Light Surfing The Boundary: A TSTOEAO Hypothesis For The Vacuum Speed Of Light Between Gravitational Obligation And Expansion Freedom
Light Surfing The Boundary
A TSTOEAO Hypothesis For The Vacuum Speed Of Light Between Gravitational Obligation And Expansion Freedom
DOI: To be assigned.
John Swygert
July 13, 2026
Abstract
This paper extends the TSTOEAO distinction between expressed energy and unexpressed energy by examining the physical position of light between gravitational binding and universal expansion. Earlier TSTOEAO work proposed that expressed energy is energy committed to matter, structure, inertia, and gravitational participation, while unexpressed energy remains unlocalized, uncommitted, and comparatively free to participate in outward expansion. Gravity was therefore described as the inward signature or burden of expression, while cosmic expansion was described as the outward signature or freedom of energy not locally committed.
The present paper proposes that light occupies the moving boundary between those two conditions. Light is expressed: it carries energy, momentum, information, and observable consequence. Yet light is not committed to a rest-mass-bearing form. It therefore does not inhabit the inward gravitationally obligated condition in the same manner as matter, nor does it remain wholly unexpressed as latent substrate potential. It travels the boundary between commitment and freedom.
From this perspective, the vacuum speed of light may represent the characteristic equilibrium propagation rate of that boundary. It should not be understood as a simple arithmetic average between an inward force and an outward force. Rather, it may be an emergent response rate determined by the relationship between an outward substrate-response property and an inward inertial or localization-response property. A preliminary wave-response form is proposed:
c0^2 = Ku / Ix
where Ku represents the effective outward response modulus of the unexpressed substrate and Ix represents the effective inward inertial response associated with expression and localization. This is not presented as a derived physical law. It is a mathematical target for determining whether the speed of light can emerge from the expressed/unexpressed distinction rather than being inserted into the theory as an unrelated constant.
The paper also distinguishes the locally measured vacuum value c0 from reduced propagation through matter and from route-dependent or coordinate-dependent travel times through gravitational gradients. In this model, light locally remains on the equilibrium boundary, while matter, geometry, and other gradients alter the route through which that boundary condition must propagate.
Prologue
The speed of light is usually introduced as a fundamental constant.
Its measured vacuum value is:
c0 = 299,792,458 metres per second
Within the International System of Units, this value is now exact because the metre is defined using the fixed numerical value of the speed of light in vacuum. That metrological definition does not, by itself, explain why physical reality possesses this particular invariant propagation rate.
TSTOEAO must ask a deeper question:
Why should the universe possess a maximum vacuum propagation rate at all?
If gravity is the inward-binding signature of expressed energy, and cosmic expansion is the outward signature of energy not locally committed, then light should not remain conceptually disconnected from those two conditions.
Light appears to stand between them.
It is real and expressed, yet it has no rest mass.
It transports energy without remaining localized as matter.
It participates in gravity but does not settle naturally into a stationary material identity.
It may therefore be understood not merely as something moving through the universe, but as the universe propagating a disturbance along the boundary between inward commitment and outward freedom.
This paper develops that possibility.
01
The Prior Expressed And Unexpressed Distinction
The earlier TSTOEAO framework divided the total energy condition of a system into expressed and unexpressed components.
Let:
ET = total energy condition
Ex = expressed energy
Eu = unexpressed energy
Then:
ET = Ex + Eu
The expressed fraction was defined as:
chi = Ex / ET
The unexpressed fraction was defined as:
upsilon = Eu / ET
Therefore:
chi + upsilon = 1
The preliminary relationships were:
Binding burden rises with chi.
Expansion freedom rises with upsilon.
Or:
B is proportional to chi.
F is proportional to upsilon.
Expressed energy was defined as committed potential: energy localized or actualized into matter, inertia, structure, and gravitational participation.
Unexpressed energy was defined as uncommitted potential: energy remaining unlocalized, substrate-level, latent, or not condensed into matter-bearing form.
The condensed statement was:
Matter is energy that has become committed.
Gravity is the burden of that commitment.
Expansion is the freedom of energy not locally committed.
The present paper adds a fourth statement:
Light is energy expressed without rest-mass commitment, and the speed of light is the characteristic propagation rate of the boundary between commitment and freedom.
02
The Missing Position Of Light
The expressed/unexpressed distinction initially creates two broad conditions.
