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On the Ontological Theory of the Four-Element Dynamic Field Based on Natural Completeness

Author: Zhang Suhang

Affiliation: Luoyang School of Mathematics

Date: October 2026

Abstract

Classical field theory, gauge field theory, and quantum field theory exhibit long-standing structural incompleteness in their descriptions of fields. Traditional theories rely solely on field strength as the core descriptive quantity, artificially separating static fields from oscillating fields, and geometric structures from dynamical evolution, resulting in field models that are static, passive, and phenomenological. Adhering to the principle of natural completeness, this paper transcends the definitional limitations of traditional fields and establishes a complete, four-element integrated field ontology system encompassing field strength, field curvature, field frequency, and field dynamics. This theory unifies geometric morphology, intrinsic oscillation, dynamical evolution, and intensity attributes as native, intrinsic characteristics of the field, thereby reconstructing the fundamental physical picture of fields. This framework rectifies the structural degrees of freedom and dynamical mechanisms missing in traditional field theories, achieves the natural unification of static and dynamic fields, as well as geometric and oscillatory attributes, and provides a novel foundational framework for the underlying mechanisms of interactions and unified field theories.

Keywords: Field Theory; Field Ontology; Four-Element Field; Field Curvature; Field Frequency; Field Dynamics

1. Introduction

Since the establishment of classical electromagnetic field theory, the field has become the core physical carrier for describing interactions in nature. Through the development of Gauss's vector field theory, the curvature field theory of general relativity, gauge field theory, and quantum field theory, humanity has acquired mature mathematical tools for field theory, capable of precisely characterizing field flux, integral relations, geometric curvature, and quantum excitation effects.

However, for a long time, the ontological definition of the field has remained incomplete, exhibiting evident artificial simplification and natural fragmentation:

1. The fundamental description of traditional fields relies solely on field strength, treating geometric structures, oscillatory rhythms, and autonomous evolution as derivative phenomena rather than native attributes.

2. Curvature is exclusively attributed to gravitational spacetime geometry and has not been established as a universal intrinsic structure of all fields.

3. Frequency is restricted solely to dynamic oscillatory fields (such as electromagnetic waves, gravitational waves, or quantum probability waves), while static fields are stripped of oscillatory attributes, fragmenting the unified natural form of fields.

4. Field evolution is predominantly a passive response to external conditions, lacking native, self-consistent field dynamical mechanisms, causing fields to appear static, invisible, and passive.

Existing field theories focus separately on numerical distribution, spacetime curvature, and quantum fluctuations. They fail to construct a complete ontological structure of fields from the perspective of natural completeness. Based on this, this paper abandons the traditional paradigm of artificial separation, aligns with natural ontological laws, and establishes a four-element complete dynamic field system, achieving a unified description of field intensity, morphology, rhythm, and dynamics.

2. Core Structural Defects of Traditional Field Theories

2.1 Single Descriptive Dimension

Classical field theory uses field strength as the sole core physical quantity, focusing on the numerical distribution and propagation laws of fields in space while ignoring the geometric structures and oscillatory essence, thereby reducing fields to pure numerical representations.

2.2 Separation of Geometry and Field Ontology

General relativity equates gravity with spacetime curvature, and gauge field theory equates interactions with fiber bundle curvature. However, these two types of curvature belong to the base spacetime and the fiber layer, respectively, and are not unified as intrinsic curvature attributes of the field, failing to adapt to the geometric description of global fields.

2.3 Localization of Frequency Attributes

In traditional theories, frequency is an exclusive derivative characteristic of dynamic wave fields, and static steady-state fields have no defined frequency. This artificial division violates the law of natural unity, fragments static and oscillatory fields, and fails to explain the origins of field state evolution and force gradients.

2.4 Absence of Dynamical Mechanisms

Traditional fields are mostly passive, with their morphology, strength, and variations determined by external sources, spacetime backgrounds, or external perturbations. They lack the field's own structural motion, frequency evolution, and self-coupling dynamical systems, failing to completely describe the natural evolutionary laws of fields.

3. Ontological Definition of the Four-Element Complete Dynamic Field

Adhering to the construction principles of respecting nature, completeness, and self-consistency, this paper defines the four intrinsic native attributes of natural fields. All macroscopic, microscopic, static, and dynamic physical fields uniformly satisfy this ontological structure. The four are inseparable and synergistically coupled, collectively constituting the complete form of a real natural field.

