Gravity as an Emergent Effect of Projected Radiation
The preprint version is available on SSRN: Gravity as an Emergent Effect of Projected Radiation (August 08, 2026). http://dx.doi.org/10.2139/ssrn.7251340
Gravity as an Emergent Effect of Projected Radiation
Juliet Zhong
Independent
Researcher | London, United Kingdom | August 2026
ORCID:
0009-0006-5099-3671
Abstract
This paper proposes that gravity is not a fundamental
interaction but an emergent effect arising from the interaction between
projected matter and a background radiation field within the SxD dimensional
cascade. Drawing on a prior analysis of the matter-radiation classificatory
inconsistency in modern physics, and on the mass-energy equivalence E = mc², it
is argued that mass is condensed radiation and radiation is released mass.
Within the SxD framework, observable three-dimensional spacetime (S³D) is a
structural projection from a six-dimensional primordial nucleus (S⁶D), and matter
is a high-density condensation of the projected radiation field. A body of
projected mass necessarily perturbs the ambient radiation field; a second body
experiences an anisotropic flux, a radiation shadow, producing a net
directional force. Under two minimal postulates, that radiative source strength
and coupling cross-section are each proportional to mass in the weak-field
limit, the Newtonian inverse-square law F = G_eff Mm/r² emerges from spherical
flux geometry. The radiation potential recovers the classical Newtonian
potential, and the weak-field metric perturbation reproduces the linearised
general-relativistic result. The stress-energy tensor is reinterpreted as the
S³D representation of the projected radiation field, and the metric curvature
of general relativity is proposed as an effective geometric encoding of the
underlying radiative process. The equivalence principle is derived as a
structural consequence rather than an independent postulate. Three conditions
for empirical distinguishability and the principal limitations, including the
absence of explicit non-linear radiation-field dynamics, are stated. Newton
described the phenomenon; Einstein described the geometry; this paper proposes
the source.
Keywords: emergent gravity; projection cosmology;
dimensional cascade; radiation field; Newtonian limit; general relativity;
mass-energy equivalence; ontology of spacetime; SxD model; philosophy of
gravity
I. Introduction: The Missing Cause of Gravity
Gravity is the oldest recognised force and the least
understood. Newton's Principia (1687) established that every massive body
attracts every other with a force proportional to the product of their masses
and inversely proportional to the square of their separation [Newton, 1687].
This law describes what gravity does with extraordinary precision but says
nothing about why it does it. Newton himself acknowledged this explicitly:
"I have not yet been able to discover the cause of these properties of gravity
from phenomena, and I frame no hypotheses" [Newton, 1687].
Two centuries later, Einstein's general theory of relativity
(1915) reframed the question [Einstein, 1915]. Mass does not attract other mass
at a distance; rather, mass curves the geometry of spacetime, and objects
follow geodesics through that curved manifold. The explanatory gain is
substantial: gravitational phenomena are reduced to geometry. Yet the
foundational question persists in a new form—why does mass curve spacetime?
General relativity provides no answer. The Einstein field equations, G_uv =
8piG T_uv, assert a correspondence between the energy-momentum content of
spacetime and its geometric curvature, but the correspondence is postulated,
not derived from a deeper mechanism [Misner, Thorne, & Wheeler, 1973].
The programme of quantum gravity—initiated by Rosenfeld
(1930) and Bronstein (1936) and pursued for nearly a century through string
theory, loop quantum gravity, and related frameworks—has sought to unify
gravitation with quantum mechanics by quantising the gravitational field itself
[Bronstein, 1936; Rosenfeld, 1930]. This programme rests on an unstated
assumption: that because the electromagnetic field admits quantisation (Planck,
1900; Einstein, 1905), the gravitational field must admit it as well. Yet gravity
and electromagnetism differ in a fundamental respect. Electromagnetic quanta
(photons) have been observed directly and repeatedly. No graviton has ever been
detected, and no experiment has ever revealed a discrete quantum of
gravitational interaction. The analogy between the two fields, while
mathematically suggestive, has no empirical foundation. After ninety years of
effort, quantum gravity remains without a single experimentally confirmed
prediction.
