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How do we know for sure that the Shapiro time delay effect is as a result of curved space time and not simply the photons slowing down.

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Because the speed of photons is constant, as measured in many experiments.

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We take for granted that photons travel at C=1ls/s in space. That's an axiom of Einstein's relativity and it can't be questioned inside its own theory. We will need to step out of Einstein's relativity to ask such questions.

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