Why Gravity is Hard to Quantize from the Nature of Quantization

——From the Perspective of Spectral Constraints in Natural Quantum Theory

I. The Nature of Quantization: Spectral Representation, Not Operator Algebra

Within the framework of Natural Quantum Theory (NQT), "quantization" is not a metaphysical operation that introduces abstract operators or probability amplitudes, but a natural result of spectral analysis on constrained oscillatory systems:

• A system with definite boundary conditions (such as a string, cavity, or atomic orbital) can only support standing waves of certain discrete frequencies;

• These allowed frequencies form the system’s eigen-spectrum, with energy given by \(E_n = \hbar\omega_n\);

• "Quantum equations" like the Schrödinger equation are essentially mathematical tools for finding this spectrum, not fundamental laws.

Thus, the prerequisite for quantization is that the system possesses definable global constraints, making the spectrum discrete or at least structurally clear.

In other words: No boundaries, no spectrum; no spectrum, no quantization.

NQT’s positioning statement succinctly summarizes this stance:"Quantization" is not about forcing all physics into particles/operators, but about "expressing the system as a sum of discrete eigenmodes if and only if global boundaries and stable phases exist."

II. Why Can Electromagnetic Systems Be "Effectively Quantized"?

Although the universe as a whole is unbounded, electromagnetic interactions satisfy the key prerequisites for spectralization at the atomic-molecular scale:

• Effective local boundaries: The Coulomb potential forms a strong confinement, "trapping" electrons in a finite region;

• Negligible propagation delay: At the angstrom (Å) scale, the light travel time is much smaller than the system’s dynamic period (\(\tau_{\text{prop}}/T_{\text{osc}} \ll 1\)), so electromagnetic feedback is approximately instantaneous;

• Existence of steady phases: Time translation symmetry ensures energy conservation, allowing global energy eigen-decomposition.

Even in fully relativistic Quantum Electrodynamics (QED), its success relies on the existence of asymptotically free states—which implicitly assumes the flatness and separability of spacetime at infinity, constituting an effective boundary condition.

Therefore, while the electromagnetic system is "unbounded" on the cosmic scale, it possesses a "frequency-locking" cavity structure on the physically relevant local scale, thereby achieving effective spectralization and quantization.

III. Why Can’t Gravitational Systems Be "Quantized"?——Four Structural Barriers from the NQT Perspective

In contrast, gravity fundamentally lacks the necessary conditions for spectralization. Specifically, it faces the following four structural barriers:

1. No global boundaries and unshieldable long-range interactionsGravity is unshieldable and acts over infinite distances. On the cosmological scale, there are no boundaries or barriers that can "trap" gravitational energy, so there is no macroscopic "cavity" to discretize frequencies.

2. Finite and non-negligible propagation speedGravity propagates at the speed of light, and on large scales, the propagation delay is comparable to the system’s intrinsic evolution time. Even if some boundaries existed, information could not be synchronized globally, making it difficult to form stable standing wave resonance.

3. The background geometry itself is evolvingThe gravitational field is the very ontology of spacetime geometry. On large scales, geometry continuously changes with matter distribution and cosmic expansion, lacking a global time-energy benchmark. Without a stable phase reference, global energy eigen-decomposition is impossible.

4. Nonlinear self-coupling and accumulation of soft modesGravity is highly nonlinear and self-coupled, with an infinite number of extremely low-frequency ("soft") modes. These modes continuously drain energy into the continuous spectrum, producing memory effects and hysteretic responses. The result is not a few clear discrete eigen-peaks, but a broad continuous spectrum and a dissipative tail.

Summary: Gravity lacks "frequency-locking" boundaries, a global time for "unified phases," and has a "soft tail with continuous dissipation." These three points make "spectral representation" impossible on the cosmic scale, let alone "quantization."

IV. Analysis of "Special Cases": Why Don’t They Undermine the Above Judgment?

Some phenomena that seem like "quantum gravity" actually belong to different categories:

• Gravitational wave modes under linear approximation: In local nearly flat, weak-field regions, perturbations can be treated as linear waves and "modes" defined. However, this is only a local approximate spectrum, relying on artificial truncation and a static background—it fails once outside the linear window.

• Black hole "ringdown" and quasi-normal modes: Their frequencies are complex (including attenuation), essentially representing the classical dissipative characteristics of an open system. They describe the time scale of energy radiation, not stable quantum eigenstates that can be occupied.

• Planetary/stellar seismic "gravity modes": These modes arise from elastic or fluid constraints within matter (essentially the eigen-spectrum of a material cavity); gravity only participates as an external coupling field, unrelated to the "quantization of spacetime geometry itself."

These examples precisely confirm NQT’s core view: Spectralization is physically meaningful only when the system has closed, steady, non-radiative boundary conditions.

V. Essential Differences from the Electromagnetic "Infinite Boundary"

The universe is also "unbounded" for electromagnetism, but their fates are drastically different due to the matching between scale and dynamics:

Characteristics	Electromagnetism (atomic scale)	Gravity (cosmic scale)
Coupling strength	Strong (fine-structure constant \(\alpha \sim 1/137\))	Extremely weak (unfavorable \(G_N\) dimensionality)
Propagation delay vs dynamic period	\(\ll 1\), approximately instantaneous	\(\sim 1\) or larger, non-negligible
Effectiveness of boundaries	Local potential well sufficiently "locks frequencies"	No effective closed boundaries
Energy conservation	Time translation symmetry holds	Cosmic expansion breaks steadiness

When the scale expands to the point where gravity dominates, propagation delay, background evolution, and nonlinear dissipation jointly destroy the prerequisites for spectralization.

VI. Testable Empirical Criteria (NQT-style)

NQT provides three operable criteria to judge whether a system truly has a physical basis for "quantization":

1. Boundary-removal limit criterion

After removing boundaries, any genuine quantum spectrum must degenerate from discrete to continuous. The electromagnetic system satisfies this; the gravitational system, however, is already in the "boundary-removal limit" from the start, so there is no discrete spectrum to speak of.

2. Geometric reversibility criterion

The discrete peaks of a constrained spectrum should be reversibly modulated with changes in cavity geometric parameters. The ontological geometry of gravity is macroscopically unshieldable and unclosable, lacking such regulatory means.

3. Non-radiative stability criterion

Eigenstates should exhibit "near-zero dissipation" in time-averaged energy flux. Large-scale gravity universally has soft-tail dissipation and memory effects, failing to meet the prerequisite for non-radiative steadiness.

These criteria reduce "quantization" from a formal operation to observable physical conditions.

VII. Conclusion: A Structural Fact, Not a Technical Failure

As defined by NQT:"Quantization = Spectralization."Spectralization requires three major prerequisites: boundaries, unified phases, and non-radiative eigenmodes.

Electromagnetism satisfies these prerequisites in locally constrained systems, hence it "can be quantized";Gravity lacks these prerequisites on the cosmic scale, hence it "cannot be quantized."

This is not a temporary failure of current theoretical technology, but a structural fact:The ontology of spacetime geometry has no cavity for "frequency locking."

The real way forward may not be to force gravity into the spectral framework of quantum mechanics, but to develop a dynamic language beyond the spectral paradigm—one that can explain the discreteness of quantum phenomena while accommodating the geometricity, causality, and openness of gravity. This is precisely the direction advocated by Natural Quantum Theory: starting from reality, not from form.