Eckard.
It is simply exposed by analogy.
A boat has a maximum speed of 'c' kph. It is moving on a river, which is flowing at v kph. 20 observers (Ob1-20) are given video cameras and told to record it so it's speed can be analysed. The first 17 take the video from cars going up and down the bank, and back and forth over bridges, from trains, cycles, aeroplanes, the space station, the moon, jogging across adjacent fields and from other moving boats. They all get different results!! Ob18 is standing still, on Earth, on the river bank. So.. Does he get the result 'c'?
Of course not he get's c plus v.! ...Ob19 then uses the Hubble space telescope camera! SO... Does he get 'c'? ...Of course not - he gets c plus v plus v2(=orbital v of Hubble).
So.. one left! Ob20 is the only intelligent life form. He jumps into the water, or onto another boat, and float at rest wrt the water, videoing the boat as it comes past close by (LOCALLY), and his result gives precisely 'C'.
The stream from the Quasar is the river. it has 'incentric' (graded) motion, going slow beside the bank and fast at it's centre. (There are some super cross sections through the jet streams from spectroscopy in some papers on the web). In all this time the boat was complying with 'c' and knew nothing of all the fools rushing around with cameras, who might as well have been on another planet!
Was that understandable?
The sq root formulae was originally Fresnels, for another (proper) purpose. The term was wrong, is there a handy term for the infinite curve produced?
I DON'T actually prefer a 'digital' field theory. Nature may be called whatever we wish but the model consists of an unknown condensate field of energy potential which is of limited compressibility, equivalent to Edwins 'C' field or the old 'ether', so may be as continuous as the waves it propagates. When perturbated or compressed (by meeting a medium doing 'a' relative speed) particles are condensed. These are initially ions, i.e. a plasma. These then impliment the change in f and or lambda (subject to which way the observer is rushing around with his camera!) to maintain 'c' and conserve E locally within the new co-moving medium. These ions can bunch together to make more or less intelligent life forms and their houses.
i.e. Matter would not exist without discrete particles, but the field they condense from is continuous. It is not however entirely a continuum! as it is in what might trendily be termed 'blocks' of continuum. Whether we call a wave continuous is semantics! (see Ken Whartons excellent and very readable essay).
If you'd like any of the evidence follow the references or do just ask.
This is mega paradigm changing stuff you know!
Best wishes
Peter