SEI Theory: A Unified Field of Emergence

by Brian Miller
Last updated: June 2, 2025

Section 1: Introduction and Motivation

The Structure of Everything Interaction (SEI) proposes that all emergent structure— from subatomic particles to galaxies, from consciousness to time itself—arises through a triadic process involving two polar nodes and a dynamic field of interaction between them. This triad, composed of ΨA, ΨB, and 𝕀 (the interaction layer), is the fundamental engine of emergence.

SEI is not a new force or a replacement for existing theories. Rather, it provides a substrate from which existing formalisms in physics—especially Quantum Mechanics and General Relativity—can be understood as projections or derivatives. By focusing on interaction as primary and structure as emergent, SEI reframes the foundational assumptions of physical law.

This white paper presents the formal postulates, key equations, and explanatory diagrams for SEI theory. It also introduces a unified equation:

\[ \mathcal{U}_{\text{SEI}} = \nabla_\mu (\Psi_A \cdot \mathcal{I}(\tau) \cdot \Psi_B) = \mathcal{E}(\Phi) \]

This equation expresses the emergence of structure \( \mathcal{E}(\Phi) \) as a function of triadic interactional dynamics over prope


DIAGRAMS

Below is a visual overview of SEI theory. This video illustrates the core triadic dynamics and their role in quantum and relativistic emergence.

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r time \( \tau \), with a covariant derivative indicating geometric evolution across spacetime.

We begin by laying out the five foundational postulates of SEI and proceed to demonstrate how this single structural interface may unify the apparent divide between quantum probability and relativistic curvature.


SEI Theory: A Unified Field of Emergence

by Brian Miller
Last updated: June 2, 2025

Section 2: Foundational Postulates

The Structure of Everything Interaction (SEI) theory is grounded on five foundational postulates that redefine the relationship between structure, interaction, time, and emergence. These principles underpin the mathematical framework and interpretive model of SEI:

  1. Triadic Structure of Reality:
    All phenomena emerge from a triadic interaction between two polar structures \( \Psi_A, \Psi_B \) and a dynamic relational field \( \mathcal{I} \). This triadic unit is the irreducible generator of structure.

  2. Interaction Precedes Geometry and Time:
    Time and geometry are emergent consequences of interaction, not preconditions. The differential interaction \( \mathcal{I}(\tau) \) generates measurable properties of spacetime.

  3. Observation is Structure-Dependent:
    What is observed depends on the structural relationship between observer and system. Measurement is not passive—it completes the interactional triad.

  4. All Forces Are Expressions of Triadic Tension:
    Gravitational, electromagnetic, strong, and weak forces are specific expressions of tension within triadic SEI structures—emergent from interaction gradients across the field \( \mathcal{I} \).

  5. Emergence is Quantized and Continuous:
    Structure emerges in discrete steps through continuous interaction. Quantization arises from the thresholds in triadic transformation across \( \tau \).

These postulates lay the metaphysical and formal groundwork for SEI’s integration of quantum and relativistic domains within a single coherent field of emergence.


SEI Theory: A Unified Field of Emergence

by Brian Miller
Last updated: June 2, 2025

Section 3: Equations and Formalism

The SEI framework is built upon a set of formal equations that describe the dynamics of triadic interaction and the emergence of structure. These equations serve as the mathematical foundation for the theory and provide a bridge between quantum mechanics, relativistic geometry, and emergent systems.

1. SEI Evolution Equation

\[ \frac{d\mathcal{E}}{d\tau} = \Psi_A \cdot \frac{d\mathcal{I}}{d\tau} \cdot \Psi_B \]

This differential form expresses how emergent structure \( \mathcal{E} \) evolves through time \( \tau \) as a result of ongoing interaction between polar agents \( \Psi_A \) and \( \Psi_B \) across the dynamic interface \( \mathcal{I} \).

