Pathways, Boundaries, and Phases: The Relational Expression of Reality

Pathways, Boundaries, and Phases: The Relational Expression of Reality

DOI: To be assigned

John Swygert

July 18, 2026

Abstract

Human knowledge of reality is built from expressions that become available through particular interactions. Photons reaching the retina can be converted into neural activity and organized as vision, while a neutrino may encounter the same region of matter through a radically different interaction profile. The difference is not exhausted by saying that one carrier is blocked and another is transparent. For a given entity, field, detector, or observer, an organized object or boundary may be strongly expressed, weakly expressed, transformed into another response, or fail to become an operative object at all. This paper develops a carrier-agnostic framework in which pathways, boundaries, phases, coupling relationships, timescales, and receiving architectures jointly determine what one condition can become to another. It distinguishes underlying reality from physical reality as presently described; physical expression from registration and interpretation; relational non-expression from unregistered expression; and apparent nonexistence from demonstrated absence. The framework does not claim that consciousness creates physical events, does not reject established physics, and does not propose a new force as a known fact. It instead treats the recognized forces and particles as the presently validated interaction map while remaining open to additional pathways or couplings as possibilities that would require independent evidence. Within The Swygert Theory of Everything AO (TSTOEAO), the proposal supplies a clearer foundation for route availability, boundary-selected expression, phase-conditioned response, cost-location, and possible unification. It concludes with experimentally disciplined implications: change the receiver as well as the source, distinguish absent expression from inaccessible expression, compare multiple carriers and probes, and search for repeatable residual relationships only after known mechanisms and artifacts have been exhausted.

1. Introduction: The Accessible World Is Not Automatically the Completed World

Modern physics is one of humanity’s most successful intellectual achievements. It describes particles, fields, forces, spacetime, matter, radiation, and collective behavior with extraordinary precision inside the domains where its models have been tested. Nothing in the present paper diminishes that achievement. The question is narrower and more fundamental: what exactly has become known when an observer, instrument, particle, material, or field registers an interaction?

Every empirical statement enters science through an available relationship. Human senses provide some relationships directly. Instruments extend those relationships across scales, energies, frequencies, times, and interaction types that biology alone cannot reach. Mathematics then organizes stable regularities among the registered results. The resulting account may be exceptionally accurate without requiring the further assumption that every possible form of expression, interaction, or relationship has already entered human observational reach. CERN itself describes the Standard Model as the best current description of the subatomic world while emphasizing that it does not contain gravity and does not explain the complete picture [1].

The central proposal is that what is present does not determine by itself what is encountered. Encounter also depends upon what arrives, the routes through which it can interact, the boundary and phase conditions governing the meeting, the coupling profile permitted by known or unknown interactions, the relevant timescale, and the architecture capable of receiving the result.

Reality is not described completely by identifying what things are in isolation. It must also be described by identifying what things are capable of being to one another.

This is a relational claim, but it is not a claim that reality is imaginary, subjective, or manufactured by consciousness. A receiver need not be conscious. An atom, field, detector, crystal lattice, membrane, molecule, cell, or particle can enter a relationship by changing state. Conscious interpretation is a later and unusually elaborate case of a more general physical sequence: interaction, response, registration, organization, and meaning.

The proposal is also broader than any single quantum interpretation. Relational approaches in quantum foundations have argued that facts or states may be relative to physical systems [3]. The present framework is not offered as a restatement of relational quantum mechanics. It extends the question across classical, quantum, biological, materials, and engineering domains by asking how pathways, boundaries, phases, forces, and receiving architectures select the form in which reality becomes consequential.

2. Foundational Distinctions

2.1 Underlying Reality

Underlying reality means whatever exists independently of whether humanity presently detects, models, or names it. The term is deliberately modest. It does not specify what the underlying level must contain. It may be fully exhausted by present physics, may require extensions of present physics, or may be describable only through deeper relations not yet known. The framework begins by refusing to confuse the current map with proof that no unmapped territory remains.

