This answer to this is actually known and is a consequence of Heisenberg's uncertainty principle. Here's a youtube video about it: https://www.youtube.com/watch?v=QPAxzr6ihu8
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.
Heisenberg's uncertainty principle should probably be put the rest at this point. From the beginning it was more "capturing" our inability to move beyond the physics as we know it. It's like tying your shoe laces. I always found it fascinating how firmly most physicists believe in the equations someone came up with, just because it agree with measurements. I mean that's real nice and all, but just because something agrees with measurements, doesn't make it a fact. There are literally infinite ways to create equations that satisfy measurements. But sure, a few decades of research in the early 20th century and that's it. This is all we can do. Let's just accept that lol.
Our current models are only good until we find a better model that replaces them, one which can explain phenomena we observe , which the old model didn't.
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same assumption; I think "putting ideas at rest at this point" should be relegated to old theories that have been fully superseded, and even then they can be still useful: even Newtonian mechanics can still be quite useful even if we know it falls short.
That's how all of physics is constructed. Even things you may think are obvious, like Newton's 3 laws of motion, are only accepted because they agree with our measurements. How else should we determine their validity?
> 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?
The uncertainty principles are inequalities, not equations. And that is something you can write with multiple forms.
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.
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.