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Is it true that, while the speed is constant for all observers, the frequency is not?
The propagation of light in a vacuum is allowed by properties of the vacuum itself, which are different from those of matter. This is why the speed of light in a vacuum ends up being constant for all observers, while in a medium it isn't.
JP said, "The propagation of light in a vacuum is allowed by properties of the vacuum itself, which are different from those of matter.". Properties (vacuum) which are man made definitions. There is no way to directly look at those properties except by how radiation performs in it. In of words they don't have a clue as to what is space.