Hi Eckard
You took a brave step indentifying the departure of mathematical constructions from physical reality. One more similar step will give you the proof. But you can see the start of that step when you say;
"Let me invert your idea and assume propagation of light, for instance from the sun, towards points A and B of nearly opposite directions. You are arguing that this corresponds to the sum of both velocities, i.e. 2c, right? If we look at this, does it contradict to gamma? I do not think so."
So now consider 2 suns. They send photons at 'c' towards each other, so their relative velocity when they cross is 2c, or just a little less when relativised. Agreed?
Now consider giving your students TWO 50 Ohm cables, side by side, but sending the signals similtaneously in opposite directions. The signals will cross at a relative speed of around 400,000km/sec. I also assume you agree with that.
And if you happen to be moving one of the cables longitudinally at the same time you will simply add or subtract that additional velocity. ok?
Now you're nearly there. Consider each cable as a 'field', and EM pulses HAVE to travel at a given constant speed wrt that field. (with photons through a vacuum it is 'c'). OK?
Now if you re-read what I previously stated, remembering that but not any previous 'assumptions', you should see the whole picture.
Using M87 is a bit of an overstatement as you're right, it's a special case, but there are dozens of others at less than 2c. We have a strong theory for M87 which worlks if it's ejected from a fast rotating black hole, but that's another matter.
Nimtz wasn't alone, and there were dozens of 'explanations', but his work was repeated, or extended, at Berkeley. It's only ever been the Spanish Inquisition who have banned it's acceptance. Len Hau has also done the reverse at Harvard. None of the results have broken either postulate of SR.
Sound isn't my subject, though aspects of waves are, and I quite understand your view, however you're failing into the same trap you've exposed in saying superposition 'works well'. I'm doing this work with colleague Judith Whiffen, springing partly from the work of Davis Whiffen (ex UK NPL Head) new Deceased who was a top man in spectroscopy and superposition. The latter works well as a mechanical construct describing results, but there's no real evidence from physical reality, and we've now forgotten it's even needed! You cannot similaneously physically bash a billiard ball against all it's surrounding neighbours. Maths can agree with final results as much as it likes, but it does not actually explain any physical process!! All top physicists have recognised this. What I'm saying is that the physical process is more subtle and involves particle spin/oscillation and frequency modulation. (The model so derived is entirely physical and, frighteningly, explains almost all observed and mathematical anomolies.)!
There's now stacks of evidence for this but the mathematicians are complacently saying it's not only wrong but not necessary as maths has got it sorted. So do you really beleive sound only needs 'discrete molecule' billiard balls!?? And, if not, do you have another theory?? Do you think we should just trust maths and look elsewhere for answers? (Where?). So now, at this level not that of a student, what options can you see to particle oscillation/frequency involvement?
Peter