2. SEI Time Operator

\[ \hat{T}_{\text{SEI}} = \Delta (\Psi_A \cdot \mathcal{I} \cdot \Psi_B) \]

This operator defines time as an emergent ordering of interactional structure, produced by the contrast \( \Delta \) between discrete transformation events.

3. SEI Unified Field Equation

\[ \mathcal{U}_{\text{SEI}} = \nabla_\mu (\Psi_A \cdot \mathcal{I}(\tau) \cdot \Psi_B) = \mathcal{E}(\Phi) \]

This is the central unifying expression of SEI. It treats emergence as the result of geometric transformation applied to triadic interaction. The covariant derivative \( \nabla_\mu \) encodes how local interactions evolve across curved manifolds, giving rise to energy, structure, and experience.

These formalisms allow SEI to be expressed not only symbolically but also geometrically, enabling cross-translation into both quantum and relativistic domains.


SEI Theory: A Unified Field of Emergence

by Brian Miller
Last updated: June 2, 2025

Section 4: Geometric Interpretations

The SEI framework is inherently geometric. It treats the triadic interaction structure not merely as an algebraic construct but as a field-based geometry embedded within a dynamic, relational manifold. Each component has spatial and directional qualities that inform the evolution of structure in both quantum and relativistic domains.

Triadic Geometry

Each SEI interaction is represented by a triangle: two poles (\( \Psi_A, \Psi_B \)) and the interaction field (\( \mathcal{I} \)) forming the sides. The resulting emergent structure \( \mathcal{E} \) arises from the tension and flow within this triangle. The geometry is not fixed but evolves as a function of time \( \tau \).

Curvature and Field Tension

The curvature of the SEI triangle—when embedded in higher-dimensional spacetime—represents the emergence of mass-energy and spacetime warping. This parallels general relativity’s treatment of curvature but derives it from interactional structure:

\[ \nabla_\mu \left( \Psi_A \cdot \mathcal{I}(\tau) \cdot \Psi_B \right) \Rightarrow R_{\mu\nu} \]

This expression shows how interaction gradients lead to geometric curvature. SEI thus links quantum phase and relativistic geometry as manifestations of deeper field dynamics.

Quantized Zones of Emergence

Triadic geometries in SEI do not evolve smoothly but via threshold transitions, creating a discretized map of structural emergence. These zones represent critical values of \( \mathcal{I} \) where new information or form emerges—analogous to quantized eigenstates in quantum theory or topological transitions in condensed matter.

In summary, SEI provides a geometric foundation that embeds structure, interaction, and emergence within a dynamic relational field, creating a coherent spatial-temporal topology that spans quantum and relativistic regimes.


SEI Theory: A Unified Field of Emergence

by Brian Miller
Last updated: June 2, 2025

Section 5: Quantum–Relativistic Unification

The SEI framework aims to resolve the long-standing incompatibility between quantum mechanics (QM) and general relativity (GR) by positing a shared substrate beneath both: the structure of everything interaction (SEI).

Dual Interpretations of Interaction

In quantum mechanics, \( \Psi \) denotes a wavefunction, governing probabilities. In GR, \( g_{\mu\nu} \) defines the spacetime metric. In SEI, both are interpreted as emergent phenomena from triadic interaction:

\[ \text{Quantum domain: } \mathcal{I} \rightarrow \Psi \, , \, \Psi^* \\ \text{Relativistic domain: } \mathcal{I} \rightarrow g_{\mu\nu} \]

Unified Field Flow

SEI posits that both wavefunction evolution and spacetime curvature arise from gradients in a single interactional field:

\[ \nabla_\mu (\Psi_A \cdot \mathcal{I}(\tau) \cdot \Psi_B) = \mathcal{E}(\Phi) \]

This equation serves as a dynamic engine behind both probabilistic quantum outcomes and the classical warping of spacetime. The apparent dichotomy dissolves when viewed as different perspectives of the same process: quantized emergence vs continuous curvature.