On one side is expressed matter:
localized;
rest-mass-bearing;
inertially committed;
gravitationally participating;
structurally persistent;
capable of remaining within a local frame.
On the other side is unexpressed potential:
unlocalized;
not committed to material rest form;
comparatively free from local binding burden;
substrate-level;
expansion-capable;
not yet differentiated into persistent matter.
Light fits perfectly into neither category.
Light is clearly expressed. A photon can be emitted, transmitted, absorbed, detected, redirected, redshifted, blueshifted, and converted into other energetic or material outcomes. Light carries momentum and contributes to the stress-energy condition relevant to gravitation.
Yet light possesses no rest frame and no nonzero rest mass. It cannot be brought gradually to rest and preserved as stationary light in the same sense that a rock, atom, or person can remain at rest relative to a local frame.
Light therefore represents a third condition:
Expression without rest-mass localization.
It is neither wholly unexpressed nor fully committed into the material condition.
It is expressed potential remaining propagationally free.
This suggests that light does not merely move between the two sides. It inhabits their moving interface.
03
Light Surfing The Boundary
The phrase surfing the boundary is important.
Light should not be pictured as sitting at a motionless midpoint between two opposing forces. A surfer does not remain motionless between the ocean and the air. The surfer travels because the boundary itself supports a continuously resolved route.
Similarly, light may travel because it remains on the continually resolved boundary between:
Inward commitment
and
outward freedom.
The inward side includes:
localization
rest mass
inertia
binding
gravitational obligation
structural commitment
The outward side includes:
delocalization
uncommitted potential
expansion freedom
substrate openness
route availability
nonlocal commitment
Light occupies the seam:
INWARD CONDITION
matter
rest-mass commitment
binding burden
gravitational obligation
LIGHT
expressed energy
without rest-mass commitment
boundary propagation
OUTWARD CONDITION
uncommitted potential
expansion freedom
substrate availability
The light state is therefore not a static compromise.
It is an active, propagating resolution.
Light continually remains expressed enough to carry information and energy while remaining uncommitted enough to avoid acquiring a material rest condition.
In that sense, light surfs the line that matter crosses when energy becomes localized.
04
Relation To The Causal Boundary
The boundary interpretation has an important adjacency to relativity.
In relativity, light follows null paths. The null condition forms the boundary between timelike-separated events that can be connected by slower-than-light matter and spacelike-separated events that cannot be connected without exceeding the causal limit.
Light therefore already occupies a mathematical boundary in established spacetime theory.
For a light path:
ds^2 = 0
This does not mean that nothing occurs along the path. It means that the spacetime interval has the null form characteristic of massless propagation.
In TSTOEAO language, this may be interpreted as more than a geometric classification.
The null path may be the route along which expression occurs without rest-mass commitment.
Massive matter follows timelike paths because it has crossed into localized inertial obligation.
Light follows null paths because it remains at the commitment boundary.
A fully unexpressed substrate condition would not appear as a locally transmitted particle or signal at all.
The resulting three-part classification is:
Unexpressed substrate condition:
no locally differentiated excitation
Light or radiative condition:
locally differentiated expression
without rest-mass commitment
Matter condition:
locally differentiated expression
with rest-mass commitment
This can be written schematically as:
Unexpressed:
X = 0
M = 0
Light:
X > 0
M = 0
Matter:
X > 0
M > 0
Where:
X = degree of distinguishable expression
M = degree of rest-mass commitment
The exact numerical meaning of X and M remains to be developed. The classification is presently conceptual.
05
The Speed Of Light Is Not A Simple Arithmetic Average
The vacuum speed of light should not be described as:
c0 = inward force plus outward force divided by two
The inward and outward tendencies are not yet defined as directly comparable numerical forces. Gravity and cosmic expansion are also observed at very different scales and cannot simply be inserted into a conventional average.
The relevant relationship must be deeper.
The observed gravitational field near a planet and the measured cosmic expansion rate are likely macroscopic signatures of underlying response properties. The proposed speed relation must therefore use the substrate-level properties from which those signatures emerge, not merely the surface observations themselves.
The word average can nevertheless retain an important meaning.
The vacuum speed may be an equilibrium-selected average in the same sense that a large-scale physical property can emerge from many smaller interactions while remaining extremely stable.
It would not mean that light is continuously measured moving randomly above and below c0.
It would mean that the substrate resolves an enormous number of microscopic possibilities into one stable macroscopic propagation rate.
