Dear Eckard
The plasma science basis is quite well covered in the references here; http://vixra.org/abs/1102.0016
It seems kind of accepted in the relevant specialist journals that ion plasma as the 3rd state of matter, makes up most of the 'matter' in the universe! Only when it gets joined up does it become gas or 'ponderable mass' as Einstein called it. If we look at our own ionosphere/plasmasphere, or the halo's of galaxies (see the refs) stretching out hundreds of Kiloparsecs at densities up to those refered we can see how it may have some influence!
Abel and Babel can do this but need calculators, the relative 'v', and the distances involved at the moment of synchronisation (including how far each is from the relevant end of his train). To be accurate they'd also need air temperatures, windspeed, 'n' of the windscreen glass, humidity, gravity etc, but the air each end of the train is turbulent anyway so we'll stop at the 2nd order approximation. [Godel rules!] We'll also assume both trains are receding/moving apart (moving wrt the tracks/air).
Strictly the em waves will propagate at c/n of air, approx n = 1.0003. They will however change speed a number of times, including twice at each glass screen where (as we well know!) they do the c/n of glass, say n = 1.55, on entry, and then speed up again entering the outside air, but of course speed up MORE than they slowed down (as the air in the train was moving with the train).
We don't really need to know the speed of each train as we can just use the reciprocal v and average the two out, (unless we're only relying on one person to speak at the co-ordination moment, - but they must remember the arrival times may be different and must be averaged).
The signals move through the air at c/n of the air (Doppler shifted subject to 'n', and train & wind speed) then go through the glass slow down/speed up process again, (obviously with blue shift inside the glass) then speeds up (and red shifts back again - but this time not as much) to go through the air in the train at c/n wrt the train. There will be a residual red shift to each directly proportional to the relative v.
They can do their sums either in advance or afterwards, then synchonise the clocks.(as Georgina's principles) They may need to pre set two points so each can do it individually. It is still possible if they don't have the speed/distance data, but they'd each need a spectrometer to record and analyse the travel history of each signal via absorption bands etc. (EM waves are compelled by the laws of physics to keep a log of their travels, so when humans reach a certain intelligence level their history can be fully analysed).
Of course if one of them decides to walk to the toilet at the wrong time....!
You'll see from the references to the paper that if we replace the glass screens with dense plasma the effect is the same, and if we move it laterally the time signal ('Time averaged Poynting Vector') is deflected, or curved through space (space-time).
Sorry if that got a bit complicated, but physics may actually really be more simple than folk.. once we can handle the moving variables in our minds. There were only 3 inertial frames (fields) and 2 observers involved. The 'transformation' between them is simply refraction, and c or c/n always rules.
That was straight 'off the cuff' so please do query any confusing bits, or throw me any others.
Peter