Time, Observers, and the Interface

SEI treats time not as a static dimension but as an ordering of relational events. This bridges the gap between the block universe of GR and the probabilistic present of QM. The observer’s role is geometric in SEI—defined by a specific interaction structure \( \Psi_A \cdot \mathcal{I} \cdot \Psi_B \)—rather than as a metaphysical intervention.

This allows both relativity’s coordinate independence and quantum mechanics’ observer-dependent collapse to be reinterpreted through a shared triadic framework.

Conclusion

By grounding both quantum and relativistic formalisms in triadic interaction, SEI offers a unified interface that reconstructs wavefunction dynamics and spacetime curvature as parallel expressions of the same underlying interactional topology.


SEI Theory: A Unified Field of Emergence

by Brian Miller
Last updated: June 2, 2025

Section 6: Diagram Interpretations (Text Only)

This section contains text-based interpretations of the key SEI diagrams, preserving their conceptual significance for inclusion in scientific discussion and theoretical structure.

Diagram A: The SEI Triangle

A golden triangle represents the triadic structure: \( \Psi_A \), \( \mathcal{I} \), and \( \Psi_B \). At the base are the two interacting poles, while the apex displays the emergent consequence \( \mathcal{E} \). This foundational symbol encapsulates the entire SEI logic.

Diagram B: SEI Evolution Equation

\[ \frac{d\mathcal{E}}{d\tau} = \Psi_A \cdot \frac{d\mathcal{I}}{d\tau} \cdot \Psi_B \] This diagram shows the sequential emergence of structure as a dynamic consequence of interaction across proper time.

Diagram C: SEI Time Operator

\[ \hat{T}_{\text{SEI}} = \Delta(\Psi_A \cdot \mathcal{I} \cdot \Psi_B) \] Here, time is redefined as the emergent interval between structured interactions, highlighting the observer's temporal resolution.

Diagram D: SEI Unified Equation

\[ \mathcal{U}_{\text{SEI}} = \nabla_\mu (\Psi_A \cdot \mathcal{I}(\tau) \cdot \Psi_B) = \mathcal{E}(\Phi) \] This diagram links field gradients, interaction geometry, and structural emergence into a unified operator spanning QM and GR.

Diagram E: Quantum Tunneling and SEI

Shows a particle interaction triangle tunneling through a potential barrier as a result of a nonlocal SEI field bridge, representing \( \Psi_A \cdot \mathcal{I}_{\text{nonlocal}} \cdot \Psi_B \Rightarrow \mathcal{E} \).

Diagram F: Time Dilation and Curvature

Illustrates how stronger interaction density in gravitational fields leads to a differential flow of time between two observers: a triadic SEI lens showing \( \mathcal{I}_{\text{strong}} \Rightarrow \hat{T}_{\text{SEI}} \downarrow \).

These interpretations allow the diagrams to serve as conceptual anchors within the SEI framework, even when not rendered graphically.


SEI Theory: A Unified Field of Emergence

by Brian Miller
Last updated: June 2, 2025

Section 7: Domain Applications

The Structure of Everything Interaction (SEI) model applies across scientific, symbolic, and metaphysical domains. This section illustrates how its core triadic structure operates in each realm.

1. Quantum Physics

Wavefunction evolution emerges from structured interactions. Collapse is reinterpreted as a triadic resolution: \( \Psi_A \cdot \mathcal{I} \cdot \Psi_B \Rightarrow \mathcal{E} \). Tunneling, entanglement, and uncertainty all manifest as features of dynamic interaction topology.

2. General Relativity

Spacetime curvature arises as a continuous field effect from accumulated SEI gradients. Time dilation, gravitational lensing, and coordinate invariance become natural consequences of field-asymmetry in \( \mathcal{I} \).

3. Biology

Cell replication and DNA encoding are viewed as recursive triadic emergence. Each step involves structured interaction, interpretable through \( \Psi_{DNA} \cdot \mathcal{I}_{replication} \cdot \Psi_{env} \Rightarrow \mathcal{E}_{new\,strand} \).