A better phrase is:
equilibrium-effective rate
or:
characteristic boundary propagation rate.
Thus:
The speed of light in vacuum may be the stable equilibrium-effective rate at which energy can remain expressed without becoming committed to rest-mass localization.
06
Why A Vacuum Rate Exists
The term speed of light in vacuum is essential.
A vacuum is not necessarily absolute nothingness. Quantum field theory does not treat the vacuum as a featureless absence of all structure. It is a lowest-state or reference condition possessing fields, correlations, and measurable consequences under suitable circumstances.
The TSTOEAO concept of unexpressed energy should not be declared identical to the quantum vacuum. The earlier expressed/unexpressed paper explicitly warned against prematurely identifying unexpressed energy with zero-point energy or any single accepted physical quantity.
A more disciplined possibility is:
The physical vacuum may be the observable reference condition nearest to the expressed/unexpressed boundary accessible to measurement.
In an ideal vacuum, there is no material lattice, molecular population, plasma density, or other local matter structure repeatedly interacting with the propagating electromagnetic excitation.
Light is therefore able to follow the least-obstructed boundary route.
This does not mean that a vacuum is always globally free from gravity or curvature. A vacuum region may exist near a massive body and therefore possess nontrivial spacetime geometry.
The precise claim should be:
In a sufficiently local freely measured vacuum region, with no material interaction imposing additional route delay, light propagates at the invariant boundary rate c0.
The vacuum is therefore not the absence of the boundary.
It is the condition in which the boundary can propagate without additional material obligation.
07
Gradients Change The Route
The intuition that light changes as it enters gradients is correct, but several different effects must be separated.
Material Gradients
When light travels through water, glass, gas, plasma, or another material, it interacts with expressed structure.
The effective propagation speed through the material may be written:
v = c0 / n
Where:
v = effective propagation speed in the medium
c0 = vacuum speed of light
n = refractive index
The material does not simply act as empty space with a lower universal speed limit. Its charged particles and fields interact with the electromagnetic disturbance, creating delay, dispersion, absorption, re-emission effects, phase change, or altered group propagation.
In TSTOEAO language:
Boundary propagation
plus
expressed structural interaction
equals
additional route cost.
The effective route becomes slower because the propagating expression must continually negotiate locally expressed matter.
Gravitational Gradients
A gravitational field alters geometry, clock relationships, frequency, direction, and end-to-end travel time.
A distant observer may assign a coordinate-dependent speed or measure a greater total travel time than would be predicted for the corresponding route through flat spacetime.
Yet a sufficiently local freely falling observer measuring light in vacuum still obtains c0.
The correct TSTOEAO interpretation is therefore not:
Gravity locally forces light below c0 in empty space.
It is:
Gravity changes the geometry and cost of the route
while the local boundary condition remains c0.
This distinction preserves the experimentally established local invariance of the speed of light while allowing route-averaged travel to change across gradients.
Expansion Gradients
Cosmological expansion changes the separation and scale relationship between distant regions and stretches the wavelength of propagating light.
The light remains locally measured at c0, but the geometry through which the signal travels evolves during the journey.
Thus, at cosmic scale, the total route cannot always be understood as motion through a rigid, unchanging container.
08
Local Speed And Route-Averaged Speed
The word speed can refer to more than one constructed quantity.
The local vacuum speed is:
c0
The route-averaged progress between separated reference points can be represented as:
vroute = Lassigned / Delta troute
Where:
Lassigned = distance assigned between the endpoints
Delta troute = measured or calculated travel duration
This route-average may differ depending on:
the chosen coordinates;
gravitational curvature;
the clocks used;
expansion during propagation;
the path taken;
material interaction;
refractive structure;
dispersion;
route lengthening or bending.
Therefore:
Local vacuum boundary rate = c0
Route-effective or coordinate-assigned rate = variable
This resolves the apparent contradiction.
Light does not need to abandon the boundary rate locally for the overall journey to take longer, bend, redshift, or appear slower between distant reference locations.
In TSTOEAO terms:
The boundary rule remains locally stable while the route supplied to the boundary changes.
This aligns with the recent TSTOEAO emphasis on route-space.
A propagating system is not defined solely by an intrinsic speed. It is also defined by the route made available through the gradients, boundaries, and structural obligations it encounters.
09
The Wave-Response Form
A broad family of wave systems has a characteristic structure:
wave speed squared
equals
restoring response
divided by
inertial response.
