Why Are Atoms and Molecules Always Quantum?
From Rapid Electromagnetic Relaxation to Eigenmode Locking: A Natural Picture

I. The Core Question: Why Is the Microscopic World Inherently Discrete?

In textbook quantum mechanics, we are accustomed to statements like: “electrons in atoms or molecules occupy quantum states,” energy levels are discrete, transitions are instantaneous, and spectral lines correspond to energy differences. While this framework is computationally spectacularly successful, it glosses over a crucial question that is usually taken for granted:

Why do atomic and molecular systems almost always appear in clean quantum eigenstates—rather than lingering for long durations in messy superpositions or complex transient configurations?

Conventional quantum theory often treats eigenstates as a priori given “modes of existence” without asking: How are these eigenmodes dynamically selected, populated, and maintained during physical evolution?

From the field-ontological perspective of Natural Quantum Theory (NQT), we can offer a coherent physical answer:

• At atomic and molecular scales, electromagnetic interactions dominate everything; other forces are either confined within nuclei or relevant only in rare processes.

• For such tiny systems, the propagation time of electromagnetic influence is effectively “instantaneous” compared to their characteristic dynamical timescales.

• Whenever a system possesses a set of dominant eigenmodes (i.e., preferred electromagnetic resonance modes), it rapidly relaxes into them via radiation, coupling, frequency locking, and collective synchronization.

• Because this relaxation occurs far faster than our observational resolution, we empirically encounter only the already-selected eigenstates—and mistakenly conclude that the microscopic world is “inherently discrete.”

As systems grow larger and more complex, this ultrafast “quantum mode selection” slows down and becomes susceptible to disruption, allowing decoherence and classical causal dynamics to emerge. This provides a natural bridge from quantum to classical behavior.

II. Electromagnetic Dominance and “Nearly Instantaneous” Internal Communication

At atomic and molecular scales (～10⁻¹⁰–10⁻⁹ m), key physical facts include:

1. Electromagnetism is the dominant interaction

• The strong force confines nucleons within nuclei.

• The weak force participates only in rare decays or reactions.

• Electron shell structure, covalent/ionic bonds, van der Waals forces, lattice vibrations, conductivity, and optical properties—all are governed by electromagnetism.

2. Electromagnetic signals propagate extremely fast at this scale

For an atomic size $a\sim 10^{-10}\text{m}$ and light speed $c\sim 3\times 10^8\text{m/s}$ , the characteristic communication time is:

$${\tau }_c\sim \frac{a}{c}\sim 3\times 10^{-19}\text{s},$$

which is orders of magnitude shorter than typical electronic transition times, spontaneous emission lifetimes, or molecular vibration periods (10⁻¹⁵–10⁻⁹ s).

Thus, for internal degrees of freedom, electromagnetic influence propagates almost instantaneously across the entire system.

In NQT language:

At atomic–molecular scales, the electromagnetic field self-consistently adjusts to matter distributions with extreme speed. Any local perturbation is rapidly communicated, fed back, and redistributed throughout the system, strongly “pulling” it toward certain electromagnetically stable configurations.

This lays the dynamical foundation for the rapid emergence and occupation of eigenmodes.

III. Eigenmodes: The Schrödinger Equation as a Catalog of “Preferred Electromagnetic Resonances”

In operator formalism, for a given atom or molecule, the Hamiltonian is:

$$\hat{H}=\hat{T}+{\hat{V}}_{\text{nucleus}}+{\hat{V}}_{e\text{-}e}+\cdots$$

and the Schrödinger equation:

$$\hat{H}{\psi }_n=E_n{\psi }_n$$

is solved for discrete eigenstates $\{{\psi }_n\}$ .

From the NQT ontological viewpoint, this procedure has a clear physical interpretation:

• Interaction terms (Coulomb potential ${\hat{V}}_{\text{nucleus}}$ , electron–electron repulsion ${\hat{V}}_{e\text{-}e}$ , spin–orbit coupling, etc.) encode how the electromagnetic field couples electrons and nuclei.

