watch?v=FJ2SVPahBzg "The light is perceived to be falling in a gravitational field just like a mechanical object would. (...) The change in speed of light with change in height is dc/dh=g/c."
Integrating dc/dh=g/c gives:
c' = c(1 + gh/c^2)
Equivalently, in gravitation-free space where a rocket of length h accelerates with acceleration g, a light signal emitted by the front end will be perceived by an observer at the back end to have a speed:
c' = c(1 + gh/c^2) = c + v
where v is the speed the observer has at the moment of reception of the light relative to the emitter at the moment of emission. Clearly, the speed of light varies with both the gravitational potential and the speed of the observer, just as predicted by Newton's emission theory of light.