For a stretched string, propagation depends on tension relative to mass density.
For sound, propagation depends on elastic response relative to inertial density.
For electromagnetic propagation, the vacuum speed is related to the electromagnetic response properties of the vacuum.
This suggests a preliminary TSTOEAO form.
Let:
Ku = outward substrate-response modulus
Ix = inward inertial or localization-response density
Ku represents the effective ability of the unexpressed or minimally committed substrate condition to restore, transmit, or open a propagational route.
Ix represents the effective resistance associated with localization, inertia, expression, or conversion toward committed form.
The proposed boundary disturbance equation is:
Ix times d2psi/dt2
minus
Ku times Laplacian(psi)
equals
0
Or:
Ix (d2psi/dt2) - Ku Laplacian(psi) = 0
Rearranging:
d2psi/dt2 = (Ku / Ix) Laplacian(psi)
The characteristic speed is therefore:
c0^2 = Ku / Ix
And:
c0 = sqrt(Ku / Ix)
Where:
psi = the propagating boundary disturbance
Ku = effective outward response property
Ix = effective inward inertial response property
For the dimensions to produce speed squared:
Ku must have dimensions comparable to energy density or pressure.
Ix must have dimensions comparable to mass density.
Then:
Ku / Ix
= (joules per cubic metre)
divided by
(kilograms per cubic metre)
= joules per kilogram
= metres squared per seconds squared
Therefore:
sqrt(Ku / Ix) = metres per second
This dimensional compatibility does not prove the equation. It shows that the proposed structure is physically developable rather than dimensionally impossible.
10
The Meaning Of The Two Response Terms
The outward term should not be interpreted as the observed Hubble expansion rate inserted directly into the equation.
The inward term should not be interpreted as the surface gravitational acceleration of Earth.
Neither of those quantities possesses the proper universal role.
Instead:
Ku
would describe the local substrate’s effective ability to permit, restore, or transmit nonlocalized propagation.
And:
Ix
would describe the local substrate’s effective resistance to expression becoming instantaneously and infinitely localized.
The resulting ratio would establish a finite boundary speed.
If the outward response existed with no inward resistance, propagation might become formally unbounded.
If inward commitment existed with no outward route freedom, propagation would collapse into localization.
The finite value c0 may therefore represent the stable relationship between:
the substrate's permission to propagate
and
the substrate's resistance to unlimited localization change.
This is the deeper meaning of the boundary.
The outward condition keeps expression from collapsing immediately into static localization.
The inward condition prevents propagation from becoming instantaneous and unlimited.
Their relationship generates a finite causal rate.
11
Equilibrium Rather Than Cancellation
The two tendencies do not cancel into zero.
Opposing conditions can produce motion when they establish a stable dynamic interface.
An ocean wave is not motionless merely because gravity pulls water downward while pressure and displacement drive restoration.
A vibrating string is not motionless merely because tension opposes displacement.
Likewise, inward obligation and outward freedom may create propagation rather than cancellation.
The proposed light condition is:
Outward route availability
balanced by
inward localization resistance
equals
stable boundary propagation.
This is not necessarily an equality of raw energies:
Ex = Eu
Nor is it necessarily:
chi = upsilon = 0.5
The expressed and unexpressed components may have different coupling strengths, geometric roles, scales, and response coefficients.
The balance is a balance of effective tendencies, not necessarily equal quantities of energy.
Let:
Ru = effective outward route response
Rx = effective inward commitment response
At the light boundary:
Ru and Rx form a stable propagating relation.
The important condition is not numerical sameness.
It is dynamic compatibility.
12
Light As Expression Without Rest Commitment
A photon carries energy:
E = h f
It also carries momentum:
p = E / c0
Yet its invariant rest mass is zero.
This makes light an ideal candidate for the state described here.
It possesses expression but not rest commitment.
A preliminary TSTOEAO expression map can therefore be written:
Eu
unexpressed potential
transition into distinguishable expression
Er
radiative expression
energy and information in propagation
no rest-mass commitment
transition into localization or absorption
Ex
committed expression
matter, inertia, structure, binding burden
Where:
Eu = unexpressed or minimally differentiated potential
Er = radiative boundary expression
Ex = localized or materially committed expression
The fuller accounting relationship may eventually require:
ET = Eu + Er + Ex
This is a refinement of the earlier two-part model.
The original relationship:
ET = Eu + Ex
treated all expressed energy together.