2.2 Physical Reality as Presently Described

Physical reality as presently described is the validated portion of underlying reality that becomes accessible through existing experiments, instruments, theories, mathematics, and repeatable inference. It is not “merely subjective.” It is disciplined, shared, and constrained by measurement. It is nevertheless accessed through human-designed and human-interpreted relationships. Instruments may detect what human senses cannot, but the choice of instrument, variable, threshold, geometry, and explanatory model still defines which expressions become legible.

2.3 Expression

Expression is used here without implying consciousness or intention. A condition is physically expressed to another system when an available interaction produces a consequential difference in that system’s state, trajectory, phase, energy, momentum, configuration, probability distribution, or organized response. An expression is therefore relational: it is not simply what leaves a source, but what becomes physically consequential through an encounter.

2.4 Receiver, Registration, and Interpretation

A receiver is anything whose state can be changed through an interaction. Registration occurs when that change is preserved or amplified sufficiently to distinguish it from background variation. Interpretation occurs when the registered change is assigned to an organized category or functional meaning. A photoreceptor registers light through phototransduction; retinal and neural circuits organize the resulting signals; the brain participates in the experienced interpretation called vision [4,5]. A particle detector registers a collision differently, through tracks, light, charge, timing, or heat. A crystal may “interpret” an applied field only in the limited physical sense that its polarization, magnetization, lattice, conductivity, or phase changes in an organized way.

2.5 Relational Non-Expression and Apparent Nonexistence

Relational non-expression means that no consequential interaction occurs through the specified relationship under the stated conditions. Apparent nonexistence means that the selected receiver obtains no identifiable expression and therefore experiences or records the condition as operationally absent. These are not automatically identical. An expression may occur below sensitivity, outside the selected channel, through an unrecognized conversion, during an unmeasured time window, or in a form the receiver cannot organize. Conversely, genuine relational non-expression may occur because no permitted coupling or accessible pathway exists.

Failure to register an expression is not proof that no expression occurred. Absence through one relationship is not proof of underlying nonexistence.

3. A Candidate Relational Expression Formalism

The following notation is proposed as an organizational grammar rather than an established physical law. Let A denote a source condition and X a receiving system. The expression of A to X under experimental or natural conditions C may be represented conceptually as:

E(A → X | C) = F(S_A, S_X, P, B, Φ, G, K, τ, Q_X)

Here, S_A is the state of the source; S_X is the state of the receiver; P is the available pathway set; B is the applicable boundary architecture; Φ represents phase states and phase relationships; G represents the relevant coupling or force relationships; K represents energetic, dissipative, stability, and conversion costs; τ is the available timescale; and Q_X represents the receiving, registering, and resolving capacities of X.

The notation makes one point explicit: the source alone does not determine the expressed outcome. The same source condition can become different things to different receivers, and the same receiver can obtain different expressions when pathway, phase, boundary, energy, orientation, or timing changes.

An equivalent accessible-state formulation can be written as:

Ω_E^(X) = Ω_A ∩ Ω_P ∩ Ω_B ∩ Ω_Φ ∩ Ω_G ∩ Ω_K ∩ Ω_τ ∩ Ω_X

Ω_E^(X) is the set of states that become expressible to receiver X under the complete condition. Ω_A contains states supported by the source; Ω_P contains states reachable through available pathways; Ω_B contains states admitted by boundary geometry and constraints; Ω_Φ contains states compatible with phase conditions; Ω_G contains states permitted by applicable couplings and forces; Ω_K contains states affordable within energetic and stability costs; Ω_τ contains states reachable and retainable within the available time window; and Ω_X contains states the selected receiver can register or resolve.

This notation should not be used to manufacture numerical authority. Every term must ultimately correspond to a measurable variable, a validated model, or an explicitly identified unknown. Its purpose is to prevent a conceptual omission: an outcome cannot be characterized fully without specifying the system to which the outcome is expressed.

