Originally Posted By: Bill S.
Correct me if I am wrongly interpreting you, but you seem to be saying that an emitting source that is accelerating relative to a beam of light will observe that light as travelling at less than "c".
If that is the case, and the source were able to accelerate to the speed of light, would it not observe the light as stationary?

I had intended to refer to the following as a response to your OP but carelessly let the chance go by.

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In their book 'The Matter Myth' Paul Davies and John Gribbin wrote (110, Viking, 1991):-

"As the recession speed of galaxies grows with distance, there comes a point at which this speed is so great that it exceeds the speed of light."

(and, page 111)

"This elasticity of space, a feature of general relativity, allows galaxies to effectively separate from one another faster than the speed of light."

and in his book 'Einstein's Universe' Nigel Calder writes (92, BBC, 1979) "If you are accelerating towards a source of light, its speed [i.e. the speed of the light it emits] seems greater. If you are accelerating away from it, its speed seems diminished."

And, whilst wearing his science hat, Isaac Asimov wrote (104, 'Understanding Physics, Light, Magnetism and Electricity', Mentor, 1966)

“To put it briefly, it is possible to deduce from Einstein’s assumption of the constant measured velocity of light that the velocity of any moving body will always be be measured as less than the velocity of light.”

and, in a footnote -

“This is often expressed as ‘a body cannot move faster than light’ but that is not quite right. It is only the measured velocity that is less than the measured velocity of light. It is quite conceivable that there are objects in the universe that are travelling at velocities (relative to ourselves) that are greater than the velocity of light, but we could not see such bodies or sense them in any way and therefore could not measure their velocities.”

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So, in relation to your question - yes - if a source were able to accelerate to the speed of light it would observe previously emitted light as being stationary then, as the above references suggest, as a result of further acceleration that light would be moving away from it thus would not be observable or detectable.