The present paper suggests dividing expressed energy into:
propagating expression
and
rest-committed expression.
Thus:
Eexpressed = Er + Ex
And:
ET = Eu + Er + Ex
This may prove to be one of the paper’s most important refinements.
Light is not excluded from expressed energy.
It is a distinct phase of expression.
13
The Information-Theoretic Bridge
Ted Jacobson demonstrated in 1995 that the Einstein equation can be derived by requiring the thermodynamic relationship between heat, entropy, and temperature to hold across local causal horizons. He interpreted the Einstein equation as comparable to an equation of state rather than necessarily a microscopic fundamental law.
More recent work by Philipp Dorau and Albert Much established a rigorous relationship between quantum relative entropy, energy flux across a bifurcate Killing horizon, horizon-area variation, and the semiclassical Einstein equations, under an entropy-area assumption. Their work focuses on the distinguishability between a vacuum state and coherent quantum-field excitations.
This suggests a possible formal meaning for TSTOEAO expression.
Let:
sigma = the vacuum or reference state
rho = an excited or expressed state
D(rho || sigma) = quantum relative entropy
Quantum relative entropy provides a measure of how distinguishable one state is from another.
A future TSTOEAO expression measure might therefore take the form:
X(rho, sigma) approximately related to D(rho || sigma)
Where:
X = degree of locally distinguishable expression
The classification then becomes:
Unexpressed or reference condition:
D(rho || sigma) = 0
or approximately 0
Radiative boundary expression:
D(rho || sigma) > 0
rest-mass commitment = 0
Materially committed expression:
D(rho || sigma) > 0
rest-mass commitment > 0
This is not an established identification.
It is a candidate bridge.
The significance is that expression may eventually be defined not only as an energy quantity, but as measurable departure from a reference condition.
Gravity could then be interpreted as geometric obligation associated with distinguishable committed expression.
Light would be distinguishable expression that remains below the threshold of rest-mass commitment.
14
The Possible Meaning Of E = mc0^2
The relationship:
E = m c0^2
shows that mass corresponds to an enormous quantity of energy scaled by the square of the vacuum propagation constant.
TSTOEAO should not claim to have re-derived this equation merely by interpreting it.
However, the boundary hypothesis suggests a possible future meaning.
If c0 is the characteristic rate separating propagating expression from rest-mass commitment, then:
c0^2
may represent the conversion scale between:
propagational energy freedom
and
committed inertial form.
Mass would then be energy whose free propagational condition has been reorganized into persistent localization.
This does not mean that light simply slows down and becomes matter.
Particle creation, binding, symmetry, conservation laws, field interactions, and other physical requirements remain essential.
The claim is more limited:
The appearance of c0^2 in mass-energy equivalence may be consistent with c0 being the fundamental conversion boundary between freely propagating expression and inertially committed expression.
This is a direction for future development, not a completed derivation.
15
Why Gravity And Gravitational Waves Matter
If gravity represents the geometric or binding burden of committed expression, while light represents propagation along the expression boundary, then the speed of gravitational disturbances becomes important.
Gravitational waves propagate at the same invariant causal rate as light within general relativity.
The TSTOEAO boundary model would interpret this as evidence that electromagnetic disturbances and gravitational disturbances, though physically different, resolve through the same underlying causal substrate boundary.
They need not be the same type of wave.
They may share the same limiting rate because the substrate only possesses one local boundary propagation condition.
Thus:
electromagnetic disturbance
and
gravitational disturbance
may both obey:
vlocal = c0
because:
c0 is a property of the route-space boundary,
not merely a private property of photons.
This interpretation is necessary if the theory is to explain why c0 governs causality more broadly rather than only describing visible light.
16
Gradient-Dependent Effective Propagation
A fuller model would permit the effective response coefficients to vary with environment:
Ku = Ku(x, t, state)
Ix = Ix(x, t, state)
A naive variable-speed form would be:
ceffective(x,t)^2 = Ku(x,t) / Ix(x,t)
However, this expression must be interpreted carefully.
In a material medium, ceffective may correspond to an actual phase or group propagation speed below c0.
In curved spacetime, it may correspond only to a coordinate-assigned or route-effective speed, while the locally measured vacuum value remains c0.