4. The Expressive Life of a Photon

A photon provides a familiar example because human vision depends upon electromagnetic radiation, yet the photon is not intrinsically “an image.” Light becomes visual information only within a receiving architecture capable of converting and organizing it. The eye focuses incident light onto the retina; photoreceptors convert light into electrical signals; retinal circuits and the brain organize those signals into experienced vision [4]. Classic psychophysical work showed that human vision can respond at extremely low photon counts under optimized conditions [5], demonstrating the sensitivity of the receiver without implying that the photon already contained a completed picture.

From origin to termination or transformation, a photon may become consequential in many ways. It may be emitted through an atomic, molecular, nuclear, thermal, or collective process. It may propagate through vacuum, couple to a medium, interfere with other amplitudes, diffract through an aperture, change direction through an interface, scatter, transfer momentum, excite an electron, initiate chemistry, generate electrical current, deposit heat, produce a detector event, or contribute to vision. At sufficiently high energy and under suitable conditions, photon interactions can produce additional particles. These are not merely different descriptions of one identical visible object. They are different relational outcomes enabled by different receivers and boundary conditions.

The productive question is therefore not only “What is a photon?” but also “What can a photon become to everything it encounters?” The number of possible expressions is not a fixed list detached from context. It expands with source state, energy, frequency, polarization, coherence, geometry, material composition, interfaces, phase, timing, and receiving architecture.

A carrier is not information-rich or information-poor in isolation. Its expressive significance depends upon the relationship through which another system can receive it.

For a human being, photons in a limited electromagnetic band can become color, form, motion, depth, contrast, warning, beauty, text, and orientation. For a photovoltaic material, related photons may become charge separation and electrical power. For a photosynthetic organism, they may become chemical potential. For a thermal absorber, they may become heat. The photon remains a valid physical entity across these cases, but its operative identity is not exhausted by a single universal role.

5. The Neutrino Example and the Carrier-Agnostic Principle

Neutrinos provide one illustrative example among many, not the boundary of the proposal. In present particle physics, neutrinos are produced and detected through weak interactions and do not carry the color charge required for strong interactions. Their low interaction probabilities allow them to traverse large amounts of ordinary matter, which is why very large detectors are used to obtain sufficient events [2,6].

It is common to say that a wall or planet is transparent to a neutrino. That description is often useful, but it still imports the human-defined object into the neutrino’s operative relationship. A stronger relational description is sometimes appropriate: the organized surface, obstruction, interior, and passage that constitute “wallness” for a human body may fail to instantiate as a meaningful boundary for the neutrino except through a very small interaction probability. The matter has not been declared absolutely nonexistent. Rather, the human object map may not be the object map expressed through the neutrino’s available coupling profile.

This distinction permits both possibilities the framework requires. To one entity, a structure may be transparent: the structure remains operationally expressed but does not block transmission. To another, the structure may not become an organized object at all. Between those cases lies a continuum of scattering, absorption, conversion, delay, phase alteration, partial detection, and probabilistic interaction. The outcome depends less on the isolated label attached to what is present than on the relationship between what is present and what arrives.

The thought experiment can then be reversed. What if neutrinos, or some other known or unknown carrier, are to a differently organized receiver what photons are to human vision? This does not mean neutrinos would become photons. It means they could occupy an analogous functional role: a structured incoming expression converted by a compatible receiver into differentiated information. Neutrino astronomy already demonstrates the limited engineering form of this principle. IceCube converts rare neutrino interactions into secondary light patterns from which direction, energy, and interaction type can be inferred [6,7]. Neutrinos can reveal energetic regions that are difficult to observe electromagnetically because their propagation relationship with dense matter differs from that of light.

The principle must remain carrier-agnostic. Known candidates include electromagnetic radiation outside human vision, electrons, ions, phonons, magnons, excitons, polaritons, spin textures, orbital angular momentum, chemical gradients, pressure waves, gravitational signals, and collective modes not reducible to one isolated particle description. Phononics and magnonics already treat phonons and magnons as controllable carriers for heat, sound, spin, and information processing [8,9]. The same reasoning also leaves open presently unknown carriers or interactions, without asserting that any particular unknown entity exists.

What appears to one receiver as darkness, emptiness, noise, or nonexistence may be another receiver’s field of illumination.

