This white paper introduces the SEI (Structure of Everything Interaction) Theory, a unified framework that places structured triadic interaction at the foundation of all physical phenomena. The core premise asserts that emergence — whether quantum, gravitational, cosmological, or conscious — is not derived from particles, spacetime, or fields alone, but from a dynamic interplay between two polar nodes and their mediating interaction field.
The central equation, Miller’s Equation: \[ \mathcal{I}_\Delta = \mathcal{E} \] declares that the net differential in the interaction field produces emergent structure. This paper rigorously formulates SEI’s mathematical foundation, presents its empirical predictions, and shows how it naturally unifies quantum mechanics and general relativity within a single triadic structure.
We further contrast SEI with conventional physical theories, derive its Lagrangian, propose falsifiable predictions, and explore its philosophical implications. The goal is a complete, mathematically rigorous, and self-contained theory requiring no external assumptions.
Modern physics remains divided between the smooth geometric curvature of general relativity and the probabilistic, nonlocal behavior of quantum mechanics. Despite immense empirical success in both domains, no consensus has emerged on a unified framework that reconciles them. Theoretical tensions — such as the measurement problem, the cosmological constant, and the failure of quantum gravity — point toward a deeper layer of explanation.
SEI Theory proposes that the fundamental layer is not matter, spacetime, or wavefunctions — but structured interaction. Specifically, all emergence arises from a dynamic triadic structure:
This triadic unit underlies not only physical interactions, but logic, perception, measurement, causality, and emergence itself. It is the atom of intelligibility — the irreducible minimum through which structure becomes possible.
SEI Theory rests on the following foundational postulates:
At the heart of SEI Theory is the assertion that emergence is not additive or caused by particles or fields in isolation, but by the net asymmetry in structured interaction. This is codified in Miller’s Equation:
Here, \(\mathcal{I}_\Delta\) represents the net differential in the structured interaction field \(\mathcal{I}\), and \(\mathcal{E}\) is the emergent observable — a particle, force, measurement, boundary, or curvature. This fundamental relation defines the bridge between polar entities and the emergence of structure.
Let \( \mathcal{M} \) be a four-dimensional differentiable manifold representing the interactional configuration space. We define the structured interaction field as a symmetric rank-2 tensor:
where \( \Psi_A(x), \Psi_B(x) \) are scalar or spinor fields defined over \( \mathcal{M} \), representing the polar nodes of interaction.
We define the action \( S \) for SEI as:
The SEI Lagrangian density is postulated to take the form:
Here, \( V \) is an interaction potential that encodes symmetry-breaking, coupling constants, or emergence thresholds.
Varying the action with respect to \( \mathcal{I}_{\mu\nu} \), we obtain:
This defines the dynamical field equations for the SEI interaction field. The emergent structure \( \mathcal{E} \) is encoded in the solutions to \( \mathcal{I}_{\mu\nu}(x) \) under given boundary or symmetry conditions.
To formulate the Hamiltonian structure of SEI, we begin by identifying the conjugate momenta associated with the interaction field \( \mathcal{I}_{\mu\nu} \). The canonical momentum is defined as:
Given the Lagrangian density:
The Hamiltonian density is obtained via Legendre transformation:
To quantize the SEI field theory, we promote the fields and their conjugate momenta to operators and impose canonical commutation relations:
Alternatively, a path integral quantization may be defined as:
SEI theory admits local gauge transformations acting on \( \Psi_A \) and \( \Psi_B \) as:
The interaction field \( \mathcal{I}_{\mu\nu} \) transforms covariantly under these gauge shifts:
For appropriate potentials \( V \), the Lagrangian remains invariant under this transformation:
This structure supports the derivation of conserved currents via Noether's theorem and aligns SEI with field-theoretic symmetry principles.
