Isn't it rather the case that all three have practical applications, they all get results, but none gives a true description of reality at the subatomic level? They don't, for example, fulfil Einstein's aspiration that "the programmatic aim of all physics is the complete description of any real situation, as it supposedly exists".
No, they are all literally different interpretations of exactly the same math. The particles and waves are NOT classical particles and waves: they are *quantum* particles and waves. And those are also quantum fields.
And Einstein was wrong when it comes to quantum mechanics, as shown by actual experiments he dreamed up as thought experiments. His intuition was that they would come out in a different way than they, in fact do.
The problem is that, ultimately, the philosophy of realism (where things have definite properties at all times) is simply false. Einstein would be disappointed, but ultimately, he was wrong in his intuitions on this.
I'm sure you're familiar with the statement attributed to Feynman and also David Mermin, that the Copenhagenists approach to QM could best be characterised as "shut up and calculate". And why not if that approach works so well in developing new technologies?
Only that hasn't satisfied those who want to know what QM means for the material world. Beginning, presumably, with wave/particle duality.
I think one of the problems is that people are trying to interpret quantum mechanics based on a metaphysics based on classical physics and that simply doesn't work with what we know about the universe now.
What we need is new metaphysics, not new physics, I think.
"Quantum mechanics is the most useful and powerful theory physicists have ever devised. Yet today, nearly [100] years after it's formulation, disagreement about the meaning of the theory is stronger than ever."
- N. David Mermin
You're right, I'm not sure if "fundamental substance" is even a meaningful concept. If it isn't, does that mean that fundamental particles may in fact be abstractions? And if that is the case, is our entire universe constructed from abstraction and metaphor?
No. There are properties that can be detected. But the way those properties change and are correlated is not consistent with classical ideas. if you use the same metaphysics to attempt to understand quantum mechanics as what you used to understand Newtonian mechanics, you will fail.
The problem is in the philosophy, not in the physics.
Mermin again;
"Having once removed the mystery from electrodynamics, let me immediately do the same for quantum mechanics:
Correlations have physical reality; that which they correlate does not."
Precisely. The universe works on probabilistic principles, not classical/realist principles. That makes a huge difference.
But it is a serious error to try to interpret the new, more accurate description of things (quantum mechanics) in terms of the old, less accurate description (classical mechanics). That is the origin of most of the 'paradoxes' of quantum mechanics.
Whatever mystery that observation removes, it seems to open the door to a galaxy of new ones.