6. Pathways, Boundaries, Phases, and Force Relationships

6.1 Pathways

A pathway is an admissible route through which a source condition can become consequential elsewhere. Pathways may be spatial, energetic, electronic, chemical, mechanical, quantum, temporal, or composite. They include propagation channels, conversion chains, transport modes, coupling networks, and sequences of intermediate states. A pathway is not guaranteed merely because initial and final states are imaginable. The intermediate route must be physically available within the boundary, cost, and timescale conditions.

6.2 Boundaries

A boundary is not merely a wall that acts upon an already completed signal. A boundary can help determine which expression becomes possible in the first place. Interfaces, symmetry changes, confinement, geometry, fields, membranes, phase fronts, detector thresholds, and biological receptors can admit, suppress, redirect, delay, amplify, convert, or differentiate available routes. In TSTOEAO language, a boundary selects from a portfolio of possible expressions rather than simply reducing the strength of one universal response [15,16].

A boundary is therefore relationally indexed. The statement “this is a barrier” is incomplete until the encountering entity, energy range, direction, phase, state, and timescale are specified. The same region may be mechanically solid, optically transparent, acoustically reflective, thermally conductive, ion-selective, spin-active, and nearly irrelevant to another carrier.

6.3 Phases

Phase has two linked meanings in this framework. A system may occupy a material phase, such as solid, liquid, magnetic, superconducting, ordered, disordered, coherent, or metastable. Interacting waves and quantum amplitudes may also possess relative phases that determine reinforcement, cancellation, directionality, coherence, and conversion. Phase therefore changes not only how much of a response is expressed, but which relationship is available. A boundary that is closed in one phase may become transmissive, resonant, or transformative in another.

6.4 Force and Coupling Profiles

Current physics recognizes strong, weak, electromagnetic, and gravitational interactions, while the Standard Model itself describes the strong, weak, and electromagnetic interactions and excludes a quantum account of gravity [1]. Entities do not encounter these interactions identically. Their charges, quantum numbers, masses, states, and environments define different coupling profiles. The neutrino example depends in part on this difference: it participates in weak interactions but not strong interactions in the presently accepted framework [2].

The paper does not replace these established descriptions with a generic word such as “relationship.” Rather, it places the established forces inside a broader organizational question: which interaction permissions make one entity consequential to another under a given boundary and phase condition? Known forces provide the validated answers presently available. The relational framework asks whether the inventory is complete and how a missing relationship would appear if it were not.

7. What Things Are to One Another

An object’s composition matters, but composition alone does not determine its operative identity. A wall is assembled from atoms and organized into a persistent structure. For a human body, electromagnetic interactions among matter establish mechanical resistance. For visible light, the same wall may absorb, reflect, scatter, or transmit depending on its composition and structure. For radio waves, sound, heat, ions, electrons, neutrons, or neutrinos, the operative boundary can differ dramatically.

This does not require saying that the wall is unreal. It requires saying that wallness is a stabilized bundle of relationships, not a universally identical expression imposed upon everything. Surface, interior, solidity, opacity, resonance, temperature, electrical potential, and chemical activity are accessed through different pathways. The object is physically persistent, but the form in which it exists operationally is receiver-dependent.

The phrase relational dimensions of expression can name these distinct ways of becoming accessible. The word dimensions is not intended to assert additional spatial dimensions. It identifies independent relational axes such as optical, mechanical, thermal, chemical, electrical, magnetic, weak-interaction, biological, informational, temporal, and phase-sensitive expression. One entity may strongly occupy several dimensions for one receiver and almost none for another.

A boundary exists operationally to the extent that something can encounter it as a boundary.

The strongest formulation is therefore neither “the object is always there in exactly the same form” nor “the observer creates the object.” It is: an underlying condition can support multiple operative identities, and the identity expressed in a particular encounter is selected by the complete relationship.