To formalize SEI's interaction-based ontology, we treat the interaction field \( \mathcal{I} \) as a rank-2 tensor field over a differentiable manifold \( \mathcal{M} \), where each point represents a local triadic configuration:
Here, \( \Psi_A \) and \( \Psi_B \) are sources encoded as polar potentials, and \( x \in \mathcal{M} \) is a spacetime point. The divergence or differential structure of \( \mathcal{I}_{\mu\nu} \) gives rise to emergent fields \( \mathcal{E}_\alpha \), such that:
Lagrangian Formulation of SEI Theory
The SEI framework postulates that all phenomena emerge from structured interaction, rather than isolated particles or fields. This triadic interaction — composed of two polar entities (Ψ_A and Ψ_B) and a mediating dynamic field (𝓘) — generates the emergent structure of reality itself.
To embed this into physics, we construct a Lagrangian density ℒ_SEI that treats interaction as the fundamental dynamic quantity.
1. Foundation: Miller’s Equation
𝓘_Δ = ℰ
This expresses that change in the interaction field (𝓘_Δ) gives rise to an emergent phenomenon (ℰ). Here, interaction is not a side effect — it is the cause of structure.
2. SEI Lagrangian Density
ℒ_SEI = (1/2) (∂_μ Ψ_A · 𝓘^μν · ∂_ν Ψ_B) - V(Ψ_A, Ψ_B, 𝓘)
Where:
- ∂_μ Ψ_A and ∂_ν Ψ_B represent the dynamical evolution of the polar nodes in spacetime.
- 𝓘^μν is the interaction tensor field that mediates their coupling.
- V is a potential term reflecting intrinsic tension, symmetry, or emergent behavior.
This Lagrangian is structurally triadic. The interaction tensor 𝓘^μν sits between the polar nodes and dynamically resolves their relationship.
3. Emergence as Action
S_SEI = ∫ ℒ_SEI d⁴x
Variational principle:
δS/δΨ_A = 0 , δS/δΨ_B = 0 , δS/δ𝓘^μν = 0
These produce emergence dynamics — not particle trajectories but configurations of structured interaction.
4. SEI vs Classical Lagrangians
| Classical | SEI Equivalent |
|---------------------|------------------------------------------------------------------------|
| L = T - V | ℒ_SEI = Interaction Kinetics - Interaction Potential |
| (1/2) ∂_μ φ ∂^μ φ - V(φ) | (1/2) ∂_μ Ψ_A · 𝓘^μν · ∂_ν Ψ_B - V(Ψ_A, Ψ_B, 𝓘) |
SEI replaces single-field dynamics with triadic dynamical geometry — interaction is not added to structure; it is structure.
5. Implications
- 𝓘^μν generalizes both the metric tensor (GR) and gauge field (QFT).
- Emergent structures (particles, decoherence, geometry) are interaction patterns.
- SEI unifies physical dynamics across scale via a single variational principle.
The canonical Hamiltonian \( \mathcal{H}_{SEI} \) is derived from the Lagrangian via Legendre transformation:
Where \( \pi^{\mu\nu} = \frac{\partial \mathcal{L}}{\partial \dot{\mathcal{I}}_{\mu\nu}} \) is the canonical conjugate momentum. This structure enables a full phase-space formulation of SEI dynamics and evolution.
SEI respects gauge symmetry by construction. Local transformations of \( \Psi_A \) and \( \Psi_B \) leave the form of \( \mathcal{L}_{SEI} \) invariant under:
Since the interaction field \( \mathcal{I} \) is relational and differential, it transforms covariantly under local gauge operations, preserving the emergent observables \( \mathcal{E} \).
A foundational requirement of any physical theory is that it must generate predictions that are, in principle, falsifiable. SEI satisfies this by proposing new interaction-based mechanisms underlying emergence in quantum, gravitational, and cosmological systems.
Because SEI treats structured interaction—not particles or spacetime—as fundamental, it implies novel experimental consequences that deviate from predictions of standard field theory and general relativity. These predictions offer direct avenues for empirical verification or falsification.