• Boundary conditions and symmetries (spherical symmetry, periodicity, nuclear charge distribution) constrain allowable spatial field configurations.

• Under these physical constraints, the discrete solutions $\{{\psi }_n\}$ are precisely the system’s preferred electromagnetic resonance modes—stable, energy-minimized field–particle structures with well-defined frequencies and spatial shapes.

Thus:

The Schrödinger equation does not impose quantization arbitrarily. Instead, it lists all long-lived, stable configurations permitted by the actual physical potentials, boundaries, and interactions. These are the “orbital resonance modes” of the atom–electron system.

The spectrum gives us a catalog of possible end states—the question then becomes: How does real dynamics drive the system into these states so quickly?

IV. From Single to Many Electrons: Chaos to Frequency-Locked Coordination

4.1 Single Electron: Rapid Projection onto Shell Orbitals

Even if we assume a hydrogen-like electron starts in an arbitrary wave packet or turbulent field near the nucleus:

• It can be expanded in the eigenbasis $\{{\psi }_n\}$ .

• Non-eigen components radiate away or dephase through environmental coupling.

• Due to ultrafast electromagnetic response, this “mode filtering” occurs on timescales far below experimental resolution.

Hence, what we observe is always an electron in a stable shell eigenstate.

“The electron is in a quantum orbital” is really just the empirical expression of a post-relaxation stable state.

4.2 Many Electrons: From Chaotic Orbits to Resonant Selection

In multi-electron atoms:

• Immediately after formation or strong perturbation, electron trajectories, phases, and energies are highly complex—resembling a chaotic many-body system.

• Yet the combined Coulomb potential and electron–electron interactions act as a powerful resonance filter.

• The Schrödinger equation yields a discrete set of many-electron eigenmodes (incorporating spin configurations, exchange symmetry, spatial–spin coupling).

• Non-resonant, highly entangled motion patterns decay rapidly via electromagnetic dissipation and scattering.

The system quickly converges to a small set of dominant resonance modes—which, in spectroscopic language, correspond to shell filling, Hund’s rules, spin pairing, etc.

4.3 Frequency Locking and Coordination: Electromagnetic–Topological Origins of Filling Rules

Electrons further establish frequency-locked coordination through electromagnetic and magnetic interactions:

• Certain configurations (e.g., spin-paired filling, closed shells) achieve better energy balance, current distribution, and pinch–pressure equilibrium.

• These become attractors in the dynamical landscape, locking electrons into specific phase and frequency relationships.

• External fields, heating, or collisions can temporarily disrupt this coordination, leading to excited or atypical states—but only under limited conditions.

Thus:

Although the instantaneous ontological electron orbits may initially be chaotic, ultrafast electromagnetic coupling and radiation rapidly funnel the system into a few resonant, frequency-locked modes. These are precisely what traditional quantum theory calls “quantum states.”

V. Spin–Orbit Coupling as Rapid Mode Compression: From Complex Geometry to “Parallel/Antiparallel” Duality

Spin–orbit coupling is not a sustained “geometric battle” but a rapid mode-projection process that simplifies complexity.

Classically, if electrons were tiny spinning planets orbiting a nucleus, one could imagine:

• Arbitrary angles between each spin axis and its orbital plane;

• Non-coplanar orbital planes undergoing mutual precession;

• Complex, evolving geometries resembling celestial mechanics with multiple nutations and resonances.

Yet real atoms show none of this long-lived geometric richness. Instead, we observe:

• For a given orbital angular momentum $l$ , total angular momentum $j$ takes only two values: $j=l\pm \frac{1}{2}$ .

• The effective spin–orbit degree of freedom collapses to just two modes: parallel alignment (spin roughly aligned with orbital angular momentum) and antiparallel alignment.