The scale of investment in this programme deserves emphasis.
String theory, the most prominent approach to quantum gravity, has engaged
thousands of theoretical physicists over five decades and has generated a
landscape of approximately 10^500 possible vacuum solutions—none of which has
yet produced an experimentally confirmed prediction at accessible energies [Smolin,
2006]. Loop quantum gravity, the principal alternative, predicts a discrete
structure of spacetime at the Planck scale (approximately 10^-35 metres)—a
regime inaccessible to any conceivable experiment. The empirical sterility of
these programmes is not a temporary setback; it may be a structural signal that
the foundational premise—gravity must be quantised because electromagnetism can
be—is incorrect.
More recently, alternative approaches have explored the
possibility that gravity is not fundamental but emergent. Jacobson (1995)
derived the Einstein field equations from thermodynamic considerations applied
to local Rindler horizons [Jacobson, 1995]. Verlinde (2011) proposed that
gravity arises as an emergent force associated with information on holographic
screens [Verlinde, 2011]. Padmanabhan has independently developed a systematic
case that the Einstein equations have the character of emergent thermodynamic
relations rather than fundamental field equations [Padmanabhan, 2007]. These
programmes share the insight that gravity may not require quantisation because
it may not be a fundamental field interaction at all. Independently, the
holographic principle, arising from the discovery that a black hole's
information capacity is determined by its surface area rather than its volume
[Bekenstein, 1973; 't Hooft, 1993; Susskind, 1995], has established that the
information content of a spatial region is determined by its boundary, not its
interior. This result, while not invoked as a foundation for the present model,
is independently consistent with an ontology in which three-dimensional space
is a projection surface rather than a fundamental container. The present paper
shares this premise but proposes a distinct mechanism grounded in the SxD
dimensional cascade framework [Zhong, 2026a; Zhong, 2026b].
The SxD model, formalised in Ripple-Instantiation
Cosmogenesis [Zhong, 2026a], proposes that observable three-dimensional
spacetime (S³D) is not ontologically fundamental but is generated as a
structural projection from a six-dimensional primordial nucleus (S⁶D) through a
cascade of intermediate dimensional layers: S⁶D → S⁵D → S⁴D → S³D. In this
framework, matter is not an independent substance occupying space; it is a
condensed, high-density region within a pervasive radiation field that
constitutes the projection medium itself. The radiation field is the
ontological ground; matter is derivative.
If matter is embedded within a radiation field—as a fish is
embedded within the sea—then the presence of a massive body necessarily
perturbs the radiation environment surrounding it. A second body, immersed in
the same field, experiences an anisotropic radiation flux: the first body
partially shadows or restructures the radiation arriving from one direction,
creating a net directional pressure. In S³D, this directional pressure is
observed as gravitational attraction.
The remainder of this paper develops this proposal in six
stages. Section II establishes the ontological framework and the identification
of matter as condensed radiation, drawing on both the SxD dimensional cascade
and the mass-energy equivalence of special relativity. Section III formalises
the relationship between projected mass, radiative source strength, and
coupling cross-section. Section IV derives the Newtonian force law from
radiative flux geometry and addresses the mechanism of radiation shadowing.
Section V establishes the relationship between the radiation-field model and
general relativity through the energy-momentum tensor and the effective metric
correspondence. Section VI discusses the status of quantum gravity within this
framework. Section VII identifies conditions for empirical distinguishability
and states the principal limitations.
II. Matter as Condensed Radiation: Ontological and Physical Foundations
II.1 The Matter-Radiation Distinction Reconsidered
The classical ontological opposition between matter and
radiation—matter as localised, massive, and substantial; radiation as
propagating, massless, and immaterial—has been progressively undermined by the
development of quantum field theory. In a prior analysis [Zhong, 2026c], it was
shown that the coexistence of the Standard Model's fermion/boson taxonomy with
the inherited nineteenth-century matter/radiation terminology produces a
genuine classificatory inconsistency. Beta radiation is an electron flux—the
electron being a fermion conventionally classified as a matter particle. Gamma
radiation is a photon flux—the photon being a massless gauge boson classified
as a force carrier. The single term "radiation" thus encompasses
entities that the Standard Model places in ontologically distinct categories.