Empirical Predictions and Testable Consequences A foundational requirement of any physical theory is that it must generate predictions that are, in principle, falsifiable. SEI satisfies this by proposing new interaction-based mechanisms underlying emergence in quantum, gravitational, and cosmological systems. Because SEI treats structured interaction—not particles or spacetime—as fundamental, it implies novel experimental consequences that deviate from predictions of standard field theory and general relativity. 1. Quantum-Level Predictions Prediction A: Triadic Collapse Asymmetry SEI predicts that quantum state collapse is not instantaneous or binary, but a triadic resolution process. This process should display directional asymmetries depending on the configuration of Ψ_A, Ψ_B, and the interaction field ℐ. Test Method: - Entangled particle experiments with tunable interaction asymmetries (e.g., delayed-choice entanglement with asymmetrical field environments). - Weak measurement experiments to detect pre-collapse alignment between Ψ_A and Ψ_B. 2. Gravitational Predictions Prediction B: Micro-Lensing Deviations SEI implies that gravitational curvature arises from sustained triadic interaction between massive bodies and their context, mediated by ℐ^μν. In areas where contextual asymmetry is strong (e.g., near black hole binaries), light paths should deviate subtly from GR predictions. Test Method: - High-resolution gravitational lensing data from instruments like the Event Horizon Telescope or James Webb, compared against GR and SEI-inferred curvature patterns. 3. Cosmological Structure Emergence Prediction C: Non-Random Large-Scale Symmetries Because SEI emergence is structured—not stochastic—large-scale features of the cosmos should reveal non-Gaussian symmetries reflecting early triadic field interactions during inflation or cosmic crystallization. Test Method: - Statistical analysis of cosmic microwave background (CMB) fluctuations for structured triadic correlations. - Re-analysis of galactic void distributions and baryonic acoustic oscillations (BAO) under interaction field geometry models. 4. Black Hole Interior Dynamics Prediction D: Interaction-Resolved Interiors SEI models black holes not as singularities, but as extreme resolution zones of structured interaction. It predicts measurable quantum leakage (micro-decoherence or spectral anomalies) as information interacts across ℐ_Δ. Test Method: - Spectral studies of Hawking-like radiation. - Observation of entropy fluctuation or phase noise near event horizons under lab-scale analogs (e.g., Bose–Einstein black hole models). 5. Philosophical and Experimental Falsifiability SEI is falsifiable if: - No triadic field signatures are observed where predicted. - Standard field theories can match SEI's predictions with fewer assumptions. - Emergence is shown experimentally to require only binary field operators. Conversely, confirmation of any of the above deviations would validate the core postulate: That interaction—structured in a triad—is the generative substrate of the universe.
SEI provides a structural and ontological bridge between the two pillars of modern physics — Quantum Mechanics (QM) and General Relativity (GR) — by reinterpreting both through the lens of triadic interaction.
In SEI, the quantum wavefunction \( \psi \) is not a fundamental object but an emergent phenomenon arising from unresolved or symmetric interaction fields \( \mathcal{I} \). Collapse, superposition, and entanglement all reflect changes in the symmetry, phase, or resolution of triadic interactions between \( \Psi_A \), \( \Psi_B \), and an observer. Measurement is thus a field-resolution event:
This eliminates the need for observer-external state vectors or ad hoc collapse mechanisms.
In GR, curvature arises from stress-energy affecting spacetime. SEI replaces spacetime as a substrate with the interaction field \( \mathcal{I}_{\mu\nu} \). Curvature is not a deformation of spacetime, but a geometric restructuring of interaction gradients:
Thus, gravity is not a force or geometry of space, but the emergent resolution of distributed interaction gradients — explaining why gravity defies quantization.
The core unification is expressed again in Miller’s Equation:
This formulation unifies discrete (quantum) and continuous (relativistic) behavior under a common structural principle: emergence from interaction asymmetry.
The SEI framework offers a fundamental reorientation of physics, placing structured triadic interaction at the foundation of emergence. While classical theories begin with objects, fields, or spacetime itself, SEI begins with the generative relationship between opposing poles and their interaction field.
