Why is this happening? That's the question worth 1000 Nobel prizes.
I'm not sure in what sense it is a reality. On observable scale the reality seems to be more tied to particles, at least in our human understanding. Wave-particle duality concept to me seems just as hard to reconcile as the concept of irrationality or infinity.
These concepts work well to power our present explanation of the world around, yet can't naturally root in human brain (not mine at least).
Of course, Heisenberg's uncertainty principle is a mathematical description of observed behaviour so one could rightly argue that it doesn't really explain anything - it merely describes things.
> There are literally infinite ways to create equations that satisfy measurements.
There really aren't. You seem to be thinking of something like in the movie The Number 23. But we're talking about equations, not numbers. Take Newton's Second Law (f = m • a). What equation can you write that expresses that relationship that can't be simplified to f = m • a?
As for equations, notice that many equations in Physics have a constant which turns a proportion to an equation. This is where you have leeway in constructing more or less arbitrary equations based on the variables you think are important enough to observe.
Coming to your example, Newton's f = ma equation is really f/m proportional to a. The units are chosen carefully to make the constant 1. This works under the assumption that mass is constant and acceleration is measured measured from a non accelerating frame of reference with non relativistic speeds. So, yes there are several other ways to write that equation.
IIRC, in this context the mass m is considred as a proportionality coefficient. Such that the force is propotional to the acceleration.
Sure, rewriting this would fix the constant to 1, but this introduces a concept of specific force, force per unit-mass.
So, yes, it's possible there is some physics "beyond" the one we know, and yes in order to go beyond what we know we have to consider the possibility that some of the stuff that lay at the foundation of the current physics is wrong (or, correct up to an approximation). And many working physicists are well aware of that fact and they do consider all the options on the table.
The problem is, you have to find something to replace it and it has to work.
Thinking about all crazy things is great. "Temporarily" throwing away some assumptions can be a productive thinking tool. The Heisenberg principle (like many other things) can be both something you want to keep and use as a foundation for other explorations, and it can be something you question. The field is made up of many people, not everybody should be working on the same thing on the same assumption; I think "putting ideas at rest at this point" should be relegated to old theories that have been fully superseded, and even then they can be still useful: even Newtonian mechanics can still be quite useful even if we know it falls short.
"Number of particles" is an observable like position, momentum, spin, etc. It is a quantum property which may or may not commute with other properties, and occupies the same conceptual space.
OTOH it does not imply that a photon is a "particle" in the same sense a breadcrumb is, with a well-defined diameter, shape, or borders. It is a portion of energy of electromagnetic field that was sufficient to yank an election from a photo element's crystallic grid.
If I understand her correctly, she proposes that the reason waves behave like particles is because they transfer energy essentially every zero-crossing : for example a photon is just one half of a wavelength of light.
She has a much more interesting explanation of what i am very poorly tryingto spit out here on youtube. Bear with, because honestly she is a whackadoo but she is a smart whackadoo.
Lemme know if you want a link to the video
The argument is: Planck's relation says that a photon's energy is in proportion to its frequency. But a higher-frequency photon oscillates more times per second. If you look at the energy of a single oscillation, you get a constant, regardless of frequency. This is remarkable and so we should reframe Planck's constant as the fundamental "energy per cycle."
The problem is that "energy of a single cycle" cannot be related to other measures of energy, e.g. the binding energy of an electron in the photoelectric effect. Basically it seems like unit sophistry.
Physicists have received Nobels for inventing particles to balance equations. Why isn't that sophistry? Maybe we just need to spend a few more billion dollars on a brand new particle accelerator to figure that out.