Peter,
First of all I would like to correct something you have mentioned about someone else. What I meant about Lawrence Crowell is the exact opposite. In my opinion he seems to have the exceptional ability to get the essence of another's view point even with a quick browse. And I quoted his comment to confirm, that he too had come to the same conclusion as Sergey Fedosin, that all RELATED phenomena can be depicted in their concatenation by simple Euclidean algorithms, which (phenomena) SRT purports to explain (in an ad hoc and a fragmented manner) by complex mathematical formalisms and far-fetch propositions.
It is true that I did not cover the whole of your essay in my critique. In fact it is impossible for one to do this in a single post. It has to be done through a series, even to have a partial effect. I started off with your Act 1. Your position there about the frequency indicates where you were heading. Given the fact that E = hf, for you to state that frequency is a derivative appears a misconception. Am I then just to state it and leave it at that? Or am I to demonstrate that frequency is primary, by discussing it in reference to CSL and refractive index etc.? The latter is what I have done, to go step by step into other areas. So what I have done is an in-depth critique of your position than making mere statements.
My point is that physics from the very beginning has started off on a wrong footing, leading to wrong kind of mathematization, viz., linear approximation of non-linear processes. It has started off with Newton's corollary to the second law. "If any force generates a motion, a double force will generate double the motion, a triple force triple the motion ......".
There is nothing special or magical about relativistic phenomena. It is only that at classical velocities, the EFFECTS OF NON-LINEARITY REMAIN IMPERCEPTIBLE. At very high velocities, the effects of non-linearity develop exponentially, and what were imperceptible before (at lower velocities) MANIFEST THEMSELVES PROMINENTLY. And it is these effects that (appeared as if sprung up from nowhere and unaccountable by classical mecahnics) have been given the term "relativistic phenomena". This simple point has not been grasped. Once this point is grasped, then the task is to DISCERN how the non-linearity works in all conditions.
Relativity theory asserts that laws of physics are the same in all IFR, but at the same time it is based on the idea that physics is different in one and the same frame for particles depending whether they move at classical velocities or near light velocities.
By "simplest conceivable NON mathematical idea" if you meant that we should first think in terms of physics and then DISCERN the mathematics behind it, then I agree fully with you. Well then, we must start off by correcting Newton's above proposition to "If any force generates a motion, a double force will generate LESS THAN double motion".
In trying to discern the geometry of this relationship, since the linear addition of Mc2 and pc (represented as line segments) does not get you there, then we must go for the non-linear addition. This is exactly what the energy-momentum equation confirms. But nobody has thought of considering the Pythagorean implication behind this equation and to extrapolate it downwards for motions of particles under all velocities.
Having taken the first step in discerning the geometry (of the energy-momentum equation), we then have to go back to physics. How do Mc2 and pc combine and form a system. You then look around and see such things as that when an electron and a position are created they have more energy than the photon that generated them, and when they re-combine the whole is less than the sum of the parts that combined. This gives a clue that it is by LOSING a fraction each of Mc2 and pc that they create the NECESSITY to combine. It is their mutual depravity of energy that make them share their energy to overcome their mutual deficiency. It is found the fractions lost have to be Mc2(1 -1/gamma) and pc(1 -1/gamma). Now you feed these back into your geometry and find the nexus between all the phenomena in their concatenation. And this is how the process has to go on.
You have commented: "I also agree "We need to set aside the dichotomy between particles and waves. But your explanations do look apparently rather fixed on photons". I disagree. In my essay, I have dealt with fermions (particles), and in my posts to you since they referred to whether of not frequency is a derivative and to CSL, I obviously had to refer to photons.
Best regards,
Viraj