Therefore, the theory should distinguish:
c0 = local invariant vacuum boundary rate
vmedium = effective rate through matter
vroute = endpoint or coordinate-assigned route rate
A general route-cost form might eventually be:
vroute = c0 / neffective
Where:
neffective = 1 + Gm + Gg + Ge + other route contributions
And:
Gm = material interaction contribution
Gg = geometric or gravitational route contribution
Ge = expansion or evolving-background contribution
This equation is only schematic.
A gravitational contribution cannot be treated as an ordinary refractive index in every coordinate system without qualification.
Its purpose is to express the route-space principle:
Additional gradients do not necessarily replace the local boundary law; they change the route through which the law is expressed.
17
The Meaning Of A Stable Average
The proposal that c0 is an average should now be stated precisely.
It is not proposed that every photon continually accelerates and decelerates around a numerical mean.
It is proposed that the measured macroscopic constant may be the stable result of a deeper equilibrium process.
Let:
Ku_bar = equilibrium-effective outward response
Ix_bar = equilibrium-effective inward response
Then:
c0 = sqrt(Ku_bar / Ix_bar)
The bars indicate equilibrium-effective quantities.
They do not necessarily represent a simple time average accessible to direct measurement.
They may summarize many substrate-level configurations that all reproduce the same macroscopic boundary rate.
This is comparable in general form—not in proven mechanism—to temperature, pressure, elasticity, or other macroscopic quantities that emerge from underlying systems while remaining stable and measurable.
Therefore:
The speed of light may be an average in origin while remaining invariant in local measurement.
That is the strongest form of the intuition.
18
Preliminary Predictions
A useful hypothesis must eventually produce consequences beyond metaphor.
The boundary model presently suggests the following research targets.
Prediction Target One: One Local Vacuum Boundary Rate
All massless disturbances governed by the same causal substrate should share the same local limiting propagation rate.
Prediction Target Two: Material Delay Tracks Expressed Structure
Propagation delay through matter should correlate with the material’s electromagnetic coupling, density, coherence, frequency response, and structural organization rather than merely its total mass.
This is consistent with refractive behavior being state- and frequency-dependent.
Prediction Target Three: Geometry Alters Routes, Not The Local Boundary Rule
Gravitational gradients should alter direction, frequency relationships, total travel time, and coordinate description while preserving the locally measured vacuum value.
Prediction Target Four: Expression Has At Least Two Forms
The theory should distinguish radiative expression from rest-committed expression:
Eexpressed = Er + Ex
Prediction Target Five: A Dimensional Derivation Of c0 Must Be Possible
The theory must identify physically meaningful quantities corresponding to Ku and Ix, then demonstrate:
c0^2 = Ku / Ix
without defining either term circularly using c0.
Prediction Target Six: The Same Framework Must Remain Compatible With Relativity
Any proposed microphysical mechanism must reproduce local Lorentz invariance to the precision already observed.
Prediction Target Seven: Dimensionless Observables Must Remain Consistent
Claims that c0 changed across cosmic history cannot be made solely by assigning different dimensional numerical values. Any meaningful variation must appear in dimensionless measurable relationships.
19
What Would Falsify Or Weaken The Model
The proposal would be weakened if:
no physically meaningful outward response coefficient can be defined;
no physically meaningful inward inertial response coefficient can be defined;
their ratio cannot reproduce dimensions of speed squared without circularity;
the resulting theory predicts a preferred local frame inconsistent with experiment;
the model predicts locally measurable vacuum deviations from c0 where none occur;
the model cannot distinguish radiative expression from material expression;
it simply renames established electromagnetic constants without adding explanatory power;
it cannot connect the boundary concept to testable route, gradient, or localization behavior;
it treats cosmic expansion as a conventional local force acting directly on photons;
it contradicts the local equivalence principle without superior evidence.
TSTOEAO should not avoid these conditions.
They are the path by which the idea can move from intuitive coherence toward physical theory.
20
Necessary Cautions
This paper does not claim that the speed of light has been mathematically derived from gravity and cosmic expansion.
It does not claim that the Hubble expansion rate and a gravitational acceleration can be inserted into a simple equation to calculate c0.
It does not claim that photons are half matter and half dark energy.
It does not claim that the quantum vacuum is automatically identical to unexpressed energy.
It does not claim that gravity is a conventional Newtonian force in all descriptions.
It does not claim that light locally travels below c0 merely because it crosses curved vacuum spacetime.
The paper proposes a more disciplined hypothesis:
Expressed matter represents rest-mass commitment and inward binding obligation.
