Dear Eckard Blumshein,
A tour de force! Congratulations on an incredibly information-dense essay.
I appreciate your beginning with Fourier transforms, without which quantum mechanics surely would not exist. You have for several essays focused on cosine transforms providing insight based on your audio work. Your issues concerning t = 0 are subtle. I do agree that physicists tend to stay away from the foundations of mathematics, some actually considering mathematical structure more fundamental than physics.
You note a truly fundamental assumption besides causality: "There is only one reality." My essay treats the fundamental nature of time essential to reality, which is universal simultaneity.
You observe that rigorous formalizations are notorious for causing paradoxes. I observe that all special relativity (SR) texts base the derivation of the Lorentz transformation on two inertial frames, seeming to impute that the very existence of the Lorentz transformation implies the existence of two (or more) time dimensions, per Einstein. In An Energy-Based Derivation of Lorentz Transformation in One Inertial Frame I prove that two inertial frames are not required for the existence of the LT. I believe this is both mathematically and physically significant. In the first place it gets rid of the paradoxes associated with Einstein's 'space-time symmetry'-based "gedanken" experiments [based on railway examples not subject to measurement] while retaining the relativistic [energy] particle physics so well-supported by twentieth century physics.
In a yet-to-be-published a paper I examine Einstein's faulty 'simultaneity detector' based on which he declares "the relativity of simultaneity". Deriving the Lorentz transform in one real world (one inertial frame) argues against multiple time dimensions (and all of the non-intuitive nonsense that depends from this) and leads to the classical understanding of time as universal simultaneity. His denial of this caused Einstein to admit "the now worries him seriously." Universal simultaneity is, of course, now.
CS Peirce, as you note, insisted that "axioms are not a priori truths, but synthetic statements." Einstein's two axioms are contradicted by a one-frame derivation of the Lorentz transformation and by local gravity as ether. Again you state (p5) that "unjustified rigor is to blame for [much] nonsense." Einstein's rigorous derivation of LT in two inertial frames is the basis of much nonsense that vanishes when LT is derived in one inertial frame.
I also like your treatment of symmetry. You say "in reality, symmetries tend to be rarely perfect." Amen. The SU(3) basis of the Standard Model is valid only if masses are equal. In reality the relevant masses differ by two orders of magnitude! Approximate symmetry is all that one finds in the real world.
I also like:
"Should we try and alternatively deal with some fundamentals of physics from the perspective of elapsed time-span...". I would apply this to the elapsed time of the cycle of vibration characterizing the energy of the 'clock' mechanism, and the realization that clocks actually measure energy, and only indirectly are measure 'time'. This demolishes Einstein's clock-based derivation of SR, while fully retaining the energy-time basis of relativistic particle physics. Most particle physics occurs in collisions, which obviously occur at one point in time, not in two time dimensions, as per the theology of SR.
You then note that
"Time t and circular frequency w constitute a pair of conjugate quantities."
That is, time and energy! And note that circular frequency is the basis of all clocks.
In conclusion, you say
"Let's likewise check the historic line of reasoning behind what led to Einstein's special theory of relativity for possibly not justified analogies and generalizations."
That, of course, is exactly what my essay does. I believe our conclusions are almost identical.
Congratulations on a truly magnificent essay.
Edwin Eugene Klingman
