1. The Unspoken Convention: Representation Mistaken for Ontology

In traditional quantum mechanics textbooks and the working habits of quantum theory, there exists a pervasive yet never explicitly stated convention:

To treat mathematical representations—wave functions, operators, Hilbert space structures—as direct descriptions of “what the world is.”

Typical manifestations include:

• Taking the wave function as the complete existence of a particle, without asking what underlying field structure or ontological picture might give rise to it;

• Defining “spin” solely through its two-valued representation and Pauli matrices, without inquiring into the physical origin of the electron’s internal angular momentum and magnetic moment;

• Regarding operator algebras and eigenvalue structures as the ontology of observables, rarely questioning what actual fields or motions these operators correspond to.

Under this convention:

Ontological questions are swiftly replaced by representational ones.
Asking “what the world is” becomes “how do we compute the wave function?” or “how does the operator act?”

Quantum theory thus becomes a highly efficient predictive tool—what you call “instrumental quantum theory”—
rather than a serious account of the structure of physical reality.

This convention greatly enhances operational efficiency: physics students can “learn only how to calculate, without worrying about what the world actually looks like.”
But it also produces, at a deeper level, the two consequences you identified:

• Mystery: Because ontological questions are excluded from discourse, all perplexity about “how the world could possibly be this way” gets trapped in the semantic gaps between operators and wave functions—manifesting as the “measurement problem,” “interpretation issues,” or the nebulous tangle of “wave–particle duality.”

• Incomprehensibility: For those unsatisfied with “knowing how to calculate but not what it is,” quantum mechanics appears as a rule system that “must be applied but never questioned.” Any attempt to probe deeper leads only to circling within the instrumental framework.

2. The Case of Spin: From “Two-Valued Representation” to “Mysterious Spin”

The earlier discussion on the ontology versus representation of spin provides a vivid illustration of this convention.

• Ontological level:
  Spin arises from the electron’s internal angular momentum structure and magnetic moment,
  manifesting in atoms—as observed in spectra—as two stable eigenstates: “aligned” and “anti-aligned” via spin–orbit coupling.

• Representational level:
  The two-dimensional spin space, Pauli matrices, and ${\hat{S}}_z=\pm \hslash /2$ are merely an algebraic encoding of these two spectral states and their angular momentum algebra.

Yet textbooks typically begin at the representational level and present it as ontology:

• They do not first explain the spectroscopic origin or internal angular momentum structure;
  instead, they declare outright: “the electron has spin-½,” “its spin along $z$ is $\pm \hslash /2$ .”

• They fail to emphasize that this is merely an eigenvalue structure in a two-dimensional spectral space,
  leading readers to naturally assume that “the electron itself is a tiny vector that can only point up or down.”

The result:

What was originally just a representational choice—how to encode two spectral eigenstates in the minimal linear space—
is taken as the complete rotational structure of the electron in physical space.

This is precisely representation mistaken for ontology.
And it is this substitution that makes spin appear paradoxical:
“not classical rotation, yet binary-valued, yet described by a three-component vector operator in 3D space”—hence deeply mysterious.

3. The Same Pattern Repeats Across Core Quantum Concepts

Spin is merely the clearest window. Similar confusions recur throughout quantum theory’s foundational concepts:

• Wave function:
  It could be understood as a global modal expansion and statistical encoding of an underlying field structure within a spectral method.
  But instrumental quantum theory treats $\psi (x)$ as “the full reality of a particle at $x$ ,” often instructing students: “Don’t ask what lies behind $\psi$ .”

• Uncertainty principle:
  It could be seen as a mathematical limitation inherent to global spectral representations (e.g., Fourier analysis): one cannot simultaneously sharpen conjugate variables in the same global wave function.
  But when representation is taken as ontology, it is read as: “Reality itself is fundamentally indeterminate and non-local,” leading to claims of “inherent randomness” or “the non-existence of definite properties.”

