The Computational Challenges of Natural Quantum Theory
Natural Quantum Theory (NQT) provides a coherent, causal, and physically intuitive framework for the quantum world—where spin is real rotational angular momentum, measurement is a physical reconstruction of boundary conditions, entanglement is long-range field correlation, and the uncertainty principle is a mathematical property of spectral representation. However, a common criticism is that it has not yet yielded quantitative calculation results with the same precision as Standard Quantum Theory (SQT). This paper aims to analyze the root and nature of this computational difficulty, arguing that the depth of explanatory power and the maturity of computational precision are issues of two different dimensions and should not be conflated.
This scenario is not unprecedented in the history of science. When Copernicus proposed the heliocentric model in 1543, the precision of its planetary position predictions was not superior to—and in some aspects was inferior to—the Ptolemaic geocentric system, which had accumulated 1,400 years of adjusted parameters. The geocentric model possessed carefully tuned computational devices like epicycles and deferents, capable of fitting known observational data with considerable precision. In its infancy, the heliocentric model was actually at a disadvantage in precision because it insisted on perfect circular orbits. It was not until seventy years later, when Kepler introduced elliptical orbits, that the heliocentric model thoroughly surpassed the geocentric model in computational precision. Yet, no one would argue that the geocentric model was more correct simply because the heliocentric model's precision was lower in 1543. The correctness of a theory depends on whether it grasps the true structure of nature, not on its computational fitting ability at a specific historical stage.
Standard Quantum Theory, after nearly a century of development, has established a complete set of mature computational tools—perturbation theory, variational methods, numerical methods, renormalization groups—just as the Ptolemaic system accumulated over a millennium of epicycle correction parameters. Natural Quantum Theory, as a new theoretical framework, is still in the early stages of developing its computational methods. This does not constitute a negation of its physical correctness but is precisely the mathematical and physical frontier awaiting exploration for a new paradigm.
I. The Absolute Time Assumption in Classical Electromagnetic Calculations
The basic framework of classical electromagnetic field calculation treats physical quantities and time separately, using absolute time as the global evolution parameter. Under low-energy conditions, this treatment is efficient and self-consistent—tools like Maxwell's equations, Coulomb gauge, and multipole expansion constitute a mature computational system. However, the validity of this system is built on an implicit premise: the velocity of field sources is far lower than the speed of light, propagation delays can be ignored or treated as perturbations, and time can be viewed as a universal parameter independent of space.
In the low-energy domain—i.e., under the non-relativistic approximation—NQT can effectively utilize the Schrödinger equation for calculations. At this stage, the global Hamiltonian is well-defined, the time evolution of the wave function follows a unified clock, and standard tools such as symmetry analysis, perturbation theory, and selection rules can be used as usual. NQT's reinterpretation of this domain—for example, understanding spin as the particle's real rotational angular momentum and entanglement as long-range field correlation—does not alter the mathematical structure of the calculations but endows them with a clearer physical picture.
However, when problems enter the realm of multi-electron atoms and complex molecules, the applicability of the Schrödinger equation has significantly declined. Correlation effects between electrons, relativistic corrections for spin-orbit coupling, and the inherent complexity of many-body problems make the non-relativistic framework increasingly inadequate physically, even if it barely functions mathematically. This is the first layer of computational difficulty NQT faces: Where is the boundary of the low-energy framework?
II. The Strong Relativistic Challenge in the Domain of Particle Structure
The true difficulty arises at the level of particle structure. When physics enters the internal structure of elementary particles—the finite size of the electron, the composition of protons and neutrons, quark confinement—we enter the domain of strong relativity. Here, classical electromagnetic calculation methods fail completely, for fundamental reasons: time and physical quantities may be intrinsically local.
Under strong relativistic conditions, there is no global absolute time to uniformly describe the system's evolution. Particles are no longer mass points moving under the calibration of an external clock but are local field configurations whose "internal time" is determined by local field dynamics. This means that the traditional basic operation of "writing down the state of the entire system at a certain moment t " may not be a physically meaningful procedure in this domain at all.
