> I mean, that's because the language of physics is mathematics.
But it is not a study of it! Mathematics is a tool, not the thing being studied.
This is lost on some people.
There are properties of the real world that are studied, and there are properties of the mathematical models that are used.
They are not interchangeable.
Similarly, saying that the "this specific mathematics is all there is, just understand that" when a simple verbal statement can be made that is not covered by the mathematical model doesn't mean that the statement is somehow invalid, it means the model is incomplete or narrow in scope.
There is this downright perverse notion in QM that the models are what reality is. If the model can't answer something, then the question is meaningless, etc...
Meanwhile the model has assumptions and simplifications such as linearisation, no GR or even no SR, and so forth.
My point is simply this: The mathematics of QM is not equipped to answer fundamental questions like "what is a particle" or "what is a photon".
> whether or not you want to invoke X depends on the calculation you're doing.
I'm not debating that the simplified models aren't useful, widely applicable, numerically useful, make predictions, etc... I'm simply stating that physical reality behaves in single, definite way.
> Similarly, saying that the "this specific mathematics is all there is, just understand that" when a simple verbal statement can be made that is not covered by the mathematical model doesn't mean that the statement is somehow invalid, it means the model is incomplete or narrow in scope.
Not necessarily. It may mean that the verbal statement invokes a language game to define a category that has rules incompatible with the rules of the formal model.
> My point is simply this: The mathematics of QM is not equipped to answer fundamental questions like "what is a particle" or "what is a photon".
Sure it is. A particle in QM is something that obeys the formal structure laid out. Dijkstra had some very biting things to say about being unable to cope with true novelty because you're trapped in reasoning by analogy (EWD1036).
At a risk of reiterating the same argument: You keep agreeing with me and perhaps not realising it.
> incompatible with the rules of the formal model.
Yes. I agree! In many cases this is just means that the statement is "out-of-scope" for the model. That's fine. That however has no bearing on the validity of the statement, unless the model is all-encompassing. Quantum Mechanics is not all-encompassing, it is not a TOE, and this is well known. It's just that people forget this sometimes.
> A particle in QM
Again, you're agreeing with me. The QM model has a notion of particles that is both a mathematical abstraction and a simplification. It's not what the physical world truly does. It cannot "explain" particles.
> obeys the formal structure laid out
So if I were to write a computer program with things in it that obey the same rules, are these things suddenly real, physical particles just like electrons? How about phonons? Holes? Anti-particles?
Particles are abstractions. They're labels humans assign to certain mathematical structures in certain models. Some of them, like leptons, are real things that exist whether or not they're named. Some of them aren't quite as real. Photons are questionable.
Working physicists were surveyed and asked if they think photons are "just a useful abstraction" for orbital interactions or if they're truly real, in the sense that individual photons travel through space like little point particles. They didn't all agree.
Before you argue that I'm wrong somehow, first figure out why theoretical physicists don't agree about such a basic concept.
> Dijkstra had some very biting things
Dijsktra should have known better than to say that, because the converse of this is that it's easy to lose touch with reality by getting too deep in the weeds of abstract algebra.
"But it is not a study of it! Mathematics is a tool, not the thing being studied."
Who knows? Mathematics turns out to such an acute tool for understanding physics. One might be inclined to say that we live in a mathematical reality. The quoted statement is more a statement of philosophy than of fact.
One might be inclined to say this if one doesn't understand the difference between physical nature and our consciousness of physical nature.
Mathematics does not exist outside of human minds. It is a method for measuring and describing the world around us that happens to lend itself to the study of its own conceptual structure.
Nothing in nature follows mathematical laws. Protons don't consult logarithm tables before they move through space. Particles don't consult statistics textbooks before they "decide" if it's time to decay. They act according to their nature, and that's all.
But it is not a study of it! Mathematics is a tool, not the thing being studied.
This is lost on some people.
There are properties of the real world that are studied, and there are properties of the mathematical models that are used.
They are not interchangeable.
Similarly, saying that the "this specific mathematics is all there is, just understand that" when a simple verbal statement can be made that is not covered by the mathematical model doesn't mean that the statement is somehow invalid, it means the model is incomplete or narrow in scope.
There is this downright perverse notion in QM that the models are what reality is. If the model can't answer something, then the question is meaningless, etc...
Meanwhile the model has assumptions and simplifications such as linearisation, no GR or even no SR, and so forth.
My point is simply this: The mathematics of QM is not equipped to answer fundamental questions like "what is a particle" or "what is a photon".
> whether or not you want to invoke X depends on the calculation you're doing.
I'm not debating that the simplified models aren't useful, widely applicable, numerically useful, make predictions, etc... I'm simply stating that physical reality behaves in single, definite way.