The inconsistency is not a matter of imprecise language; it reflects a failure
to revise foundational terminology in light of the conceptual transformation
wrought by quantum field theory.
Within the Standard Model itself, the distinction between
matter and radiation is not categorical but modal. Both the electron and the
photon are described as localised excitations of quantum fields. They differ in
the type of field, the quantum numbers carried, and the mode of excitation, but
they share the same fundamental ontological status: field excitations. The
dynamical evidence confirms this. Pair production (a photon of sufficient
energy produces an electron-positron pair) and annihilation (an electron and
positron annihilate into photons) demonstrate that the transition between what
classical terminology calls "radiation" and what it calls
"matter" is empirically routine, governed by conservation laws, and
requires no exotic physics. An entity classified as radiation (a photon)
becomes an entity classified as matter (an electron) and vice versa.
This paper adopts the conclusion of that analysis: the
ontological opposition between matter and radiation is not sustained by modern
physics. Matter and radiation are not two fundamentally different kinds of
thing. They are two manifestations of the same underlying reality—quantum field
excitations—differing in mode, not in kind.
II.2 Mass-Energy Equivalence as a Radiative Identity
The identification of matter with condensed radiation
receives independent support from the most famous equation in physics.
Einstein's special relativistic mass-energy equivalence, E = mc², establishes
that mass and energy are not merely correlated but are interconvertible
manifestations of the same physical quantity [Einstein, 1905b]. A body of rest
mass m possesses an intrinsic energy content E = mc²; conversely, any
concentration of energy E possesses an effective mass m = E/c².
Quantum field theory further establishes that radiation is a
form of energy. A photon of frequency v carries energy E = hv (Planck, 1900;
Einstein, 1905a). Radiation is not merely associated with energy; it is energy
in its propagating, delocalised form.
The conjunction of these two established results points
toward a conclusion whose dynamical core is already confirmed within the
Standard Model itself—in quantum chromodynamics, the overwhelming majority of
hadronic mass arises not from intrinsic constituent masses but from the binding
energy of massless gluon fields [Wilczek, 2000]. What has not been drawn from
this fact is its full ontological consequence: if mass is energy (E = mc²) and
radiation is energy (E = hv), then the identification of mass as condensed
radiation and radiation as released mass becomes a natural ontological
inference. This inference is not a deductive consequence of special relativity
alone; it requires the additional ontological commitment, supplied by the SxD
framework, that the radiation field is the fundamental substrate from which
mass condenses:
E² = p²c² + m²c⁴
For a massless particle (m = 0), this reduces to E = pc—the
standard energy-momentum relation for radiation. For a massive particle at rest
(p = 0), it reduces to E = mc². The two cases are not ontologically distinct
regimes; they are limiting cases of the same continuous energy-momentum
relation. The massive case represents energy in a bound, localised
configuration—condensed radiation. The massless case represents energy in a
propagating, delocalised configuration—free radiation. The invariant mass term
m²c⁴ on the right-hand side of the full relation represents, in this reading,
the energy content locked into the bound configuration of the field excitation.
Within the SxD framework, this reinterpretation acquires a
structural ground. Mass is not an independent fundamental quantity; it is the
S³D effective measure of the degree of radiative condensation at a given
projected location. A body of mass M is a region of the projected radiation
field where the radiation density is locally elevated into a self-sustaining
bound configuration. The greater the mass, the more radiation is condensed at
that location.
II.2.1 The Photon-Electron Continuum and the Meaning
of Invariant Mass
The full relativistic energy-momentum relation deserves
closer examination, because it reveals something that the simplified E = mc²
obscures. Consider an electron at rest: its energy is E = m_e c² = 0.511 MeV.