The Standard Model's approach to this is Quantum Field Theory (QFT)—formally evading the difficulty of time locality through path integrals and renormalization. But as NQT points out, the "coupling" in the Standard Model is essentially a measurement-collapse-style docking rather than a true microscopic physical mechanism. The computational power of QFT is undeniable, but its physical ontology is vague. If NQT is to provide an alternative computational framework at the level of particle structure, it must confront this issue directly: How to establish a calculable physical theory without relying on global absolute time?
III. Symmetry and Multipole Moments: A Possible Direction for Thought
Symmetry analysis and electromagnetic multipole expansion are among the most powerful computational tools in non-relativistic physics. Electric dipole, magnetic dipole, electric quadrupole... this hierarchical structure is built on two premises: the spatial scale of the field source is far smaller than the radiation wavelength, and time can be treated as a global parameter. Core conclusions like selection rules, parity conservation, and angular momentum coupling all depend on the strict validity of these symmetries.
This set of tools naturally becomes a direction NQT can draw upon when moving toward quantification. However, one must be soberly aware that relativistic effects may fundamentally alter some conclusions drawn under non-relativistic conditions.
First, the localization of time destroys global symmetry classification. In non-relativistic quantum mechanics, the symmetry of the Hamiltonian directly determines conservation laws and selection rules. But when time itself becomes a local quantity, the global Hamiltonian is no longer well-defined, and the foundation of symmetry classification is shaken. Transitions that were originally "forbidden" may, from the perspective of local fields, simply be higher-order electromagnetic radiation processes. NQT's re-analysis of forbidden transitions—as higher-order electromagnetic radiation processes that naturally exist in classical fields—already hints at this direction.
Second, the validity of the multipole expansion itself is challenged. Multipole expansion assumes the field source is "small" and can be approximated order by order using spherical harmonics. But when particles have a finite size on the order of the Compton wavelength and field self-interaction cannot be ignored, the boundary between source and field becomes blurred. The traditional clear separation of "source inside, field outside" no longer holds, and the definition of multipole moments itself needs to be re-examined.
Third, magnetic properties shift from "derived quantities" to "ontological properties." In the non-relativistic framework, magnetic dipole moment is a secondary effect derived from charge motion. But in NQT's particle-field dual ontology, magnetism is an intrinsic property of fermions. This means that in the strong relativistic domain, the hierarchical structure of multipole moments may need to be understood in reverse—magnetic interaction is not a relativistic correction to electric interaction but a physical mechanism equal to or even more fundamental than it.
Fourth, the physical content of gauge symmetry changes. NQT has pointed out that gauge invariance originates from the degree of freedom in choosing the direction of the magnetic moment. Under non-relativistic conditions, this manifests as an abstract mathematical symmetry; but in the framework of strong relativity and local time, the gauge field must assume the actual physical function of coordinating the consistency of local magnetic moment directions, and its dynamical content is far richer than in the non-relativistic case.
IV. Possible Paths Toward a New Computational Framework
Synthesizing the above analysis, the computational difficulty facing NQT can be summarized as a core contradiction: NQT possesses a clearer physical ontology than standard theory—finite-sized particles, real rotational angular momentum, long-range field correlation, magnetic moment direction freedom as the origin of gauge symmetry—but it is precisely this physical clarity that demands a matching, brand-new computational method that respects local causality.
The way out may not lie in simply generalizing non-relativistic multipole analysis to relativity (an "upgrade" like going from the Schrödinger equation to the Dirac equation) but in starting from the ontology of local fields to re-establish a method of field configuration classification compatible with local causality. In this new framework, non-relativistic symmetry and multipole conclusions should emerge naturally as low-energy limits, not serve as the starting point.
This is the core barrier NQT must break through when transitioning from qualitative interpretation to quantitative theory, and from the low-energy domain to the level of particle structure. This breakthrough requires not only innovation in mathematical techniques but also a rethinking of the basic question "what is a calculable physical quantity"—in a world where time itself is local, what does calculation mean?