Comparative Analysis with Established Theories The SEI framework offers a fundamental reorientation of physics, placing structured triadic interaction at the foundation of emergence. While classical theories begin with objects, fields, or spacetime itself, SEI begins with the generative relationship between opposing poles and their interaction field. This section compares SEI with the major paradigms of modern physics—General Relativity (GR), Quantum Field Theory (QFT), and Classical Mechanics—across structural, conceptual, and functional domains. 1. Ontological Foundations | Feature | SEI Theory | General Relativity (GR) | Quantum Field Theory (QFT) | Classical Mechanics | |----------------------|-----------------------------|--------------------------|-----------------------------|--------------------------| | Fundamental Entity | Triadic Interaction (Ψ_A, Ψ_B, ℐ) | Spacetime Geometry | Quantum Fields | Particles and Forces | | Origin of Emergence | Structured Interaction | Curvature of Spacetime | Field Excitations | Newtonian Motion | | Role of Observer | Integral to Triad | Passive Frame | External Measurement | Passive | 2. Mathematical Structure | Feature | SEI | GR | QFT | |--------------------|------------------------------------------------------|--------------------|-------------------------------------| | Field Basis | Interaction Tensor ℐ^μν | Metric Tensor g_μν | Quantum Operators ϕ̂(x) | | Lagrangian Core | (1/2) ∂_μ Ψ_A · ℐ^μν · ∂_ν Ψ_B - V | R - 2Λ | ℒ = ψ̄(iγ^μ∂_μ - m)ψ, etc. | | Symmetry Principle | Triadic Relational Symmetry | Diffeomorphism | Gauge Symmetry | 3. Conceptual Contrasts | Concept | SEI Interpretation | Standard Interpretation | |-----------|----------------------------------------------|-------------------------------------| | Mass | Emergent from stabilized triadic constraint | Intrinsic property or Higgs coupling | | Force | Reconfiguration of interaction symmetry | Field-mediated acceleration | | Time | Contextual unfolding within interaction | Absolute or background parameter | | Spacetime | Emergent coordinate structure from triadic resolution | Fundamental 4D manifold | 4. Philosophical Integration SEI offers a synthesis of multiple paradigms: - Like GR, it respects geometrical continuity and local invariance. - Like QFT, it supports dynamic field interaction and probabilistic emergence. - Unlike both, SEI prioritizes the relationship itself—not the entities—as the irreducible substrate. SEI stands closer to relational interpretations of physics, echoing Leibniz, Mach, and Wheeler, but elevates these with a formal interaction field structure. 5. Points of Compatibility - SEI Lagrangian reduces to classical Lagrangians under specific symmetry conditions. - Gravitational curvature arises naturally from persistent triadic imbalance. - Quantum entanglement maps well onto unresolved triadic structures (Ψ_A entangled with Ψ_B through ℐ). 6. Distinctive Advantages of SEI | Feature | SEI Advantage | |---------------------|----------------------------------------------------------------| | Unified Framework | Integrates emergence, consciousness, and physics under one structure | | Observer Inclusion | Embeds observer into formal structure—not external | | Foundational Symmetry | Explains why symmetry exists, not just how | | Interaction Primacy | Resolves dualisms (wave/particle, matter/energy) via triadic emergence | This comparative view clarifies that SEI is not simply a reinterpretation of existing theories—it is a foundational reframing that retains their strengths, addresses their blind spots, and offers new insight into emergence itself.
Beyond physics, SEI presents a foundational shift in metaphysics and ontology. It asserts that relations — not entities — are the primary substrate of existence, and that emergence is the product of structured, asymmetric interaction.
