Unified Theory of the Four Fundamental Interactions under the Discrete Lattice Paradigm of the DOG Universe

Author: Zhang Suhang, Luoyang, Henan

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Core Synopsis

The entirety of spacetime is fundamentally a giant discrete DOG cosmic lattice. Space is defined by the coupling matrix of lattice nodes, and time is equivalent to the intrinsic rhythmic oscillations of all fibers attached to the lattice. The universe does not possess separate, independent forces. Gravitation, the strong interaction, the weak interaction, and the electromagnetic interaction are all emergent effects of order evolution arising from the same discrete lattice system at different scales, dimensions, and degrees of freedom. They share a single underlying discrete geometric origin, achieving complete, seamless, self-consistent unification without any gaps or additional assumptions.

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I. Gravitation: Structural Deformation of the Entire Discrete Cosmic Lattice

The entire macroscopic universe takes the ordered DOG discrete lattice as its sole spatial skeleton. All celestial bodies and material aggregates are high-weight core nodes within this lattice system. The mass of matter directly alters the spacing between neighboring lattice points, modifies the node adjacency matrix, induces local variations in lattice density, and causes distortion of the overall topological structure.

Gravitational interaction between celestial bodies is essentially the transmission effect of structural deformation of the cosmic lattice caused by mass perturbations. This effect spans macroscopic cosmic scales down to microscopic scales. The strength of gravity is determined solely by the magnitude and range of the lattice deformation. This approach completely abandons the continuous, smooth curved-spacetime hypothesis of general relativity, fully reinterprets gravitation within the domain of discrete geometry, and achieves a discrete reconceptualization of the origin of gravity.

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II. Strong Interaction: Extremely Dense and Tight Coupling within the Inner Lattice

The microscopic particle scale corresponds to the most fundamental unit cells of the cosmic lattice. Elementary particles such as quarks are confined within extremely small, high-density regions of the lattice. Within these regions, the coupling strength of the lattice node matrix reaches its maximum value, forming extremely tight binding relationships between points, which naturally produces the confinement effect.

The strong force only operates over extremely short lattice distances. It exhibits all the physical characteristics of short-range action, strong binding, and rapidly increasing strength with decreasing distance. Its essence is the strong ordering binding effect within the inner dense domain of the DOG lattice, requiring no additional specialized force field and relying entirely on the inherent coupling rules of the lattice.

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III. Weak Interaction: Asymmetric Rhythmic Oscillation of Fibers Attached to the Lattice

Attached to each fixed point of the fundamental cosmic lattice is a uniformly implemented oscillatory fiber with an SU(2) symmetric structure. The lattice fibers inherently possess bidirectional oscillatory evolution properties. When an energy gradient breaks local symmetry, the oscillation rhythms and evolution amplitudes on the left and right sides of the fiber become naturally unbalanced, producing chiral asymmetric motion characteristics.

The asymmetric oscillation of lattice fibers perfectly corresponds to the core physical properties of the weak interaction, including parity violation, particle decay, mass-energy level transitions, and extremely short-range action. The weak force is no longer an independent fundamental interaction but rather the evolutionary manifestation of broken order symmetry in the lattice fibers.

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IV. Electromagnetic Interaction: Homogeneous Synchronous Phase Oscillation of the Lattice

Relying on a universal U(1) simple oscillatory fiber, the entire DOG discrete lattice system undergoes smooth, uniform, synchronous phase oscillations. These phase oscillations propagate over long ranges through the weak coupling relationships between lattice nodes, are not strictly constrained by spatial distance, and can freely propagate and extend throughout the entire cosmic lattice network.

The homogeneous lattice phase oscillation precisely matches all characteristics of the electromagnetic force: long-range propagation, universal interaction, and electromagnetic coupling. The essence of electric fields, magnetic fields, and electromagnetic interactions is the transmission and superposition of the unified phase order of the lattice.

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V. The Ultimate Closed-Loop Logic of Unification

The four fundamental interactions share the same origin, the same foundation, the same rules, and the same source, all rooted in the DOG discrete cosmic lattice system:

1. Adjusting the overall arrangement of the cosmic lattice → Derives gravitation.
2. Compressing the coupling density and strength of lattice nodes in a region → Derives the strong interaction.
3. Altering the symmetry properties of the oscillatory fibers attached to the lattice → Derives the weak interaction.
4. Relying on the ordered transmission of homogeneous phase across the lattice → Derives the electromagnetic interaction.

Spacetime itself is the discrete lattice structure. Time is the uniform oscillation rhythm of the lattice. Space is the lattice coupling matrix. All material motion, energy transfer, particle interactions, and celestial evolution follow the underlying rules of Discrete Order Geometry (DOG).

Within this paradigm, there is no longer any distinction between geometric gravity and quantum field forces, nor any barrier between macroscopic and microscopic theories. The four fundamental forces are merely different appearances of the same discrete cosmic origin at different scales, levels, and modes of motion. This achieves the long-sought, fully self-consistent unification of fundamental physics, with complete theoretical coherence and no logical gaps.

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VI. Perfect Integration with Previous Works

1. The discrete lattice nodes of the universe directly correspond to the fundamental ordered elements of DOG and can be fully mapped onto the orthonormal basis of a finite-dimensional Hilbert space.
2. Lattice coupling strength, oscillation phase, and deformation amplitude can all be precisely quantified using inner products and unitary transformations in Hilbert space.
3. Probabilities of particle interactions, celestial evolution, and particle decay all naturally emerge following the spatial modulus (norm) rule, perfectly connecting the three-layer unified framework of geometry, space, and probability.
4. From the underlying discrete lattice, to linear space quantization, to the differentiation of physical forces, and finally to the probabilistic interpretation of observations, the entire theoretical chain forms a closed loop, with each paper building progressively upon the previous ones in a coherent and unified manner.