8. Non-Expression, Unregistered Expression, and Epistemic Discipline

The greatest conceptual danger is collapsing every null result into one category. The absence of a recognized signal may arise from several physically different conditions. No relevant source may be present. A source may be present but no permitted pathway may connect it to the receiver. A pathway may exist but the coupling may be too weak. An interaction may occur outside the measured time window. A response may be converted into another channel. Two contributions may cancel. A detector may lack sensitivity. A classification model may assign the event incorrectly. Background may conceal the response. The receiver may register a change without possessing the architecture required to interpret it.

A disciplined experiment should therefore distinguish at least six categories:

1. Physical expression: an interaction produces a consequential change.

2. Registered expression: the change is detected above an independently established uncertainty or noise floor.

3. Interpreted expression: the registered change is assigned reliably to a defined route or physical cause.

4. Relational non-expression: no consequential interaction occurs through the specified relationship.

5. Unregistered or unrecognized expression: an interaction occurs, but the selected receiver cannot detect, isolate, or classify it.

6. Underlying absence: the relevant source condition is not present.

Apparent nonexistence is an observational outcome, not automatically an ontological conclusion. To move from apparent absence to a stronger claim, investigators should vary the receiver, interaction channel, geometry, energy, polarization, phase, timing, and boundary condition; use complementary probes; quantify detection limits; test conversion channels; and predeclare what would count as failure.

This is especially important when searching for new physics. A residual anomaly is meaningful only after known interactions, emergent behavior, material complexity, systematic error, calibration drift, environmental contamination, and model limitations have been tested seriously. Openness without discipline becomes speculation. Discipline without openness can mistake the reach of the instrument for the reach of reality.

9. Open-Minded Physics Without Declaring Unknown Forces

The framework does not propose a fifth force, several new forces, an unknown particle, or a hidden carrier as a known fact. It proposes a scientifically modest posture: the presently recognized forces and particles are the validated interaction map available today, not a logical proof that no additional interaction, mediator, coupling regime, collective route, or deeper unifying structure can exist.

A scientifically responsible statement is therefore conditional. If a repeatable expression, non-expression, transition, timing relationship, or cost relocation cannot be reconciled with known interactions, established emergent mechanisms, accepted material behavior, measurement limits, or ordinary artifacts, the surviving discrepancy could be suggestive of an unrecognized coupling, mediator, interaction pathway, or force. It would not by itself establish one. Independent replication and targeted discrimination among alternatives would still be required.

Do not close the framework before reality has demonstrated that it is closed.

This position is not hostile to modern physics. It follows the history of physics, in which broader frameworks have repeatedly preserved successful earlier descriptions inside expanded domains. Electromagnetism unified electric and magnetic phenomena; electroweak theory linked electromagnetic and weak interactions at a deeper level; general relativity changed the description of gravity; quantum theory changed the description of matter and radiation. The lesson is not that every anomaly hides a new force. The lesson is that completeness must be earned experimentally rather than assumed philosophically.

10. Relational Expression and the Search for Unification

Unification is often pursued by seeking a common mathematical structure beneath interactions that appear different at accessible scales. The relational framework suggests a complementary question: could the known forces be differentiated expressions of a deeper rule governing what entities are permitted to become to one another under distinct boundary, symmetry, phase, and energy conditions?

This is a research question, not a result. Gauge theories, quantum field theory, the Standard Model, and general relativity contain precise structures that cannot be replaced by metaphor. Any deeper account must recover their successful predictions in the appropriate limits. The potential value of the relational grammar is organizational: it directs attention to common roles played by gradients, admissible routes, boundary conditions, phase selection, coupling permissions, cost-location, timescale, and equilibrium or metastable targets.

Within TSTOEAO, the recurring sequence is gradient, boundary condition, route availability, correction, cost-location, and equilibrium target. Relational expression clarifies what “route availability” means. A route is available not merely because a source contains energy, but because source, pathway, boundary, receiver, phase, coupling, cost, and time jointly admit an expression. It also clarifies why energy may appear to “choose” different forms: the active architecture permits some expressions while excluding or disfavoring others.

A future unifying program based on this view would ask: Which relational variables remain invariant across known forces? Which boundary operations change the effective interaction portfolio? Can apparently distinct couplings be derived as different admissible sectors of a deeper state space? Where does suppressed expression relocate its energetic or informational cost? Which timescale separates immediate route opening from delayed structural response? These questions do not answer unification, but they may organize where to look.

