I wonder is a theory of gravity that assumes constancy of speed of light globally will make any progress towards building a quantum theory of gravity?
Dear Amrit
This can be taken into account by assuming differences in the amount of bending of space time. Actually I'm asking about the advantage of constancy of speed of light in unification in case if there is such theory that respects this constancy globally
If you take into account the bending of spacetime, that means that the global speed of light between two points is not constant anymore: it depends on the gravitational fields present between the two points. Locally, that is, measured in a small neighborhood of the passing light ray, the vacuum speed of light is constant in general relativity.
I.e., given a ray of light between, say, a distant spacecraft and the Earth, if you could examine that ray of light at any point along its trajectory, you'd find that (ignoring media effects, such as charged particles from the Sun) it is propagating exactly at c (local measurement). However, if the light ray passes near the Sun, it takes longer to arrive at the Earth due to spacetime curvature (that is, the Shapiro effect), so its global speed is less than c and variable. This is standard relativity.
In reviewing the question though, I wonder if perhaps you had something other than the standard meaning in mind when you used the word "global".
Dear V. T. Toth
There are two options which can give you the same result of Shapiro effect one of them is assuming the speed of light is changed the other one is assuming the path length is increased. Why the first one is always assumed while the second is excluded?
Dear Sadeem: I don't think that the "first one is always assumed" is really true. Everyone familiar with relativistic physics knows that in the presence of a gravitational field, geodesics (including null geodesics) are not straight lines, and therefore, it takes somewhat longer for light to arrive at a destination. In practical scenarios (e.g., when calculating the Shapiro delay for a space-based radio science experiment) we are not necessarily interested in the path, only the cumulative effect: that effect is that the light takes longer to arrive, i.e., it is the same as though the light had traveled slower than c. But nobody actually assumes that the light is traveling slower than c along a straight line, instead of traveling at exactly c along a curved trajectory.
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