If we want to understand the underlying reality of QM we have to know a couple of “facts”. First of all we have to know the primary properties – inclusive the structure – of the involved basic quantum fields, the electric field and the corresponding magnetic field. If we want to incorporate rest-mass carrying particles in our model, we also have to know the primary properties of the scalars of the Higgs field (and the mutual interactions of these 3 fields).
The formalism of QM is dominated by the mathematical theory of Probability. However, probability isn’t an “invented” mathematical model, it is a theory that originates from experiments, throwing dices. In other words, probability represents a basic property of the involved basic quantum fields so we have to understand “the emergence of probability” by the basic quantum fields.
So your question is: “Are we not smart enough to develop/discover the knowledge mentioned above?” Because I cannot see how these facts/knowledge can disobey human logic. Actually your question is about the intellectual capacities of the present theorists.
Well, I love it to read all those comments from the active members of ResearchGate (physics) who admit that their intellectual capacities are indeed too limited. ;-))
Anyway, Gerard 't Hooft will not agree: Article Fast Vacuum Fluctuations and the Emergence of Quantum Mechanics
As an indigenous member of the Southwesten region of the United States, I would cast your query in different terms. Specifically, Modernist ideology and Scientific ideology is exclusionary and confused. My Mexica ideology would suggest that the foundational basis of QM, more clearly delineated, would reveal that the core of QM is yet to be discovered under its' scientific explorations and when more ap-propriately understood, the flow of energy that flows within our universe and existence is fundamentally poetic in nature. Logical research will never be able to discover the deepest levels of truth until indigenous poetics are better understood. Heidigger has written on the topic of indigenous poetic epistemology in relation to Aztec ideology.
I think Feynmann felt he did not understand as much about QM as he would have liked, and that no one he spoke with could answer his questions to his satisfaction. I doubt his statement was much more than that.
I think, in answer to your question, that there is a difference. Our logic is not a static thing. Sometimes, as we achieve new realizations, we need to expand the scope of our logic. So 2-value logic gives way to multi- and continuous-valued logic.
QM is a wonderful example of how the law of the excluded middle (long a staple of mathematics and logic, and valuable in its place) clearly and quite naturally gives way to the logic of |UP>, |DOWN>, and |superposition>.
I believe that we don’t understand QM, that we need to keep thinking, and that we constantly need to reconsider our assumptions.
Finally, perhaps QM disobeys logics we have set down, but that does not mean that it must forever escape our powers of reason and invention.
It strikes me that Courtney, just above gets Feynman about right. Who doesn't think that they know too little about QM?
Regarding the relation of standard logic to QM, I recall that Hilary Putnam wrote an interesting paper on that topic. If memory serves me, he examined specific proposals for "quantum logic," --revision of standard logic to accommodate inferences in QM --and rejected them.
See Putnam 1979, Mathematics, Matter and Method, Philosophical Papers, vol. I. (Cambridge U.P.), and "The Logic of Quantum Mechanics," (pp. 174-196) in particular.
Understanding is limited to the degree one can predict. Human "logic" is somewhat undefined. However, I suggest Human logic must encompass a concept of cause and effect. QM does not have such an process.
Neither, a succesion of experiments, and interpretation, starting with the Planck explanation of the Black Body radiation near 1900, many years of looking at the Hydrogen spectrum, till the Bohr model , and the later Schrodinger solution around 1925, diffraction experimets interpreted a la de Broglie wave model, and so on, till this day.