Eckard,
Please understand that I am acutely aware that my own lack of education might lead you and others into some ambarrassment attempting discourse with me, and I can only apologize. Until about two years ago I was in a poverty/political trap that constrained any mobility. Where I'm coming from I could carry all the hard science and math books from the new modern public library under one arm, the reactionary right-wing politics threatening European stability at present has always been pervasive where I have lived. Now I have a computer and can begin to find some intelligent reading. (And I still have two of my upper teeth in more or less one piece!) And I've relocated to a small liberal arts college town.
So... I am not familiar with Michelson's discussions with Thompson but not surprised they would have been engaged. I am aware that at the time when Maxwell conducted his exhaustive analysis of Faraday's results, the 'aether'
medium in Newtonian space was the prevailing thinking. What I find important of Maxwell's discovery of the 'c' proportional difference of electric and magnetic difference of intensity between point charges, is not only that it means light is only one segment of the spectrum, but all physical chemistry is dependent on that proportion being constant. Perhaps that it why Morely, a chemist, was interested in Michelson's efforts. I understood it is Michelson that attempted to prove the aether existence, which failed in the null result. It is an interesting footnote that some aether based caculations had determined that the physical property of the aether would have had to have a rigidity equivalent to steel for the wave form to transmit an energetic response across space (I think I read that in an Asimov book). I have wondered however if gathering evidence by the time of Michelson's first interferometer had not called the aether hypothesis into enough question that it was simply politically expedient to present the experiment in terms of 'confirming the aether wind'. It seems many concepts that become the prevailing wisdom at any time, such as we now understand the Electromagnetic Spectrum to be independent of any medium, have had a lengthy incubation period. Relativistic ideas go back to Galleo and beyond.
Actually, Eckard, though I have striven to understand both SR and GR at least conceptually, I am quite comfortable with your own 'good old notion of ubiquitous time' and also find the theoretical climate to be more productive of a 'snowstorm of mathematics' than real progress. I like the tried and true method of experimentation on a controlled workbench, and if truth were admitted the much hyped success of QM is in reality the product of engineers who having tested the theoretical predictions to no avail, have gone back to the reliable technique of 'poke it with a stick and see what it does'! And if an arbitrary scalar increment of time is acceptable in QM such that it 'zeroes out', then it's as good a methodology in classical physics of 'tick, tick, tick' to explain the null result of Michelson. I think you summed it correctly that 'all numbers are ideal', it's our science and we choose what method we restrict our inquires to, and how we want to devise our reference frames. The only final criteria is that in following any inquiry we do not violate any of our own axioms along the way.
I won't digress about mass increase with velocity, other than to propose that there might be a 'break even' point where a quantity of energy at rest will prescribe a proportional density that constitutes matter and which will behave under acceleration as a mass increase, while a smaller quantity will prescribe a proportional density which will behave as an electrodynamic charge and behave as a decreased density under acceleration with applied energy. And if Lorentz and Poincaire don't like the speed I'm going now, they sure as hell won't like the other one.
Seriously on topic of Why Quantum, first we have to resolve the 'zero point particle' absurdity. Singularity is a mathematical property not a physical property. And for more than a century science has said 'E=mc^2' and the EM spectrum is a wave and the EM spectrum is a particle. Those who write checks on a black budget (government industrial academia) want a damned particle! Put some energy in one spot and make one that will last long enough to put a dent in something else! Then and only then will science save itself from itself and the public will again think of it as was commonplace in the era of Newtonian application to industrialized progress. There has to be discrete somethings made manifest to argue about quantum probabilities in the first place. And until we do that, the public and politicos will consider science just a pissing contest among prima donnas.
I'm not versed if Fourier Analysis, but would think the direct connectivity geometrically in cosines would be readily adaptable in continuous transformation of wave characteristics.
What is the acronym, IIrc? Pardon the length of this, jrc