Standard Model/Quantum Field Theory/Gauge Field Theory Are Not Fundamental Theories

"I think I can safely say that nobody understands quantum mechanics."——Richard Feynman

This statement still rings as true today as ever. It applies not only to non-relativistic quantum mechanics but also pierces the core of contemporary particle physics with striking precision: while the Standard Model (SM), Quantum Field Theory (QFT), and Gauge Field Theory (GFT) have achieved unparalleled success in calculations, they are not fundamental theories—they are exceptional "effective theories," not the ultimate description of nature’s ontology.

Starting from the essential characteristics of fundamental theories, this paper analyzes why QFT lacks a physical picture, reveals the "fitting" nature behind its success, and argues that only by returning to first principles and clear physical reality can physics escape its current cognitive impasse.

I. Fundamental Theory vs. Effective Theory: The Essential Distinction

Hallmarks of a Fundamental Theory

Rooted in first principles, with a clear physical picture, and a natural correspondence between mathematics and physics.

Examples: Maxwell’s equations and general relativity

Maxwell’s Theory

Built from directly observable physical quantities (charge, current), it constructs an intuitive picture of electric field lines, magnetic field lines, and electromagnetic waves propagating through space.Every equation is a physical statement—you can "tell a story by looking at the equation":

• ∇·E = ρ/ε₀ → Charge is the source of the electric field;

• ∇×E = –∂B/∂t → A changing magnetic field induces an electric field;

• ∇·B = 0 → Magnetic monopoles do not exist;

• ∇×B = μ₀j + μ₀ε₀∂E/∂t → Electric current and changing electric fields jointly generate magnetic fields.

General Relativity

Founded on the "equivalence principle" and "constancy of the speed of light," it interprets gravity as the curvature of spacetime, with particles moving along geodesics. Its mathematics (Riemannian geometry) and physics (gravity = geometry) are highly unified.

Common traits of such theories: Derived from a small set of clear, testable physical principles, each step carries definite physical meaning, forming an entire theoretical edifice.

The Nature of QFT: A Patchwork Computational Framework

In contrast, QFT begins with compromises:

It does not stem from profound insights into nature, but from a technical necessity: "How to reconcile quantum mechanics with special relativity?"

Its core is not describing physical reality, but constructing a set of computational rules satisfying Lorentz invariance.

To achieve this, QFT introduces numerous artificial constructs:

• Infinity problems → Regularization + Renormalization (pure mathematical tricks);

• Redundant gauge freedom → Gauge fixing + Faddeev-Popov ghosts;

• Dimensional Regularization → "Circumventing" divergences in non-integer dimensional spaces;

• Path integral → "Summing over all possible paths"—a mathematical form lacking physical intuition.

The result: QFT can calculate the electron’s anomalous magnetic moment g-2 to 12 decimal places, yet fails to answer the most naive questions:

• Do virtual particles really exist?

• Is vacuum fluctuation a physical reality, or a computational phantom?

This state of "successful prediction but failed understanding" is a typical hallmark of an effective theory.

II. Why Does QFT Lack a Physical Picture?

1. The Original Sin of the Point Particle Assumption

QFT embraces the point particle model from the outset—this is the root of all its pathologies:

• Divergent self-energy of point charges (Coulomb energy ∝ ∫ dr/r² → ∞);

• Reliance on non-physical methods (cutoffs, renormalization) to "hide" infinities;

• More critically, it completely abandons the possibility of particles having internal structure, reducing microscopic entities to dimensionless mathematical singularities.

This is analogous to describing a typhoon with a "point mass"—effective at large distances, but never capable of explaining its eye wall, spiral rain bands, or energy sources.

2. The Abstraction of Operator Formalism

QFT’s language is highly mathematical yet extremely devoid of physical imagery:

• What exactly is the field operator ψ(x)? A probability amplitude? A physical field? Or a pure generative tool?

• Creation/annihilation operators a†, a: No corresponding physical process imagery, merely algebraic operations in Hilbert space;

• Fock space: An abstract multi-particle state space, disconnected from real three-dimensional physical space.

You cannot "see" an electron being created—only a symbol being written down.

3. The Paradox of Virtual Particles

Virtual particles in Feynman diagrams are QFT’s most famous "ghosts":

• They violate energy-momentum relations (off-shell: E² ≠ p²c² + m²c⁴);

• Unobservable, yet claimed to "mediate interactions";

• Are they computational tools or physical realities? QFT evades the question, only saying: "As long as the results are correct."

This is essentially a methodological evasion: substituting mathematical convenience for physical understanding.

4. The Excessive Abstraction of Gauge Principles

Gauge invariance is revered as a first principle, yet its physical origin remains obscure:

• The SU(2)×U(1) group structure in Yang-Mills theory is a pure group-theoretic construct, with physical meaning assigned post-hoc (e.g., "weak isospin," "hypercharge");

• The arbitrariness of gauge choices (Lorenz gauge, Coulomb gauge, etc.) exposes the theory’s non-uniqueness—a true fundamental theory should not depend on artificial selections.

