I. True Magnetic Moment: A Vector Generated by the Rotation of Physical Current

In the natural (classical or semi-classical) physical picture, the definition of magnetic moment (μ) is rooted in the spatial rotational structure of current distribution:

μ = 1/2 ∫ r × J(r) d³r

It is an observable physical quantity with direction, featuring the following properties:

• It originates from real charge flow;

• It can generate a magnetic field and interact with external magnetic fields;

• It has a definite geometric direction and couples with angular momentum.

Therefore, the existence of a magnetic moment necessarily requires matter to have an internal rotational structure.

Without spatial distribution and rotation, a magnetic moment cannot exist.

II. In Quantum Field Theory, the "Magnetic Moment" Loses Its Physical Origin

In QFT, electrons are regarded as point particles and excitations of the Dirac field:

L = ψ̄(iγ^μ D_μ - m)ψ

There is no concept of charge distribution, rotation, or flow here.

Spin is merely an algebraic property under the (γ)-matrix representation, not a spatial motion.

The magnetic moment of an electron is defined as:

μ = g (eħ)/(2m) S

where:

• (S) is the spin operator (an abstract algebraic vector);

• (g) is an empirical correction (higher-order correction term in QED).

Under this definition:

• There is no physical current;

• There is no real rotation;

• "Direction" is only a label for the eigenstate of the operator.

Thus, the magnetic moment obtained in this way is a mathematical pseudo-vector, rather than a moment of real current.

It is an object that "exists in calculation but is absent in physics".

In other words:

It is not a source of magnetic field, but a symbol that parameterizes magnetic interactions.

III. Formal Consistency ≠ Physical Reality

The success of QED is often used to "verify" the correctness of this definition, as the theoretically predicted g-value matches experiments with extremely high precision:

g/2 = 1 + α/(2π) + ...

However, this "precision" does not imply the correctness of the physical picture.

It only indicates that this mathematical form is numerically self-consistent, not physically real.

This is a type of "abstracted success":

• Spin has no spatial rotation;

• Magnetic moment has no physical current;

• The g-factor becomes an algebraic fine-tuning parameter;

• Then, "matching experiments" is mistakenly taken as "explaining nature".

From a realist perspective, such a magnetic moment is nothing but a "shadow under algebraic symbols"—

it is effective in calculation, but loses the physical mechanism that generates it.

IV. Compensation in Gauge Field Theory: Making the False Magnetic Moment "Seem Real"

Since both spin and magnetic moment in QFT are divorced from physical geometry, to maintain consistency with experiments, new layers of compensation must be introduced:

• Gauge field (A_μ): Serves as compensation for local phase rotation, simulating magnetic interactions;

• Covariant derivative (D_μ): Ensures formal directional coupling;

• Renormalization constants and g-factor: Adjust the gap between theory and experiment.

The results are:

• The "magnetic moment" in the theory is no longer a consequence of physical current, but an algebraic pseudo-vector under group representation;

• "Magnetic field interaction" is only a cross term of the covariant derivative;

• The magnetic moment effect is merely a corrected form of higher-order terms in Feynman diagrams.

Thus, physical reality is replaced by mathematical form:

The true magnetic moment disappears, but the false magnetic moment "calculates well".

V. Perspective of Realistic/Natural Quantum Theory: Magnetic Moment Should Be Re-physicalized

Within the framework of "Natural Quantum Theory":

• An electron is a rotating charge distribution with a finite scale (Compton wavelength);

• Its magnetic moment is naturally generated by internal current loops;

• The conservation of angular momentum and magnetic energy is a geometric relationship, requiring no g-factor correction;

• Spin-orbit coupling, the Zeeman effect, etc., are all derived from real rotational coupling.

As a result:

• The magnetic moment is a real spatial vector;

• Spin is physical rotation;

• Magnetic field interaction arises from the interaction between real current and the field;

• No "gauge field compensation" or "renormalization correction" is needed.

In other words:

In Natural Quantum Theory, the magnetic moment rebecomes a physical reality, rather than a mathematical symbol.

VI. Conclusion: The Divide Between False and True Magnetic Moments

Theoretical Framework	Nature of Spin	Source of Magnetic Moment	Has Physical Direction?	Requires Compensation?
Classical Physics	Spatial rotation	Current loop	✅ Real direction	❌ No
Quantum Field Theory	Group representation	Spin operator + g-correction	⚠️ Formal direction	✅ Gauge compensation needed
Natural Quantum Theory	Physical rotation	Rotation of charge distribution	✅ Real direction	❌ No

✳️ Summary:

In quantum field theory, the magnetic moment loses its physical origin and directionality, retaining only the formal symbolic meaning of an operator;

thus, it is a "fake magnetic moment"—a quantity that exists in form but is absent in physics.

In contrast, in Natural Quantum Theory, the magnetic moment regains its physical root—the real rotational current of charge—thereby restoring its reality.