Now consider a gamma-ray photon with the same energy, 0.511 MeV: its momentum
is p = E/c, and its rest mass is zero. In the Standard Model, these are
classified as fundamentally different entities—the electron is a fermion, a
matter particle; the photon is a boson, a force carrier. Yet pair production
converts a photon of energy greater than or equal to 1.022 MeV into an
electron-positron pair, and the reverse process (annihilation) converts the
pair back into photons. The total energy is conserved; the total momentum is
conserved; but the classification of the entity changes from
"radiation" to "matter" and back.
Within the present framework, this is not a mysterious
transmutation between ontological categories. It is a change in the mode of a
field excitation: from a propagating, delocalised mode (radiation) to a bound,
localised mode (matter), and back. The invariant mass term m²c⁴ in the relation
E² = p²c² + m²c⁴ measures the energy locked into the bound configuration. When
the configuration unbinds (annihilation), that energy is released as
propagating radiation. When radiation is forced into a bound configuration
(pair production), that energy is locked in as invariant mass. Mass is not a
substance; it is a state—the bound state of radiation.
This reading resolves an old puzzle. The question "why
does mass have energy?" (answered by E = mc²) is traditionally treated as
primitive—mass just does have energy, and the equation tells us how much. But
if mass is condensed radiation, the question dissolves: mass has energy because
it is energy, in a bound configuration. The equation E = mc² is not a
conversion formula between two different things; it is a statement of identity
between two descriptions of the same thing.
II.3 The SxD Dimensional Cascade and the Radiation Sea
The dimensional notation SxD, introduced in [Zhong, 2026a],
denotes six stratified layers of cosmological structure defined not by spatial
axes but by their function within the projection cascade. S⁶D is the bounded,
spherical primordial nucleus in a state of absolute rest. S⁵D is the atemporal
five-dimensional configuration manifold receiving the direct radiation of S⁶D.
S⁴D is the quantum-field conversion interface. S³D is the observable material
universe. S²D and S¹D are sub-material layers outside the scope of the present
paper. S⁰D is the containing volume—the vacuum—within which all layers are
embedded.
The generative event is instantaneous dimensional
projection:
S⁶D → S⁵D → S⁴D → S³D → S²D → S¹D
Within S³D, the observable universe is not empty space
populated by material objects. It is a pervasive radiation field—the residual
projection medium—within which localised high-density condensations appear as
what S³D observers identify as matter. The relationship between the radiation
field and the material objects embedded within it is not analogous to that
between a container and its contents. It is analogous to that between an ocean
and the structures within it: the ocean is primary; the structures are
derivative patterns within it. A fish does not exist alongside the sea; it is
constituted by the sea and immersed within it. In the same way, a material body
does not exist alongside the radiation field; it is a condensed configuration
of the radiation field, embedded within the uncondensed remainder.
This ontological ordering has direct physical consequences.
If a body of mass M is a region of locally elevated radiation density, then its
presence necessarily modifies the radiation environment in its vicinity. The
ambient radiation field is not a passive background unaffected by the presence
of matter; matter, being condensed radiation, interacts with the field from
which it is constituted. This interaction is the physical ground from which
gravity will be derived in the subsequent sections.
III. Projected Mass and Radiative Coupling
III.1 The Projected Mass Postulate
The ontological framework established in Section II—matter
as condensed radiation, embedded within a pervasive radiation field—entails a
specific relationship between a body's mass and its effect on the ambient
radiation environment. If mass is the degree of local radiative condensation,
then a body of greater mass represents a greater perturbation of the radiation
field. This relationship is formalised in two postulates.
Postulate 1 (Radiative Source Strength).
In the weak-field, far-field regime, the effective radiative
perturbation produced by a projected body of mass M is proportional to M:
L_R(M) = alpha x M
where L_R is the effective radiative source intensity and
alpha is a coupling constant encoding the strength of the mass-radiation
interaction in S³D. This postulate is not an ad hoc assumption. It is a direct
structural consequence of the identification of mass with radiative
condensation: if mass measures the degree of condensation, and the perturbation
of the ambient field is produced by that condensation, then the perturbation
magnitude scales with the condensation measure.
