John Macken on another thread has pointed out the reason for the disagreement in my algebra. The coordinate velocity of light is proportional to K squared, not K.
This seems to be related to the Shapiro delay. It should directly verify curvature, since it is not explainable by time dilation...
Ah... a much simpler formulation and possible explanation?
Suppose the coordinate distance in A's frame from A to B and back is R. A's radius is greater than B's. Then ∫ds=S=KR where K>1. So KR meter sticks can be laid from A to B and both parties will agree.
The coordinate velocity of...
In General Relativity spacetime is described by a metric. The most common one is the Schwarzschild metric, valid at radii greater than the surface radius of a mass. If we assume constant angular position so that dθ=dø=0, then this metric relates local (proper) coordinate time and distance dτ...
This is a good question which took nearly 100 years to answer. First let me clarify what everyone agrees on (including the posters above, I believe). The light and a freely falling reference mass stay at the same "height" in all reference frames. If you look at it from a frame moving...