3.1 Field Strength: The Quantitative Foundation

Field strength is the most fundamental numerical attribute, characterizing the interaction intensity and energy distribution at spacetime points. It is the core effective physical quantity retained from traditional field theory, determining the magnitude of action, spatial distribution, and energy accumulation characteristics.

3.2 Field Curvature: The Morphological Foundation

Curvature is upgraded from an exclusive spacetime feature to a universal intrinsic geometric attribute of all fields. Any field, whether static or dynamic, possesses intrinsic curved structures. The geometric curvature of a field is no longer limited to gravitational spacetime but serves as the morphological representation of the field ontology, corresponding to structural deformation, spatial distortion, and structural potential energy.

3.3 Field Frequency: The Rhythmic Foundation
Abandoning the traditional cognition that frequency belongs only to wave fields, frequency is established as the intrinsic oscillatory rhythm of all fields. The frequency here not only includes quantum-level probability amplitude oscillations but also broadly refers to the intrinsic state oscillatory rhythm of the field as a physical entity. Static fields are not without frequency; rather, they exist in a steady-state, low-frequency, weak-gradient equilibrium. The frequency gradient of a field is the core origin of field state transitions and interactions.

3.4 Field Dynamics: The Evolutionary Foundation
Field dynamics is the core mechanism for the field's autonomous motion, self-evolution, and multi-attribute coupling. It encompasses five core evolutionary laws, rectifying the defect of traditional fields being passive and devoid of dynamics:

1. Temporal Evolution: Field strength, curvature, and frequency undergo continuous dynamic micro-adjustments over time; there is no absolutely static field.
2. Structural Motion: The curvature structure of the field can migrate, aggregate, stretch, and diffuse, achieving autonomous evolution of the field's morphology.
3. Spectral Evolution: The intrinsic frequency of the field can dynamically shift and differentiate in gradients, creating dynamical disparities within the field.
4. Four-Element Coupled Evolution: Field strength, curvature, frequency, and dynamics are interlocked in a closed loop—geometric deformation alters frequency, frequency gradients drive field motion, and field motion modifies intensity distribution, forming a self-consistent dynamic cycle.
5. Energy-Momentum Transport: Autonomous accumulation, dissipation, migration, and conversion of field energy, aligning with the laws of natural energy conservation.

4. Theoretical Innovation Value of the Four-Element Field System

4.1 Unification of Static and Dynamic Fields
Through global frequency and dynamic dynamical mechanisms, the artificial fragmentation between static and oscillatory fields is eliminated, proving that they are merely the steady-state and dynamic manifestations of the four-element field under different boundary conditions, thereby achieving the natural unity of fields.

4.2 Unification of Geometric Structure and Field Ontology
Fields are no longer additional distributions on a spacetime background but independent physical ontologies possessing intrinsic curvature geometry. This fundamentally changes the traditional cognition of "spacetime as the stage and fields as appendages."

4.3 Construction of a Truly Natural Dynamic Field Model
Traditional fields are static, incomplete fields describing only the "quantity" of the field. The four-element field in this paper is a complete natural field, simultaneously describing the quantity, morphology, frequency, and dynamics, fully aligning with the true natural existence of fields.

4.4 Providing a Novel Foundation for Unified Field Theories
The four-element field ontology is compatible with the effective conclusions of classical field theory, relativistic curvature fields, and quantum fields, while supplementing the underlying ontological structures they lack. It provides a novel theoretical foundation for the unification of interactions, field quantization, and the ontological correlation between spacetime and fields.

5. Conclusion and Outlook

The century-old limitations of traditional field theory essentially stem from the over-simplification and artificial separation of the field ontology, losing the three core natural attributes: geometry, rhythm, and dynamics. The four-element complete field system of Field Strength - Field Curvature - Field Frequency - Field Dynamics established in this paper reconstructs the fundamental physical definition of fields, achieving natural completeness and dynamic unification.

This theory completely sheds the static, invisible, and passive model defects of traditional fields, allowing all natural manifestations of fields to be explained through the coupled evolution of the four attributes. Subsequent work will build upon this complete field ontology to further investigate the force mechanisms of field frequency gradients, the quantitative equations of field curvature, and the unified dynamical equations of four-element coupling, thereby perfecting the unified system of fundamental field theory.

References

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[2] Einstein, A. General Relativity and the Theory of Spacetime Curvature [J]. Annalen der Physik.

[3] Foundations of Gauge Field Theory and Quantum Field Theory [M]. High Energy Physics Press.

[4] Zhang, S. H. Theory of Unified Curvature Topological Equations in Mechanics [EB/OL]. Luoyang School of Mathematics Corpus, 2026.