11. Testable Implications and Research Program

A conceptual framework becomes scientifically useful when it generates discriminating procedures. The following implications are stated directionally and require material-specific or system-specific formalization before experimental use.

11.1 Receiver Substitution

Hold the source and macroscopic region as constant as possible while changing the receiving architecture. If relational expression is operationally important, different receivers should produce systematically different object maps, route portfolios, timing profiles, and cost channels rather than merely different signal amplitudes. Existing multimessenger astronomy already illustrates this principle: electromagnetic, gravitational-wave, cosmic-ray, and neutrino observations can reveal different aspects of the same astrophysical source.

11.2 Boundary-Controlled Reallocation

Change one reversible boundary variable while measuring several independent channels. The framework predicts that a genuine expression-selection event can redistribute response non-proportionally among available routes. A common increase in every signal caused by heating or input power would not be sufficient. The strongest test identifies which route changes first, which changes most, what is suppressed, and where the displaced cost appears.

11.3 Receiver Engineering for Known Carriers

Design a receiver specifically around a known carrier or collective mode that presently yields sparse information. Success would not require changing the carrier’s fundamental identity. It would require creating a compatible conversion, amplification, discrimination, timing, and storage architecture that makes already-present distinctions readable. The evolution of neutrino, phonon, magnon, and polarization-sensitive detectors demonstrates partial precedents.

11.4 Distinguishing Non-Expression from Inaccessibility

Use complementary probes with different coupling profiles. If one probe returns a null result while another registers a correlated response, the first null can be reclassified as receiver-limited rather than source-absent. This procedure should be predeclared and should include detection limits, cross-sensitivity, timing, and conversion controls.

11.5 Residual-Relationship Search

After conventional explanations are exhausted, analyze whether residual anomalies cluster around a common relational condition: a symmetry boundary, phase threshold, geometry, receiver type, timing window, or cost relocation. A repeatable pattern across systems would be more informative than an isolated unexplained event.

12. Limits of Interpretation

First, relational expression does not establish that all properties are observer-created. It states that operative accessibility is interaction-dependent. Second, the word interpretation does not imply consciousness unless biological or cognitive interpretation is specifically under discussion. Third, a hypothetical unknown carrier or force cannot be inserted whenever a measurement is inconvenient. Fourth, the proposed equations are bookkeeping structures until their terms are mapped to observables and validated models. Fifth, overlap with relational quantum mechanics, operationalism, information theory, systems science, and materials physics should be acknowledged without claiming identity with those fields.

The framework’s value will depend on whether it improves classification, experiment design, material selection, receiver design, anomaly localization, and prospective prediction. If it merely restates that interactions depend on context, it adds little. Its distinctive claim is stronger: the complete engineering and scientific object is the relationship that determines what one condition becomes to another, including cases in which an ordinary object is transparent, transformed, partially expressed, or not instantiated as an operative object at all.

Conclusion

Reality known to an observer or system consists not simply of what is present, but of what becomes expressible, receivable, registerable, and interpretable through available relationships. What is present does not determine the encounter alone. The arriving entity, receiving architecture, pathway, boundary, phase, coupling profile, cost structure, and timescale jointly select the operative expression.

Photons become vision to a human because biological and neural architecture converts a narrow band of electromagnetic interaction into organized experience. Neutrinos become sparse detector events to present instruments, yet could in principle occupy a much richer informational role for a differently organized receiver. The same carrier-agnostic reasoning applies to known particles, fields, collective modes, and possibly forms of expression not yet identified.

The framework neither denies an underlying reality nor claims knowledge of physics beyond present evidence. It distinguishes possibility from fact and openness from proof. Its practical demand is precise: specify what is arriving, what is present, which relationship connects them, what expression is expected, how it will be registered, what alternatives can imitate it, and where the cost of suppressed or redirected expression must appear.

Before reality can be engineered deliberately, science must recognize that what things are to one another is part of what reality is.

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