Tom,
It was the engine that came first, powered by logic. The problem is that all only know horses so keep insisting it should look like a horse or be dismissed, so it's dismissed.
The simple transition equation from my last essay is here, reducing to c = c'.
For receding observers; (wavelength=L, speed =u)) Lc = Lc-u (1 - u/c)^-1 and observed light speed then is;
f'L' = {f (1 - v/c)} {L(1 - u/c)^-1} = f L = c. ..(all subject to gamma).
As wave equations are invariant on transformation in Euclidean space the (unobserved) incident and scattered wave are simply;
y = yo sin 2pi(f t 1/L x) and y' = y'o sin 2pi(f't' 1/L'x') [gamma].
The fuller description is in the 'Much Ado..' 2012 essay, plus other cases in the appendix (and a separate quantum mechanism deriving gamma itself in another paper). But now consider the real scalar property here; wavelength, and look at the Planck spectroscopic distributions group, which is NOT Doppler-shift invariant!
If we use the medium to medium Doppler shift equation when considering measurement by a lens it all comes out making logical sense. The confusion now is that we're so used to using frequency, and assume we're measuring something before we interact with it, that all we can ever see are horses and camels! That's where we need to look further than present ingrained beliefs and maths, and that's what I'm trying to work out how to enable. All help is welcome.
If you now re-read the middle of this years essay again the 'elephant in the room' should emerge. But it needs to be focussed on, don't let it escape!
There are a few other derivations in my last two essays but that's about the limit on my maths. When the engine was first conceived and invented it didn't arise from maths, or even need any. Advances in scientific understanding can't arise from maths, as Einstein so often pointed out and Wheeler also said ('never do maths before you know the answer'). My skills lie elsewhere, I'm afraid I can't also jump through hoops on horses. The mathematicians are the experts and are very welcome to do the relevant maths!
What I've found is equivalent to the Rubic Cube solution. It's self apparently correct and I know how to get there, but the assumptions used aren't what others use or expect. My skills don't also extend to do all but the basic maths, but that doesn't make any red squares turn white! If you're any good, be my guest. I wish someone would (or point out any colours out of place so I can get back to sailing).
Best wishes
Peter