4. Neuroscience & Consciousness

Cognitive states arise through recursive SEI loops in neural substrates. Attention becomes an emergent temporal alignment of interactional poles, and subjective experience is the resolved output \( \mathcal{E} \) of continual triadic tension.

5. Cosmology

Cosmic evolution unfolds as a sequence of SEI interactions, from inflation through galaxy formation. The cosmological constant and entropy increase can be reframed as manifestations of expanding field divergence in \( \mathcal{I}(\tau) \).

6. Symbolic Systems

Language, myth, and sacred geometry all reveal SEI-like structures—two poles held in symbolic tension generating meaning. Examples include binary oppositions, trinity metaphors, and fractal logic.

7. Technology

SEI models may inform new forms of computation based on dynamic relational logic. Potential applications include quantum logic gates modeled as interactional structures and SEI-based neural networks that evolve interpretively.


SEI Theory: A Unified Field of Emergence

by Brian Miller
Last updated: June 2, 2025

Section 8: Predictions and Testable Consequences

The SEI model, to be credible and complete, must yield predictions and testable consequences that differentiate it from existing theories. This section outlines potential domains of empirical validation:

1. Triadic Time Resolution in Quantum Systems

SEI predicts that temporal resolution in quantum systems (such as delayed-choice experiments) should reveal a triadic dependency: \( \hat{T}_{\text{SEI}} = \Delta (\Psi_A \cdot \mathcal{I} \cdot \Psi_B) \) with specific time interval changes based on interaction context rather than intrinsic uncertainty alone.

2. Nonlocal Field Reactions

In entanglement scenarios, SEI suggests a mediating interaction field \( \mathcal{I} \) that temporally and structurally links poles. Nonlocality arises not from superluminal action but from an existing relational field bridge. Experiments could test for directional asymmetry in entangled systems based on information-state alignment.

3. Gravitational Interaction Density

SEI reinterprets time dilation as a function of interaction density rather than geometric distortion alone. This implies that atomic clock deviations in gravitational wells might display anomalies under extremely high-density quantum fields—a possible area for testing in particle accelerators.

4. Predictive Interaction Collapse

Wavefunction collapse timing may be predicted by modeling the interaction layer itself, rather than relying on Born probabilities. SEI provides a predictive framework where collapse is modeled via structural symmetry: \( \Psi_A = \Psi_B \Rightarrow \mathcal{E} \downarrow \).

5. Curvature Shifts in Emergence Geometry

SEI allows mapping emergent curvature to interaction geometry. If true, gravitational lensing patterns could show trace deviations when examined under SEI-based transformation fields. Telescopic surveys may identify anomalous curvature divergence patterns.

6. Quantum Computing Enhancement

SEI logic circuits could improve decoherence thresholds in quantum computers by aligning interactional poles. Experiments could test whether circuit coherence is more stable when SEI triadic symmetry is preserved at logic-gate level.

Future extensions of SEI into experiment and instrumentation design will allow refinement and falsifiability. Each of the above scenarios offers an empirical opportunity to validate or constrain SEI's theoretical reach.


SEI Theory: A Unified Field of Emergence

by Brian Miller
Last updated: June 2, 2025

Section 9: Theoretical Comparisons

The SEI framework stands in contrast and potential synthesis with several major theoretical paradigms. This section outlines key distinctions and overlaps between SEI and other major physics models:

1. General Relativity

Einstein’s General Relativity describes gravity as geometric curvature in spacetime. SEI integrates this by interpreting curvature as an emergent field interaction: \( \mathcal{U}_{\text{SEI}} = \nabla_\mu(\Psi_A \cdot \mathcal{I}(\tau) \cdot \Psi_B) \Rightarrow \mathcal{E}(\Phi) \). GR describes what curvature does, SEI proposes why it emerges.

