Yes, each observer will measure the usual local speed of light using local clocks and meter sticks. A local clock could be, for example, based on oscillations of light emitted from a specific atom. A local meter stick might consist of a crystal with a specified number of platinum atoms in one direction. Any other type of local clock and meter stick will give the same results.
But what happens when someone at another location, up in a gravitational field, looks at the same light? They will say that it's traveling slowly. So the constancy of the speed of light in general relativity applies to local light, not light somewhere else.
Mike W.
(published on 04/22/2015)
