1. The Core of the Problem: A Misread Method
The development from quantum mechanics to quantum field theory can be seen as a long journey of correct mathematics misinterpreted by mistaken philosophy.
The key mathematical tool behind both theories is spectral analysis—the decomposition of a physical system into its natural oscillation modes, much like decomposing sound into harmonics or light into frequencies.
In this sense, the Schrödinger equation, the Dirac equation, and even the quantum field operators are expressions of spectral representation in different physical domains.
However, the crisis began when physicists forgot what spectral analysis really means:
it describes how a continuous system can be represented as a superposition of discrete frequency components under specific boundary conditions.
Instead, the method was reified—interpreted as if these mathematical modes were “ontologically real entities,” independent of the physical continuum that gives rise to them.
To be fair, this should be regarded as a historical mistake, and it's not the fault of the pioneers of quantum mechanics at that time—because spectral analysis was not yet a common method back then.
While spectral representation can accurately describe the steady-state, resonance, and statistical behavior of a system, they inherently lose several key physical pieces of information due to their mathematical nature:
Therefore, the "weirdness" of quantum mechanics is not the nature of nature, but an apparent phenomenon arising when the spectral method exceeds its scope of application. Returning to the classical field picture in the spacetime domain (such as extended charges, electromagnetic vortices, and resonant structures) can naturally restore locality, causality, and physical reality—and this is the core proposition of Natural Quantum Theory.
2. How Misinterpretation Created Quantum Mysticism
Once the spectral formalism was treated as ontological truth rather than representational method, a cascade of conceptual confusions followed:
| Mathematical property | Correct meaning (spectral analysis) | Misinterpreted as (quantum mysticism) |
|---|---|---|
| Discrete spectrum | Natural frequency quantization due to confinement | “Energy is fundamentally discontinuous” |
| Uncertainty relation | Fourier uncertainty between frequency and time domains | “Nature is inherently indeterminate” |
| Dual wave-particle description | Dual mathematical representations of the same process | “Matter is both a wave and a particle” |
| Spinor structure | Representation of rotational symmetry in complex spectral space | “Particles possess intrinsic spin without rotation” |
Thus, what were originally mathematical relations became metaphysical puzzles.
The result was the rise of instrumental quantum mechanics—a theory that renounced realism, declaring the wavefunction “not real” and the measurement process “undefined but sufficient.”
3. The Transition to Quantum Field Theory: Fixing the Symptoms, Not the Cause
When the incompleteness of quantum mechanics became apparent (e.g., in relativistic contexts), the community did not return to physical reasoning, but instead extended the same formalism into a larger mathematical framework—quantum field theory (QFT).
The result was a paradoxical success:
Correct mathematics:
QFT correctly used the spectral representation of fields via creation and annihilation operators—essentially, a harmonic analysis in spacetime.Wrong ontology:
The field was treated as an ensemble of “particles” appearing and disappearing from the vacuum, rather than as continuous physical oscillations of extended structures.
Because this ontology was inconsistent with physical intuition (e.g., point-like particles producing infinite self-energy), QFT had to introduce increasingly abstract mathematical “patches”:
Renormalization, to cancel infinities created by the point-particle idealization;
Gauge symmetry, to recover local consistency lost when magnetic and spin directions were abstracted away;
Spontaneous symmetry breaking, to simulate structural differentiation that would naturally arise in extended systems.
These techniques work computationally but erase the physical image—we can calculate everything, yet understand nothing.
4. The Physical Image Lost: From Fields to Formalism
In classical physics, the physical image was clear:
Matter had structure;
Motion had cause;
Fields carried energy and momentum in space.
After the instrumental reinterpretation, these foundations dissolved:
The electron became a “point with spin ½”;
The field became a “mathematical expectation value”;
The vacuum became a “sea of virtual particles.”
Physics, instead of explaining, became self-consistent computation.
It traded understanding for formal precision.
5. The Natural Quantum View: Recovering the Reality Behind the Formalism
In Natural Quantum Theory, we reassert the proper meaning of the spectral method:
The wavefunction, the operator, and the field mode are all representations of real, continuous, physical oscillations constrained by natural boundary conditions.
Quantization is therefore not a mystery but a manifestation of natural discreteness arising from:
the quantization of charge, and
the finite confinement of oscillating fields.
From this perspective:
The “uncertainty” is a statement about Fourier completeness, not indeterminacy;
“Spin” is a description of rotational field motion, not an abstract quantum number;
“Renormalization” becomes unnecessary once the field has finite structure;
“Gauge transformations” are just ordinary rotations of real field vectors, not mystical symmetries of hidden spaces.
6. Summary Table: The Evolution of Interpretation
| Level | Mathematical Advance | Physical Interpretation | Result |
|---|---|---|---|
| Classical Physics | Differential equations | Real physical motion and fields | Clear physical picture |
| Quantum Mechanics | Spectral representation | Misread as ontological discreteness | Conceptual paradoxes |
| Quantum Field Theory | Operator-valued spectra | Further abstraction and mathematical patching | Loss of realism |
| Natural Quantum Theory | Corrected spectral realism | Fields as structured, coherent oscillations | Restoration of physical image |
7. Conclusion: The Lost Physical Image Can Be Recovered
Quantum mechanics and quantum field theory succeeded because of their mathematics, not because of their interpretations.
They captured nature’s spectral structure, but mistook the representation for reality.
Natural Quantum Theory restores the original scientific aim—to describe how nature really works, not merely how numbers fit experiments.
By recognizing quantization as the natural spectral property of confined, structured fields, we can retain the successful formalism while recovering physical intelligibility.
The future of physics is not in deeper abstraction, but in clearer understanding.
P.S.
What has long been called the “Copenhagen Interpretation” should more correctly be described as the Copenhagen Misinterpretation —
a historical episode in which the mathematical representation of frequency spectra was mistaken for the physical reality itself.
By elevating a calculational formalism to the level of ontology, physics lost contact with the very object it sought to describe — nature herself.
The flaws of instrumental quantum theory stand where they are—
unhealed, unhidden, undeniable.
You may deny them, glorify them, or worship them as mysteries of the universe,
yet a flaw remains a flaw.
The universe is not mystical; only our understanding is incomplete.