Constantinos,
I'm glad we got to a point of some mutual understanding, too. The concept underlying your hypothesis is one that was abandoned long ago for lack of a mathematically consistent rationale that fit the experimental interpretations of the era, and is still difficult to grasp. What I found most difficult was in confronting the numerous iterations of the quanta in arguing against doing so. It just reinforced the conventional approach. A lawyer I know, whose father was also a lawyer (funny how that goes), is fond of a saying of his Dad's; "A barrel sits on its own bottom". Meaning, don't remind the court that your adversary has a case (!).
But don't feel yourself so all alone in trying to figure out what the heck physicists think they are talking about. Your message is the same that is always being sought, and in one sense goes to what Tom Ray points out - that we might not find answers until we find better mathematics to define measurement of space, time, action. Everything in front of me is in the anterior hemisphere of my observation, everything behind me is in the posterior hemisphere. Similarly, everything above is in the upper hemisphere and all below, the lower. Same with the right or left, so we can measure from one octant to another. But not as if a line from my upper left octant goes to a point in my lower right like a beam of light through a lens of barium glass. There is nothing upside-down and backwards to the physical relationship between what's in front and what's behind me. So we have to develop the math of bijective complex planes with the rules of IFF. Non-commutative algebras. There has GOT to be a simpler way! In human daily experience we don't even think about it! We just move without confusing where things are around us, and without knocking over our neighbor's beer.
Incidentally, without sorting out the whole rationale of your conditional criteria of 'if and only if', it did make me wonder if there would be an operational correspondence to the 'if and only if' criteria of complex analysis. (That, I'll leave to those who like to play with math!)Topology is a math of continuous simple connectivity.
I have often thought what physics needs is a writer in mathematics of the sort Isaac Asimov was in physics. And I still occasionally refer to my $4.49 used copy of the 1988 printing, three volumes in one, 1966 copyright, 'Understanding Physics'. It presents in conversational prose with the simplest math, how the ideas in physics developed, and what the thinking at the times were. And in hindsight, that gives a perspective of "what hadn't been known, or considered then?" The argument between the corpuscular (particle) form of light that held sway in the 18th century and the wave form that was ascendant in the 19th, was never completely resolved, and morphed into the strange world of todays physics. Today's physicists have no more difficulty accepting non-locality and superposition than did earlier physicists accepting that to be a wave and move through a solid crystal, light had to be a transverse wave similar to that on the surface of water. While if it also moved through the ether as a longitudinal wave like the compression and rarification of sound through the same water, the ether would have to be both orders of magnitude more rare than the thinnest gas yet more rigid than steel. Today the 'massless particle' would be expedient even without Lorentz, because if the 'light particle' had any mass at all the sheer numbers of them that would have struck the earth would have added up to enough to make the orb heavy enough that we would have spiraled into our star long before we climbed out of the sea.
Perhaps what makes the limiting conditions of what amount of energy materializes as a periodic waveform, is how massive gravitationally, a source is in relation to its physical size volumetrically, compared to the amplitude of the wave. Perhaps frequency is a consequence of how fast the energy of any quantity might potentially seek to stream away from the source but runs into the limit of light velocity. Like a dog getting excited by a sound on the porch, and trying to stop just as it hits the limp rug on a freshly waxed hallway floor. And... so how is it physically(?), that the probability for energy to spread across frequencies is observed as the curve of intensity of frequencies in blackbody radiation, when the domain of probability for any frequency would be f^2? If we accept the continuous paradigm, perhaps it is simply that a too feeble a quantity, will not escape the gravitational integrity of the source mass. And mass is only a 'mass of energy' until a unit quantity specific to a unit volume is determined which exhibits the characteristics we associate with matter, not least of which is longevity.
Much to chew on. It would be nice to hear what people with well developed math would have to say. I honestly get to a point, where I exceed my own limitations in trying to gather new knowledge in a way I can assimilate, and find myself as I have recently, on the threshold of not knowing a damned thing. It's time for me to step back and focus on other things that don't require much focus. Cordially, jrc
