Introduction: Is Charge a "Label" or a "Structure"?

What exactly do we mean when we say an electron has a negative charge and a proton has a positive charge? Is charge an a priori label written on a "particle's ID card", or an emergent quantity derived from deeper geometric and dynamical structures?

Mainstream Quantum Field Theory (QFT) and Natural Quantum Theory (NQT) offer two distinct answers to this question: the former emphasizes symmetry and conservation, while the latter highlights rotation-circulation and flux quantization.

The good news is that the two frameworks are highly consistent at the observable level; the difference lies primarily in "how we understand the same facts".

I. In Quantum Field Theory: Charge Originates from Symmetry, and Its Magnitude "Breathes" with the Energy Scale

What is Charge?

In QFT, charge is a conserved quantity of "electromagnetic symmetry". Just as rotational symmetry gives rise to angular momentum conservation, the U(1) symmetry of electromagnetism leads to "charge conservation". As long as the symmetry remains unbroken, the total charge is like an accounting book that always balances. This is a description, not a generation mechanism.

Duality of Apriority and "Generation"

• Apriority: The "property" of charge stems from the symmetric structure of the theory and the representation to which the particle belongs (you can understand it as "obtaining this membership card once joining the club"). Specific values are calibrated by experiments at a certain reference energy scale.

• Sense of generation: Charged particles can be "created/annihilated", but the "total charge accounting book" must always remain balanced. This is not creating charge, but transferring it from one pocket to another.

Why Does the Effective Charge Change?

When observing with different "magnification levels" (energy scales), the measured "charge strength" varies slightly. This is called "running": the polarization effect of the vacuum acts like a shielding layer, making the charge feel different when observed from a distance versus up close. Nevertheless, the total charge is conserved regardless of the observation scale.

Why is Charge Quantized?

In the Standard Model, the unit and assignment of charge result from an overall consistent arrangement (e.g., the weights of different "genealogies" exactly form integer/fractional charges while ensuring no logical contradictions). In more macroscopic unified theories or in the presence of magnetic monopoles, quantization can be "necessarily" derived from topology or larger symmetries.

Why Are Electrons and Protons Equal in Magnitude but Opposite in Sign?

The +1 charge of a proton comes from the combination of three quarks with fractional charges; the −1 charge of an electron is determined by the representation to which it belongs. Nature prefers large "electrically neutral" structures (atoms, matter), which is closely related to the stability of the universe.

II. In Natural Quantum Theory: Charge is an Integral Quantity of Rotation-Circulation, and Flux "Locks It In"

Ontological Image (Visualization)

An electron is not a "dimensionless point" but a finite-size rotation-flux configuration, like a micro-vortex. The so-called "charged property" is the total quantity of the current density and flux combined in this configuration—similar to the "total rotational momentum" of a swirling water flow.

Why is Charge Discrete?

Just as the resonance of a musical instrument can only take certain pitches, the phase and flux of a closed circulation can only take "integer quanta". This "locks" the charge unit into discrete values. In other words, charge quantization originates from geometry and topology, not abstract labels.

Why Does the "Effective Charge" Change with Context?

When placing the system in different geometries/media/resolutions, the distribution of the field undergoes fine adjustments, and the measured "effective coupling" varies slightly—this corresponds to the "running" in QFT. In the language of NQT, this is a type of "boundary-field distribution feedback".

Where Does Conservation Come From?

Continuous current and charge satisfy a strict continuity equation; the flux of circulation does not break arbitrarily in topology. Therefore, although modes can "enter and exit", the total flux (total charge) never disappears.

III. Why Are the Two Frameworks Experimentally Consistent?

Principle of Low-Energy Matching

Whether you prefer the "symmetry accounting book" (QFT) or the "circulation-flux image" (NQT), they yield the same set of values at the energy scales accessible to our experiments: Coulomb's law, the coupling strength between light and matter, scattering cross sections, the magnitude of energy level splitting, etc.

Complementarity Between Tools and Ontology

• QFT excels in computational systems: it provides a sophisticated toolbox for incorporating "spectral information" back into spacetime and tracking its evolution with energy scales.

• NQT excels in physical imagery: it tells us the intuitive reasons for "unit charge", "conservation and quantization", and "effective coupling fine-tuned by geometry and resolution".

IV. Concise Answers to Three Common Questions

Can Charge Be "Created"?

No. The number of particles can change (e.g., the creation/annihilation of electron-positron pairs), but the charge accounting book must remain balanced. What is created is "charged objects", not "net charge" itself.

Does Charge Change Over Time?

The effective strength measured in a single process changes with the "observation scale", but this is not charge being lost—it is a change in "how you look at it". The total charge is conserved.

Why Are the Charges of All Electrons Exactly the Same?

• QFT's answer: They belong to the same symmetric representation and are naturally "identical models".

• NQT's answer: They all satisfy the same flux quantization condition and are naturally "of the same unit".

V. Where Might We See "Differentiated Details" of the Two Images?

Geometric/Boundary Reversible Effects

In special geometries (cavities, metamaterials, strong gradient fields), NQT predicts that certain tiny effects can be reversibly modulated by geometric parameters; QFT describes these effects as "changes in the density of states and vertex functions". The numerical values should be consistent, but the languages differ.

Subtle Slopes at Ultra-Low Energy Scales

In precision scattering with ultra-low momentum transfer, the measured "weak energy scale dependence" can serve as a window to test the details of field distribution. Note: Such effects must be far below the existing upper limits and require precise control of systematic errors.

Conclusion: Reconciliation Between the Accounting Book and the Vortex

Treating charge as a "conserved quantity in the symmetry accounting book" gives us a powerful computational theory (QFT); treating it as the "flux of rotation-circulation" gives us an intuitive physical ontology (NQT). The two complement each other: one ensures "correct calculations", and the other ensures "understanding why".

The maturity of science often lies not in choosing one over the other, but in aligning the "map" with the "terrain". To understand charge, we need both a clear accounting book and a vision of how that micro-vortex rotates consistently.