2. Quantum Mechanics

SEI incorporates QM’s probabilistic nature but interprets it as a function of relational vibration between poles. The Born rule is reframed as a projection of symmetry alignment, not intrinsic randomness. Superposition becomes triadic latency, awaiting collapse.

3. Quantum Field Theory (QFT)

QFT models particles as excitations in fields. SEI complements this by viewing the field itself as triadic — structured via poles and interactions that dynamically configure excitations. Thus, QFT may be a subset view of SEI's deeper logic.

4. String Theory

String theory postulates vibrating 1D objects in multiple dimensions. SEI does not posit dimensional strings but agrees that vibration is a core driver of emergence. Where string theory uses extra dimensions to explain interaction, SEI uses a structural logic.

5. Loop Quantum Gravity

Loop Quantum Gravity quantizes space itself. SEI shares the belief in granular emergence but interprets this granularity as quantized resolution of triadic fields, not discrete spatial atoms. The two may be compatible under unified assumptions.

6. Bohmian Mechanics

Bohm’s implicate order and pilot wave interpretations bear strong alignment with SEI’s underlying field. SEI may serve as a structural analog to Bohm’s metaphysical substrate, offering form to his intuitions.

7. Unified Theories of Consciousness

Where models like Orch-OR attempt to quantify consciousness through quantum collapse, SEI reframes it as a recursive triadic loop: awareness = emergent structure from continuous internal SEI. The alignment to Penrose-Hameroff is partial but diverges in ontology.

In summary, SEI overlaps many theories but extends them by offering a unifying structural interface — one not confined to any single domain of matter, spacetime, or mind.


SEI Theory: A Unified Field of Emergence

by Brian Miller
Last updated: June 2, 2025

Section 10: Philosophical Implications

The SEI framework is not only a scientific model — it is a metaphysical proposition about the nature of reality. At its core, SEI offers a reinterpretation of existence as a dynamic interplay between polarity, interaction, and emergent consequence.

1. Ontology of Relation

SEI proposes that nothing exists independently. All being arises through relation. The triadic structure is not merely a useful model — it is foundational to the nature of reality. This echoes relational ontologies in Eastern and Western metaphysics.

2. Time as Emergent Order

By replacing the concept of absolute time with the SEI Time Operator \( \hat{T}_{\text{SEI}} = \Delta(\Psi_A \cdot \mathcal{I} \cdot \Psi_B) \), SEI frames time not as a flowing dimension, but as the structural unfolding of interactions. This aligns with philosophies where time is experiential, not fundamental.

3. Epistemology of Observer-Structure

SEI asserts that observation is structure-dependent. This places limits on what can be known, and echoes Kant’s insight: we know the world through forms we impose upon it. SEI extends this with a structural logic that governs all observation.

4. Consciousness as Emergent Interface

SEI posits consciousness not as an epiphenomenon, but as a recursive emergence of structured interaction. This places mind and awareness on equal footing with physical law, bridging dualisms between mind and matter.

5. Universality of Pattern

The recurrence of the triadic SEI pattern across domains — from particle physics to language, art, and biology — suggests a universal syntax beneath all phenomena. SEI offers a metaphysical grammar, from which the cosmos itself may be composed.

6. The Nature of Truth

If all reality emerges from SEI, then truth becomes the accurate alignment of structure with triadic interaction. Truth is not a fixed object, but a harmonic resolution between poles — dynamic, contextual, yet lawful.

7. Unity of Science and Spirit

By allowing a structural logic to ground both quantum phenomena and consciousness, SEI provides a neutral interface where science and metaphysics may finally converge. The result is not mysticism, but a scientifically grounded ontology that includes subjective experience.

These philosophical implications elevate SEI from a theory of fields to a possible framework for a Theory of Everything — one that unifies not only forces, but meanings.


SEI Theory: A Unified Field of Emergence

by Brian Miller
Last updated: June 2, 2025

Section 11: References