John, when it comes to you stating Einstein saying that 'light curves because the speed of light varies with position.'? First of all, if it did it wouldn't be a local constant. But it is under any and all uniform motion. "the speed of light is only guaranteed to have a value of 299,792,458 m/s in a vacuum when measured by someone situated right next to it." What that states is that it is a local definition. And that's the one working, as soon as you connect 'c' to become your local clock. If you instead try to measure between two defined anchors of matter moving from each other you can define the light otherwise, the same if you're moving towards the light source. But in a local 'two way mirror experiment' (uniform motion) it won't matter for you, there you must find 'c'. And there it won't matter what 'speed' you define yourself to either. So 'c' is a local constant, unless we assume Einstein to invalidate SR? But GR is built on 'c' too.

"Galilean relativity implies that, if a physicist on a station platform performs a mechanical experiment, and another in a smoothly passing train performs the same experiment, the two obtain identical results. (The laws of mechanics are the same in two different inertial frames.)

Einstein's principly of relativity is just like Galileo's, except that now the experiment can be either a mechanical experiment or an electromagnetic experiment. The physicist on the train measures the electric field produced by putting charges on metal conductors and the magnetic field produced by a current in a coil of wire. She will get the same result with her apparatus as would another physicist, on the platform, with similar equipment. Einstein's principle of relativity is just a generalisation of that of Galileo and Newton. If you forget about the source of the light, a light wave passing is just an experiment involving electric and magnetic fields and so its speed must be that given by the electricity and magnetism experiments. Experimentally, we find that the speed of the source does affect some things about the wave (its wavelength changes: the Doppler effect) but it doesn't influence the speed. "

And

"Einstein talked about the speed of light changing in his new theory. In the English translation of his 1920 book "Relativity: the special and general theory" he wrote: "according to the general theory of relativity, the law of the constancy of the velocity [Einstein clearly means speed here, since velocity (a vector) is not in keeping with the rest of his sentence] of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity [...] cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity [speed] of propagation of light varies with position." This difference in speeds is precisely that referred to above by ceiling and floor observers.

In special relativity, the speed of light is constant when measured in any inertial frame. In general relativity, the appropriate generalisation is that the speed of light is constant in any freely falling reference frame (in a region small enough that tidal effects can be neglected). In this passage, Einstein is not talking about a freely falling frame, but rather about a frame at rest relative to a source of gravity. In such a frame, the not-quite-well-defined "speed" of light can differ from c, basically because of the effect of gravity (spacetime curvature) on clocks and rulers.

In general relativity, the constancy of the speed of light in inertial frames is built in to the idea of spacetime being a geometric entity. The causal structure of the universe is determined by the geometry of "null vectors". Travelling at the speed c means following world-lines tangent to these null vectors. The use of c as a conversion between units of metres and seconds, as in the SI definition of the metre, is fully justified on theoretical grounds as well as practical terms, because c is not merely the vacuum-inertial speed of light, it is a fundamental feature of spacetime geometry."

http://newt.phys.unsw.edu.au/einsteinlight/jw/module3_weird_logic.htmhttp://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/speed_of_light.html