Actually, there's a theorem about that ;) Godel's Incompleteness theorem.
I would describe the problem more like: The new model matches the old model in almost everything (because we've observed a lot). But the math works out quite nicely if itty bitty particles behave this way when exploded at super high temperatures. We have a hard time watching those particles explode, so it's not really tested. Either way it works out, it's not really going to matter for anyone who doesn't explode tiny particles.
I worry that it is the pop sci presentation of physics that non-physicists look at and think wrongly that the actual people carrying out the work are blinded by training bias (which is true for anyone, but I think far less true for experts in the field than otherwise) when in fact it's just the authors of pop sci articles and books who are ignorant of the difference between metaphor and reality. These are people who are paid to figure out how to think differently about their questions, they're not just following conventions and calculating pi to more decimal points.
Is an encryption algorithm "real"? Is the process used in proving a theorem "real"? Is the way that we model an atom "real"? No, of course not; they're all ways to represent an idea/observation through metaphor by breaking down a problem to make it look more like problems we already know how to solve. And if you just decide to approach the metaphor for understanding that idea differently, you can get massively more tractable problems.
As an example, a friend of mine in undergrad was studying crystalline domains in metals and wanted to find a way to understand better the relative misorientations of neighboring crystals in three dimensions. The metaphor as written strongly suggests that the right approach is some manner of statistical approach with a random variable representing orientation that can then be statistically analyzed to provide a misorientation distribution, but the problem is generally intractable in 3 dimensions whereas in 2 dimensions it's fairly straightforward math that way.
He instead decided to represent the crystallites in four or maybe five dimensions, which by so doing he was able to show that the math looks the same as that used for adding angular momentum using Clebsch-Gordon coefficients derived from quantum mechanical spin coupling. And found that by so doing he could turn a statistical problem into one with a closed-form solution that was quicker and easier to calculate in more sophisticated cases. With apologies if I'm explaining it wrong, this one never was quite comprehensible for me, he was far better at math.
Does he then think that crystallite orientation is literally quantum mechanical spin? Of course not. Does the math produce a testably distinguishable result? No, of course not; it should be the same result. But is it likely some future scientist with greater understanding of quantum spin coupling might be able to conceptualize the system more deeply? Definitely! This example is hardly unique.
So my point is that representation and metaphor matters, even if it's not a testably different result. To say that it doesn't matter to me seems to be saying that the current model itself is real, when it's not either! There's no fundamental reason to favor one over the other if the results predicted are the same, other than personal preference, ease of manipulation, or ease of conveying the model/metaphor to future students.
By encouraging different metaphors for the same system, you enable future scientists to be taught those alternative approaches so that they have a bigger toolbox to approaching some yet unknown future problem. We're just humans, and everyone looks at things a bit differently; none of us with a clear picture of what's really "real". Much like how there are a half dozen different approaches for quickly sorting a list, some are more intuitive or powerful or quick to execute than others.
Im not criticizing hard working mathematicians and physicists like your friend- the solution he found sounds rather elegant, and the results are testable. And you are right about having no dogmas when it comes to approaching the riddles of tomorrow- and yet, if all work you do is untestable- you are not a scientist.
In my opinion, physics is and has always been about answering the big questions, the how's, the why's of our existence. That new technology sometimes comes out of it is a bonus, not the ultimate goal.
We are never "done", that's kind of the point I was trying to convey. I completely agree that we should use science to help us deal with our current problems. Once we understand more about our world and ourselves, we will automatically get better at solving them. I'm just against the whole short-term, instant results way of thinking.
The overall point was which I might not have expressed fully is that there is in my opinion too much bias in the field of theoretical physics, and to paraphrase Brian Greene again we took a giant leap and probably skipped a few steps and no one seems to want to look back and see if we missed something.
I think one of my favorite quotes that somewhat describes this view is by Rudolf Peierls: “In recent years the debate on these ideas has reopened, and there are some who question what they call ‘the Copenhagen interpretation’ of quantum mechanics’ - as if there existed more than one possible interpretation of quantum mechanics.”
And I think that this view is antithetical to the advancement of current physics, and sadly this bias is instituted even unintentionally in most new physics students especially those who take physics as part of their degree in CompSci/Engineering.
But I'd also expect that people making new theories be intimately familiar with the current ones, right? It would be silly to expect someone to come up with hamiltonian mechanics for the first time without having ever been exposed to newtonian mechanics, even though both give the same answers to every problem. Yeah, thinking outside the box is always super hard, but you have to at least deeply understand the box before you can know enough to replace it. I definitely don't understand this particular box, but I feel it's reasonable to assume that those that do are trying their darndest to escape it -- if for no other reason than fame if successful.
All of our math is an attempt to represent things or ideas. The most important thing I learned in my physics education was how to read math as a metaphor for putting together things I understand into a picture of a thing I don't understand. But I don't think anyone serious thinks that their math is "true", such an assertion just makes no sense. The point of it is to find new ways to approach the evidence to see if it gives some different metaphor that wasn't obvious before.
I don't know enough modern physics to have an opinion on whether this is the case for cosmology or string theory, but I do know that in recent history just formulating a problem slightly differently can suddenly make the solution fit in the same framework as a known simpler problem. Not unlike things I read all the time about algorithm research at all, right?
Teaching and understanding models is predicated highly on metaphor, it's much easier to explain for instance that MRI works via a quantum effect that has the same math as a harmonic oscillator than it is to just... dive in. The model isn't the universe, but humans live by metaphor and so the model is important.
Which is perhaps not the point you were trying to make; I don't know enough modern physics to know whether a critique of these new areas as purely fantastical is justified, but it's also pretty fantastical to think of a particle in a box as if it were like a weight on a spring. Who am I to say that something about this approach can't make a currently intractable, approximate, or computational impossible problem solvable with time?