Can an Unphysical Theory Explain Real Physics?

Recent posts pose the question to what degree standard Quantum Mechanics stdQM does explain (or can explain) the Periodic Table and chemical bonding. The standard answer is that for sure this is so, since stdQM gives a complete description of the world of atoms and molecules as the most successful theory of all of physics, and that this description of course includes the Periodic Table and chemical bonding. 

But this rosy picture can be questioned on several grounds, the most basic from the fact that there is no consensus after 100 years of brooding about the physical meaning of the  Schrödinger wave function $\Psi$ as the basic element of stdQM. But there is general understanding that $\Psi$ is unobservable as something without direct physical presence and in this sense is unphysical. 

The question then presents itself: Can an unphysical theory be used to explain real physics? 

The consensus is that stdQM correctly predicts outcomes of physical experiments, as far as tested. There is not a single experiment contradicting prediction by stdQM even if outcomes for the same experiment vary substantially.  Therefore stdQM is considered to be a theory that says something about the physics of atoms and molecules. Following a mantra of "shut up and calculate" it then appears as a black box capable of predicting outcomes of experiments, while the real physics is hidden to inspection. 

We can compare with a theory about the game of darts named Dart Mechanics DM stating that the spread of an inexperienced player will follow a normal distribution, which possibly can be verified by letting novice players play many games. The DM prediction of a normal distribution can thus be seen to agree with suitable experiments, but DM will say little about experienced players. More precisely, DM cannot explain anything about the real physics of the game of dart, since no such physics was put in. 

We are led to an idea that it may be very difficult to explain real physics using stdQM, since the physics of stdQM is hidden to inspection and so to explanation. In this perspective it is not strange that the efforts to explain the Periodic Table and chemical bonding have had mixed success, despite assertions that the success is total.

Here is what chatGPT has to say about stdQM vs real physics.