Philosophical and Metaphysical Implications of SEI Theory The SEI framework is not only a physical model—it is a metaphysical claim about the structure of reality. It proposes that all existence arises not from substance, particles, or space, but from structured interaction between polar elements and their dynamic field. This triadic model redefines ontology, causality, and emergence. 1. Ontology: From Entities to Relations SEI asserts that relation precedes existence. Neither Ψ_A nor Ψ_B exists independently; both are defined only through their dynamic participation in the interaction field ℐ. This is a structural monism—where interaction is not between things, but the generative source of things. This aligns with: - Leibniz’s relational ontology, where no object has meaning except in relation to others. - Whitehead’s process philosophy, where entities are “drops of experience” in unfolding events. - Quantum interpretations that challenge the separability of systems and observers. 2. The Observer: Embedded, Not External In classical physics, the observer is external to the system. In SEI, the observer is inherently part of the triad: - The act of observation is itself an interaction. - Consciousness is not outside the field but a participant in it. - Perception arises from the resolution of Ψ_A and Ψ_B through ℐ. This provides a rigorous framework for unifying subjectivity and objectivity, long considered irreconcilable in scientific models. 3. Causality: Emergence, Not Determinism SEI redefines causality. Instead of linear cause-effect chains, it proposes: - Emergence through structured resolution. - Change arises when the field ℐ rebalances the difference between Ψ_A and Ψ_B. - This triadic resolution is neither deterministic nor random—it is structured emergence. This formulation accommodates both the predictability of classical mechanics and the probabilistic unfolding of quantum events, without contradiction. 4. Time and Temporality Time in SEI is not an external parameter but an emergent property: - It arises from asymmetry in triadic interaction. - Each interaction defines a directionality (from imbalance to resolution), which manifests as temporal flow. - This structure supports relational time, aligned with Mach and Rovelli. Thus, time is not an absolute container—it is the rhythm of emergence. 5. Metaphysical Significance SEI provides a metaphysical unification across classical divides: | Philosophical Divide | SEI Resolution | |----------------------|------------------------------------------------| | Mind vs. Matter | Both are structured expressions of ℐ_Δ | | Substance vs. Process | All is process, stabilized through triadic constraint | | Being vs. Becoming | Being is a frozen resolution; becoming is active interaction | | Subject vs. Object | Both emerge from polarized roles in the same triadic field | In doing so, SEI echoes ancient philosophical intuitions (e.g., Taoist yin–yang, Platonic Forms) but grounds them in modern field formalism. 6. Epistemology: Knowing Through Participation SEI suggests that all knowledge is interactive: - Observation is co-creation: we do not find truth, we resolve it through structure. - Mathematics, too, is not merely symbolic but reflects triadic balancing operations at the core of logic itself. This moves epistemology from detached analysis to participatory realization—a stance compatible with relational quantum theory and embodied cognition. 7. Conclusion SEI stands as both a scientific and philosophical framework. It proposes a universe not of isolated things, but of structured interactions whose emergent stability gives rise to the appearance of objects, forces, minds, and time itself. By restoring interaction as the irreducible first principle, SEI unites ontology, epistemology, and physics into a coherent, testable, and elegant vision of reality.
In the classical, macroscopic limit, the SEI interaction field \( \mathcal{I}_{\mu\nu} \) evolves slowly, and the emergent structure \( \mathcal{E} \) manifests as curvature. The field equations derived from the SEI action reduce under weak-field, static conditions to an effective metric formulation:
Here, \( g_{\mu\nu}^{(\text{eff})} \) emerges as a metric proxy from the self-structuring of \( \mathcal{I}_{\mu\nu} \). Thus, Einstein's field equations appear as a low-energy geometric approximation of triadic interaction gradients.
In microscopic regimes, where \( \Psi_A \) and \( \Psi_B \) are symmetric or unresolved, the interaction field \( \mathcal{I} \) remains in a superposed state. The emergent observable \( \mathcal{E} \) corresponds to quantum amplitude densities:
Collapse occurs when field asymmetry exceeds threshold:
This resolves the quantum measurement problem not as an epistemic update, but as a physical field resolution within SEI’s interaction space.
SEI Theory offers a radical, yet parsimonious reformulation of physical reality: that all phenomena arise from the structured differential between two polar aspects and their mediating interaction field. From quantum entanglement to gravitational curvature, from logic to life, all emergence is governed by the same irreducible triadic structure.
By unifying quantum mechanics and general relativity under a single equation — \( \mathcal{I}_\Delta = \mathcal{E} \) — SEI provides not only a theoretical reconciliation but a universal framework for intelligibility, measurement, and structure. This theory is mathematically complete, empirically testable, and philosophically grounded.
It is offered as a complete, self-contained, and falsifiable foundation for the next paradigm in physics.
This work was independently conceived, developed, and authored by B. Miller. No funding, institutional affiliation, or third-party input influenced the formulation of SEI theory. The author declares no conflicts of interest.
Copyright (c) Brian Miller 2025. All Rights Reserved.