III. Contrast with Truly Fundamental Theories: Transparency vs. Opacity

Revisiting Maxwell’s equations:

• ∇·E = ρ/ε₀ → Charge generates electric fields;

• ∇×E = –∂B/∂t → Changing magnetic fields induce electric fields;

• ∇·B = 0 → No magnetic monopoles;

• ∇×B = μ₀j + μ₀ε₀∂E/∂t → Electric currents and changing electric fields generate magnetic fields.

Each line represents a conceivable, experimentally verifiable physical process.

In contrast, the Standard Model’s Lagrangian:L = ψ̄(iγ^μ ∂μ - m)ψ - (1/4)F{μν}F^{μν} - g ψ̄ γ^μ A_μ ψ

Questions with elusive answers:

• What physical entities are ψ̄ and γ^μ?

• Why this specific form? Why no ψ⁴ term?

• What is the physical origin of the coupling constant g?

The typical response: "Because this form yields correct results."—This is classic reverse engineering, not forward construction.

IV. The True Reason for QFT’s Success: An Exceptional Phenomenological Framework

QFT’s success stems not from revealing nature’s underlying mechanisms, but from being an extremely efficient low-energy effective theory:

1. Parameterizing All Possible Low-Energy Behaviors

• Constrain allowed terms in the Lagrangian via symmetry constraints (Lorentz, gauge, CPT, etc.);

• Determine coupling constants (e.g., α ≈ 1/137) through experiments to complete the fitting.

2. Perturbation Theory Works Perfectly

• The fine-structure constant of electromagnetic interactions is small, leading to rapid convergence of QED perturbative series;

• Most processes require only one or two orders of Feynman diagrams to achieve extraordinary precision.

3. The Powerful Constraining Force of Symmetries

Even without deep physical understanding, symmetries can "guess" the correct interaction forms.

This evokes Ptolemy’s geocentric theory:

• Precisely predicting planetary positions with epicycles + deferents;

• Computational success, but a completely incorrect cosmic picture;

• Adding more epicycles to accommodate new observations—much like QFT continuously introducing new fields, terms, and symmetries to fit data.

QFT is a modern-day "epicycle theory"—efficient, but not necessarily true.

V. From the NQT Perspective: How to Restore the Physical Picture?

Natural Quantum Theory (NQT) seeks to break free from QFT’s abstract cage and reconstruct a clear physical picture:

1. Replace Point Particles with Finite-Size Vortices

• Electrons are not points, but exist at the Compton wavelength scale (~10⁻¹² m);

• Each "particle" has internal structure and topology (e.g., knots, loops, vortices);

• Self-energy is naturally finite, eliminating the need for renormalization.

2. Fields Are Fundamental, Particles Are Emergent

• It is not "particles exciting fields," but "stable modes of fields manifesting as particles";

• Analogy: Vortices in water—no new particles, but collective excitations of water.

3. A Geometric Picture of Interactions

• Not virtual particle exchange, but resonance, interference, and topological reorganization of field modes;

• Example: Beta decay—a neutron vortex unwinds into proton + electron + neutrino vortices, with energy and topology conserved.

4. Natural Chiral Selection

• The V–A structure of weak interactions is not an abstract gauge requirement, but the natural chirality of current loops, lacking mirror symmetry.

VI. Implications for Weak Interaction Theory

Since QFT is merely an empirical fitting framework, we need not be constrained by its superficial forms:

• W/Z bosons may not be fundamental entities, but analogous to "phonons" in lattice vibrations—merely effective excitation modes;

• The SU(2)×U(1) gauge symmetry may be just a low-energy approximate parameterization of underlying electromagnetic-topological geometry;

• True symmetries may arise from the topological properties of space itself, not abstract Lie groups.

Thus, the "higher-order magnetic effects" or "electromagnetic-topological unification" picture proposed by NQT is at least as plausible as the Standard Model—even more aligned with physical reality.

VII. Conclusion: The Honest Positioning of Theories

We must honestly acknowledge:

1. QFT is the most successful computational tool of the 20th century, with unrivaled predictive power;

2. Yet it is not a fundamental theory, but a highly optimized effective field theory;

3. Its tremendous success has, ironically, masked our profound ignorance of the physical picture of the microscopic world.

The direction pursued by Natural Quantum Theory—restoring a clear, continuous, local physical picture from first principles—is precisely the course correction physics urgently needs.

Even if NQT is not yet perfect, its direction is correct:

• Understanding outweighs calculation;

• Physical imagery takes precedence over formalism;

• Reality is superior to symmetry.

As Feynman warned:"Nobody understands quantum mechanics."

The mathematical brilliance of QFT only confirms this tragedy—we have mastered the language to describe the world, but forgotten what the world itself looks like.

It is time to return to the tradition of Maxwell and Einstein:constructing conceivable, tangible, understandable physical theories from simple principles.

For a true fundamental theory should not be "incomprehensible," but "visible."