Viraj
I'm sorry but I'd thought the ball was 'back in your court' to respond to my Oct 1 post on my blog or to my earlier post on yours. I was also flat out fighting the slow system, reading essays and responding to (250!) posts. But my most sincere apologies must come for your rating, as I've checked, and did not indeed get to score your essay despite my genuine notification of intent. To explain; On first reads (part 'speed reading') I do a list and pencil notes, which on yours was '8-9'. I comment on good ones, but like to read again before scoring. The problem was I had a big 'log jam' at the end as the system slowed right down. I kept having to close and re-load the page as it froze. I had to prioritise those around the cusp, but was then online till 2.30 am UK time, until I fell asleep waiting for a page to change. I'm desperately sorry but yours was one of just a handful that didn't get scored. It seems even with a 9 it would still have been well out of contention. I may score all earlier next year (yours first, with the interest!)
Now to nitty gritty; I'll just zero in on areas of disagreement; You suggest AE was wrong borrowing Poincare's 'equivalence of all inertial reference frames.' I disagree, and find that consistent with Galileo's ship (all ships equivalent) and Maxwell's geometries, but each has a boundary zone where em waves change speed to the local c of each ship. All labs in all ships thus find c. If the window is open and the wind blows in at v, light does c/n with respect to (wrt) the air. If shut, the window glass re-emits it at c/n wrt each window.
You say; 'Nature's processes are inherently mathematical' which is fine, but can fool us if we forget there are underlying REAL processes. I hope you've read Wharton, Sycamore, McEachern and Schafly's excellent essays explaining why. Maths is abstraction, and we have no right to assume any algorithms we find approximate it's evolution accurately model natures far more complex mechanisms.
You agree with the 'simple idea' I identify, but fail to apply it's consequences. Wavelength lambda changing on frame transition is due to a REAL MECHANISM not some formula! This then resolves the biggest problem and paradox in physics of the 19th century, which was the reason SR was invented; CSL for all moving observers. The 'sister' problem of 'CSL irrespective of EMITTER motion' also then emerges by the same boundary mechanism. You should well understand this mechanism, as the boundary condition is equivalent to a 'fluid dynamic coupling.' One frame one side, the other on the other side, and turbulence between. Both sides particles re-emit absorbed em waves at c.
It may well then be true that; 'a fraction of energy in action is usurped to form an organic link with the background energy field.' That; 'DQ = (Mv/c).u is usurped to form the organic link with the background leaving Mvc(1 -u/c) for relative motion. But you then suggest 'This is the 'physical basis' of the Lorentz transformation.' You say; the photon loses energy to the field, and quantify it. Great, and important, but more important to understanding is How? What is the real mechanism? None of that is a real 'physical basis', but it is an equivalent mathematical model, as Lawrence points out, and if it fits with logical consistency and all observation (i.e. resolving paradoxes and anomalies) perhaps a closer match to the real mechanistic process.
So I disagree with your precise identification of the faults with the STR, and the solutions. I can say this because I provide a consistent logic for the (as observed) STR axioms. I do however entirely agree an energy draw in the boundary mechanism, which is also responsible for part of the cosmological redshift.
Don't ask me to judge any maths. There are many far better qualified. What does emerge however is that any 'general equation of motion of a particle' can only be wrt a local background! And lambda is not invariant on LT ('acceleration in non zero time').
Lastly, for now, I can't yet agree your derivation of atomic clock 'time dilation', because again 'speed' is only a relative concept. If it is an affect of relative acceleration then that might fit into the big picture. You should be aware that Hafele Keating was a crock. They were forced into an SR propaganda exercise to get published. I touch on that in this short article;
Apart from those matters, which I'd think are all resolvable, most concepts seem very consistent. I also need to better understand parts of your work, including the geometrical derivations, but think you do now also need to read my own essay again slowly to find the reasons for my comments above, which all form essential components of a consistent ontology. As with a boat, one part taken away, like the log hull fitting, means the whole lot sinks (as I found out courtesy of MDL a while ago).
Best wishes, and apologies again.
Peter