Unexpressed potential represents outward freedom from local material commitment.
Light represents distinguishable expression without rest-mass commitment.
Light therefore propagates along the boundary between commitment and freedom.
The vacuum speed c0 may be the characteristic equilibrium rate of that boundary.
Matter and geometry alter propagation routes and effective travel times while the local vacuum boundary rule remains invariant.
A successful theory must derive c0 from physically defined response quantities rather than merely describing it poetically.
21
Plain-Language Statement
The simplest statement is this:
Matter is energy that has settled into form.
Once energy settles into form, it gains mass, inertia, structure, and gravitational obligation.
Unexpressed energy has not settled into that local material burden. It retains outward freedom and route availability.
Light is between those conditions.
Light is real enough to carry energy and information, but it has not accepted a rest-mass form.
It therefore travels along the moving seam between the inward tendency to become localized and the outward freedom to remain unbound.
The speed of light in vacuum may be the natural rate of that seam.
Matter slows the effective journey because light must interact with expressed structure.
Gravity changes the geometry of the journey because committed energy changes the route.
Cosmic expansion changes the large-scale relationship between the places through which the journey occurs.
But locally, in vacuum, the boundary resolves at the same rate.
Matter inhabits commitment.
Expansion inhabits freedom.
Light travels their boundary.
22
Preliminary Model Summary
The original energy distinction is:
ET = Ex + Eu
The present refinement is:
ET = Eu + Er + Ex
Where:
Eu = unexpressed potential
Er = radiative or boundary expression
Ex = rest-committed expression
The original fractions remain:
chi = expressed fraction
upsilon = unexpressed fraction
chi + upsilon = 1
But expressed energy may now be divided:
Eexpressed = Er + Ex
The inward and outward tendencies remain:
Binding burden rises with committed expression.
Expansion freedom rises with unexpressed potential.
Light occupies:
expression greater than zero
rest-mass commitment equal to zero
The target wave equation is:
Ix (d2psi/dt2) - Ku Laplacian(psi) = 0
Producing:
c0^2 = Ku / Ix
And:
c0 = sqrt(Ku / Ix)
Where:
Ku = effective outward substrate-response modulus
Ix = effective inward localization or inertial-response density
The information-theoretic extension is:
X(rho, sigma) approximately related to D(rho || sigma)
Where:
sigma = reference state
rho = expressed state
D(rho || sigma) = quantum relative entropy
X = distinguishable expression
These equations remain preliminary scaffolds.
23
Conclusion
This paper proposes that light occupies the active boundary between expressed gravitational obligation and unexpressed expansion freedom.
Expressed matter is energy committed to localized form. It possesses rest mass, inertia, structural persistence, and gravitational participation.
Unexpressed potential is energy not locally committed to matter-bearing form. It retains comparative freedom from local binding and may contribute to outward or expansion-like behavior.
Light is expressed but not rest-mass committed.
It therefore occupies neither condition completely.
It surfs their boundary.
The vacuum speed of light may be the characteristic equilibrium propagation rate of this boundary: the rate at which distinguishable energy can move while remaining free from rest-mass localization.
This rate should not be interpreted as a simple numerical average between ordinary gravity and the observed expansion of the universe. It may instead emerge from the ratio of two deeper response properties:
c0^2 = Ku / Ix
The outward response permits propagation.
The inward response limits unlimited or instantaneous change.
Their relationship creates a finite causal boundary.
When light enters matter, it encounters additional expressed structure and route cost. When it crosses gravitational gradients, the geometry and timing of the route change. When it travels across an expanding universe, the large-scale relationship between its endpoints evolves. Yet the locally measured vacuum boundary rate remains c0.
The hypothesis therefore links four TSTOEAO statements:
Matter is energy that has become committed.
Gravity is the burden of that commitment.
Expansion is the freedom of energy not locally committed.
Light is expression surfing the boundary between commitment and freedom.
The next task is mathematical.
TSTOEAO must identify the physical meanings of Ku and Ix, demonstrate that their relationship produces the measured invariant rate without circular definition, connect distinguishable expression to gravitational geometry, and determine whether radiative expression forms a genuine intermediate condition between unexpressed potential and materially committed energy.
Until that work is completed, the proposal remains a disciplined hypothesis.
But it provides a coherent reason that light, gravity, expansion, causality, mass, and the vacuum speed may not be separate facts.
They may be different expressions of one boundary.
References
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