SR and classical Doppler shift

[JesseM]

Thanks JesseM I'll need to educate myself on worldlines. Your acceleration point is interesting as this can be measured absolutely without external reference. Also interesting in relation to C as acceleration could continue indefinitely without limit.

Yup, but note that there is a difference between "proper acceleration" and "coordinate acceleration"--a ship's proper acceleration determines the actual G-forces felt on board, while coordinate acceleration determines how its velocity changes relative to some fixed choice of inertial observer calculating the ship's motion in her own inertial rest frame (proper acceleration and coordinate acceleration coincide instantaneously if you pick the inertial frame where the ship is instantaneously at rest). A ship could experience the same proper acceleration forever, but relative to some inertial observer the coordinate acceleration would be continually getting smaller in magnitude, so the ship would never actually reach light speed in that observer's frame (or in any other inertial frame)--see http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html . On the other hand, if it were somehow possible to give a ship constant coordinate acceleration until it reached light speed, the proper acceleration (and thus the G-forces felt on board) would go to infinity as it approached light speed, and the energy required to maintain this ever-increasing proper acceleration would also go to infinity (which is one way of understanding why it's impossible to accelerate to light speed).