Yes, the field is the substrate.
"I insist upon the view that 'all is waves'."
Letter to John Lighton Synge (9 November 1959), as quoted by Walter Moore in Schrödinger: Life and Thought (1989) ISBN 0521437679
It is not a breakthrough, it is just something we refuse to see, something that was known for a century."All is a wave" is the unifying principle. I am no mathematician, but the math needs to start with that fundamental principle.
The very notion of calling it "qunatum" physics is probably wrong since quantum is "a discrete quantity of energy proportional in magnitude to the frequency of the radiation it represents."
And if everything is a wave there are no discrete quantities beyond our definition of what constitutes the end, or borders, of the wave.
> I am no mathematician, but the math needs to start with that fundamental principle.
This is a weird sort of hubris. “I’m not qualified to do this job but I can certainly tell you how it needs to be done.”
> And if everything is a wave there are no discrete quantities beyond our definition of what constitutes the end, or borders, of the wave.
This is not true in multiple ways. First, it’s known that these particles exhibit quantum behavior. This is measured and confirmed over and over. Many measures are in fact quantized.
Second, existing as a wave does not mean no discrete quantities. Even in everyday materials we observe situations like standing waves that are effectively quantized.
> It is not a breakthrough, it is just something we refuse to see, something that was known for a century.
This sounds like you're about to try selling me a crystal and a magic ritual. The wording here is far too grandiose, and I assure you physicists are not "refusing to see" that "everything is a wave". Whatever you imagine that might mean.
> The very notion of calling it "qunatum" physics is probably wrong since quantum is "a discrete quantity of energy proportional in magnitude to the frequency of the radiation it represents."
> And if everything is a wave there are no discrete quantities beyond our definition of what constitutes the end, or borders, of the wave.
Mumbo-jumbo.
It's called "quantum" physics because of the discovery that many parts of nature do indeed exist in discrete steps. Yes, electron orbitals are described with wave functions - that is, the electron exists as a probability cloud, but the functions themselves are still discrete! When an electron gains energy, it jumps from one orbital to another without passing through a continuous state in the middle. That is the fundamental insight of Quantum Mechanics - energy, momentum, etc are all quantized and not actually continuous.
The wikipedia article on quantum mechanics literally covers this in the intro - https://en.wikipedia.org/wiki/Quantum_mechanics