The maths points to it, so it was postulated, and it is found to be true.

surreptitious57 wrote:
Why is it the speed of light in vacuum is not affected by relative clock speed

Clock speed and light speed track each other. So it doesn't matter whether you are in a vacuum or not as long as the clock is there with you. But such is merely a hypothetical issue because a true absolute vacuum can never exist and even if it did, putting a clock into it would mean that it no longer existed.

surreptitious57 wrote:
Why is it the speed of light in vacuum is not affected by relative clock speed

Umm...why would it be affected by relative clock speed? According to relativity, the speed of light is the ultimate (absolute) metric of the universe. It would make more sense to talk about relative clock speed being affected by the speed of light.

The way I look at it is that light travels at c relative to itself, i.e. the displacement of a photon from its previous position is dependent upon its frequency, wavelength and source (as well as any refraction or scattering it might undergo). The instant a photon is emitted from an object it is immediately travelling from the spatial point (coordinates) of emission at c. Similarly, the instant a photon hits an object, it hits it at the spatial point of impact at c. So regardless of the relative velocities of the emitting and receiving objects, the receiving object will always "perceive" the incoming photons as travelling at c.

Hmm. Here I thought it was because the definition of "total vacuum" precludes gravitational or relativistic effects on clock speed.

Ven. Kwan Tam Woo wrote:
The way I look at it is that light travels at c relative to itself, i.e. the displacement of a photon from its previous position is dependent upon its frequency, wavelength and source (as well as any refraction or scattering it might undergo). The instant a photon is emitted from an object it is immediately travelling from the spatial point (coordinates) of emission at c. Similarly, the instant a photon hits an object, it hits it at the spatial point of impact at c. So regardless of the relative velocities of the emitting and receiving objects, the receiving object will always "perceive" the incoming photons as travelling at c.

I want to clarify/correct some of the above.

Firstly, the spatial points of emission and impact are determined with respect to the frame of reference in which the photon transmission occurs (e.g. in the case of a photon transmission between two objects located on the Earth's surface, the movement of the sun and the galaxy through space is irrelevant).

Secondly, the photon will actually seem to be travelling at c±v from the emitting/receiving object's perspective (assuming the intervening space is a vacuum). However this does not mean that c is being exceeded; on the contrary, an apparent velocity of c±v requires that photons travel at c relative to themselves. In other words, an object will still "perceive" a photon to be travelling at c once the object's velocity relative to the photon has been accounted for, and any perception of a photon velocity of c±v in a vacuum is an illusion.