The linearity of this relationship is explicitly asserted as
a first-order approximation valid in the weak-field limit. At very high mass
densities—in the vicinity of neutron stars, black holes, or cosmologically
dense regions—the perturbation produced by the body is no longer small relative
to the background radiation field, and the linear scaling L_R = alpha x M
ceases to be adequate. The non-linear regime is addressed in Section V.
Postulate 2 (Radiative Coupling Cross-Section).
A test body of mass m couples to the ambient radiation field
with an effective cross-section proportional to m:
sigma_R(m) = beta x m
where beta is a coupling constant. This postulate follows
from the same ontological ground as Postulate 1: if mass is radiative
condensation, then a body's susceptibility to radiative flux is determined by
the same quantity that defines its condensation—namely, its mass. A more
massive body, being a larger condensation of radiation, presents a
proportionally larger effective cross-section to the ambient field.
The proportionality sigma_R = beta x m further presupposes
that the shadowing produced by a body does not saturate—that is, that each unit
of condensed radiation within the body couples to the ambient flux
independently. This weak-coupling condition is the cross-sectional counterpart
of the weak-field condition stated for Postulate 1: at extreme condensation
densities, where shadowing saturates, the linear scaling fails, and the force
ceases to track mass exactly. The breakdown of both postulates in the same
regime is not a coincidence but a single non-linearity viewed from the source
side and the receiver side respectively.
III.2 Why Both Postulates Follow from a Single Ontological Commitment
It is worth emphasising that the proportionality of both
source strength and coupling cross-section to mass is not two independent
assumptions but two consequences of one: the identification of mass with
radiative condensation. In standard Newtonian gravity, the equality of
gravitational and inertial mass is an empirical fact (the equivalence
principle) that has no explanation within the theory itself—it is simply
observed to hold. In the present framework, the equivalence is a structural
entailment. A body's capacity to perturb the radiation field (its
"gravitational charge") and its capacity to respond to the radiation
field (its "gravitational susceptibility") are both determined by the
same physical quantity: the degree of radiative condensation at that location.
They are not merely empirically equal; they are the same thing measured in two
different ways. This provides a natural ontological basis for the equivalence
principle without requiring it as an independent postulate.
IV. Derivation of the Newtonian Force Law from Radiative Flux Geometry
IV.1 Spherical Flux Propagation
Consider a body of projected mass M situated within the
ambient radiation field. By Postulate 1, this body produces a radiative
perturbation of effective intensity L_R(M) = alpha x M. In S³D, this
perturbation propagates outward through three-dimensional space. By the
geometry of spherical propagation, the radiative flux at distance r from the
source is distributed uniformly over the surface area of a sphere of radius r:
Phi_R(r) = L_R(M) / (4 pi r²) = alpha x M / (4 pi r²)
This is not a physical assumption but a geometric identity:
any isotropic quantity emitted from a point source in three-dimensional
Euclidean space dilutes as 1/r² by conservation of flux through expanding
spherical surfaces.
IV.2 Force on a Test Body
Now introduce a second projected body of mass m at distance
r from M. By Postulate 2, this body couples to the local radiation flux with
cross-section sigma_R(m) = beta x m. The effective force experienced by m due
to the radiative flux perturbation produced by M is the intercepted momentum
flux—radiation flux divided by c yields momentum flux, the classical mechanism
of radiation pressure [Poynting, 1904]:
F_R = sigma_R(m) x Phi_R(r) / c
= (beta x m / c) x (alpha x M / 4 pi r²)
= (alpha x beta / 4 pi c) x Mm / r²
Defining the effective gravitational constant as:
G_eff = alpha x beta / (4 pi c)
we obtain:
F_R = G_eff x Mm / r²
This is Newton's law of universal gravitation. The
inverse-square dependence arises not from an intrinsic property of a
"gravitational force" but from the geometric dilution of radiative
flux over spherical surfaces in three-dimensional space. The proportionality to
Mm arises from the two postulates, both of which are structural consequences of
the single ontological commitment that mass is condensed radiation.