• Wave–particle duality:
  It could be interpreted as a unified field ontology manifesting wave-like patterns or localized events under different experimental scales and configurations.
  But within a language limited to wave functions and operators, it is framed as: “Microscopic objects change their nature depending on the experiment—sometimes waves, sometimes particles,” which inevitably sounds mystical.

In all these cases, the common root is the same:

“Using representation as ontology” has become an unspoken but universally practiced convention.

4. The Core Source of Quantum Mechanics’ Mystery and Incomprehensibility

From a realist or NQT perspective, this convention has several severe consequences:

• Mathematical tools are mistaken for direct images of the universe.
  Once we assume “wave function = reality itself,” “two-valued spin space = spin itself,” or “operator algebra = the logic of the world,”
  any confusion about these formal structures is misread as evidence that nature itself is absurd.
  Thus, “abstract formalism is hard to grasp” gets elevated to “the world itself is incomprehensible.”

• The continuous transition from classical/field theory to quantum theory is severed.
  If we acknowledge that classical fields and particles remain valid ontological entities at some level—and that quantum formalism is merely their spectral and statistical expression—then concepts like wave functions, uncertainty, and spin become intelligible.
  But instrumental quantum theory, by substituting representation for reality, discourages such ontological grounding.
  The result: quantum theory appears as a set of pure mathematical rules dropped from the sky, deliberately disconnected from our physical intuition—making it inherently difficult to digest.

• Interpretational debates become linguistic games.
  When ontology is abandoned, discussions of quantum interpretations can only revolve around “different ways of talking about the same mathematical object”: Copenhagen, Many-Worlds, QBism, instrumentalism, etc.—often just varying philosophical attitudes toward identical formalism.
  Many “profound disagreements” are not about competing physical models, but about rhetorical preferences regarding the same representational structure.

In this sense:

Taking representation as ontology is the default convention of instrumental and traditional quantum mechanics,
and it is precisely this convention that creates the central paradox of quantum theory:
it is immensely powerful yet “mysterious,” perfectly calculable yet profoundly unintelligible.

5. Natural Quantum Theory’s Remedy: Restoring Ontology, Demoting Representation to Its Proper Role

What Natural Quantum Theory (NQT) does is to bring this hidden convention into the open—and then reverse it.

• First, reconstruct a clear physical ontology:

• The sole fundamental entity is a continuous field, including its topological structure;

• Particles are localized, stable vortex or topological solutions of this field;

• Spin is a real-space property of the field’s internal angular momentum and magnetic moment coupling;

• Strong, weak, and electromagnetic interactions unify at higher-order or topological levels as different phases or modes of the same underlying field.

• Then, reinterpret quantum formalism as a “spectral–statistical representation” of this ontology:

• Schrödinger equation and wave function → spectral expansion and global mode encoding of the field ontology;

• Uncertainty → a mathematical constraint of global spectral methods, not an ontological prohibition;

• Two-valued spin space → linear-algebraic packaging of the two stable spin–orbit coupling eigenstates observed in atomic spectra.

• Finally, demote representation back to its rightful status as a tool:

• Wave functions, operators, and Hilbert space algebra remain extremely powerful instruments;

• But they are no longer treated as ontological declarations like “the world is this function”;

• Instead, they become the working language for performing global analysis and probabilistic prediction given a deeper field ontology.

The outcome:

• The computational power of the instrumental framework is preserved—and even strengthened by clearer foundations;

• Intelligibility at the ontological level is restored;

• The sense of mystery no longer stems from “the world being absurd,” but from the historical legacy of conflating tools with reality.

Spin is just one example. Wave functions, uncertainty, measurement, wave–particle duality, and even the gauge-group patchwork of the Standard Model can all be re-examined within this framework. The key insight is:

It is not that the quantum world is inherently mysterious—
but that we have long operated under a forgotten convention:
using mathematical representation as a substitute for physical ontology.