• Spectroscopically, this appears as the familiar fine-structure doublet: $j=l+\frac{1}{2}$ and $j=l-\frac{1}{2}$ .

In NQT’s ontological picture:

• Spin is not an abstract “intrinsic label without classical analog.” It is the real angular momentum of the electron’s internal field vortex, carrying a genuine magnetic moment.

• Orbital motion generates an effective magnetic field ${\mathbf{B}}_{\text{eff}}(\mathbf{L})$ in the electron’s rest frame.

• The vortex’s magnetic moment ${\mathbf{\mu }}_{\text{ont}}({\mathbf{S}}_{\text{ont}})$ couples to this field.

Under strong, ultrafast electromagnetic coupling:

• All unstable spin–orbit geometric configurations rapidly decay via radiation and phase relaxation.

• Only two cooperative modes survive—those achieving optimal energy and magnetic stress balance:

1. Magnetic moment aligned with $\mathbf{L}$ (parallel),

2. Magnetic moment anti-aligned with $\mathbf{L}$ (antiparallel).

Thus, spin–orbit coupling acts as a rapid compression mechanism for angular momentum–magnetic moment–orbital geometry:

While the underlying geometry could be as complex as celestial mechanics, atomic-scale electromagnetic dynamics filters out all but two stable modes. The operator form $H_{\text{SO}}\propto \hat{\mathbf{L}}\cdot \hat{\mathbf{S}}$ is merely the spectral representation of this physical compression.

We don’t see diverse “spin-axis vs. orbital-plane” geometries in atomic spectra because all complex configurations are fleeting transients, erased by ultrafast electromagnetic evolution before they can be observed.

VI. Timescales and the Visibility of the “Quantum World”

Integrating ontology, spectrum, and dynamics yields a unified picture:

表格

Level	Description
Ontological	Electrons and fields start from arbitrary initial conditions, forming highly complex, possibly turbulent motion—especially in multi-electron systems.
Spectral (Schrödinger)	Given potentials and symmetries, the eigenmodes $\{{\psi }_n\}$ constitute the complete list of long-lived, stable electromagnetic resonances.
Dynamical	Ultrafast EM propagation causes rapid decay of non-resonant modes. The system falls into eigenmode attractors within a relaxation time ${\tau }_{\text{relax}}\ll$ observation time.

To an external observer, the entire mode-selection process is invisible—only the final eigenstates and their transitions are seen.

We thus naturally interpret the microscopic world as “always being in quantum states”—as if electrons were “born in eigenstates.”

But as systems grow larger:

• Coherence establishment and mode reorganization take longer.

• ${\tau }_{\text{relax}}$ becomes comparable to observation times.

• The mode-selection process itself becomes visible and interruptible.

• Decoherence and classical causality emerge—not as new physics, but as the unfolding of the same field dynamics at slower timescales.

VII. Conclusion

From the NQT perspective, the statement “atoms and molecules are always quantum” is not a metaphysical axiom, but the consequence of three intertwined facts:

1. Electromagnetism alone dominates at atomic–molecular scales, and its influence propagates effectively instantaneously relative to internal dynamics.

2. The Schrödinger eigenstates are not abstract mathematical artifacts—they are the physically stable electromagnetic resonance modes permitted by the system’s actual potentials and boundaries.

3. Real electromagnetic evolution drives any initial chaos into these modes on timescales too short to observe.

What we see in experiments are post-relaxation outcomes, not the brief, complex convergence process.

Therefore:

The “quantization of the microscopic world” simply means: at scales where electromagnetism is the sole dominant interaction, systems evolve into discrete eigenmodes almost instantly. Quantum eigenstates are the everyday manifestation of field–matter dynamics under rapid electromagnetic relaxation.

Quantum behavior is not “more mysterious”—it is the natural outcome of electromagnetic resonance and ultrafast relaxation at atomic scales. When we step beyond those scales, the dynamical process itself becomes visible, and the classical world emerges seamlessly from the same ontological foundation.