IV.3 The Radiation Potential
The force law derived above can equivalently be expressed in
terms of a scalar radiation potential. Define:
U_R(r) = -G_eff x M / r
Then the gravitational acceleration field is:
g_R(r) = -nabla U_R = -G_eff x M / r² x r-hat
and the force on a test body m is:
F_R = m x g_R = -G_eff x Mm / r² x r-hat
This potential is formally identical to the Newtonian
gravitational potential. The physical content of the SxD model lies not in the
form of the potential—which is geometrically determined—but in the
identification of the physical medium (projected radiation) whose flux produces
the potential.
IV.4 The Mechanism of Attraction: Radiation Shadowing
The mathematical derivation of Sections IV.1-IV.3
establishes the force law from radiative flux geometry. The present section
provides the physical picture underlying that mathematics. A natural objection
arises: if both M and m are immersed in a uniform, isotropic background
radiation field, why is there a net force at all? An isolated body in a
perfectly isotropic field experiences equal radiation pressure from all
directions, yielding zero net force. Why does the background radiation not act
as a universal drag or resistance?
The answer lies in the ontological relationship between the
body and the field. In the SxD framework, a material body is not a foreign
object inserted into an external radiation medium. It is a condensed
configuration of the radiation field itself. The relationship between the body
and the field is not that of an object immersed in a fluid; it is that of a
vortex within a flow, or a knot within a rope. A knot does not experience drag
from the rope, because the knot is the rope. The background radiation field
does not exert a net force on an isolated body, because the body is the field—locally
condensed. There is no interface at which "radiation pressure" could
act, because there is no ontological boundary between "body" and
"field."
This changes when a second body is present. Body M, being a
region of elevated radiative condensation, modifies the ambient radiation field
in its vicinity. Specifically, it reduces the radiation flux propagating
through its location—it casts a radiation shadow. Body m, located at distance r
from M, therefore experiences a radiation environment that is no longer
isotropic: the flux arriving from the direction of M is reduced relative to the
flux arriving from all other directions. This asymmetry produces a net
directional force on m, directed toward M. In S³D, this is observed as
gravitational attraction.
The analogy with the ocean illuminates the mechanism. A
single fish in a uniform ocean current experiences no net force in any
particular direction—the current flows through it and around it equally. But
when a second, much larger body is present nearby, it disrupts the uniformity
of the current: the flow arriving at the fish from the direction of the larger
body is partially blocked or diverted. The resulting asymmetry pushes the fish
toward the larger body—not because the larger body pulls, but because the
current behind the fish, unobstructed, pushes harder than the current between
them.
This mechanism also explains why the gravitational force is
always attractive and never repulsive: a massive body can only reduce the
radiation flux in its shadow, never increase it. The asymmetry is therefore
always directed toward the perturbing body. This ontological point also
distinguishes the present model from the historical Fatio-Le Sage tradition of
push-gravity [Edwards, 2002]. Le Sage's mechanism posited a flux of
ultramundane corpuscles mechanically impacting material bodies, and it fails on
two well-known grounds: a body moving through the corpuscular flux experiences
a velocity-dependent drag incompatible with the observed stability of planetary
orbits, and the absorbed momentum implies an energy deposition that would heat
the body catastrophically. Both objections presuppose a mechanical interface
between body and flux—a surface at which corpuscles strike and are absorbed. In
the present model no such interface exists. The body is not an obstacle within
the field but a condensed configuration of the field; the shadowing effect is a
restructuring of the field by its own condensation, not an absorption of
momentum-carrying projectiles by a foreign object. The drag and heating
objections therefore do not transfer: they refute a mechanical corpuscular
model, not a field-ontological one. What Le Sage guessed at the level of
mechanism, the present model grounds at the level of ontology.
IV.5 The Equivalence Principle as a Structural Consequence
The equivalence principle—the empirical identity of
gravitational and inertial mass—is one of the most precisely tested facts in
physics (torsion-balance experiments confirm it to parts in 10^13 and the
MICROSCOPE space mission to parts in 10^15 [Touboul et al., 2022]) and one of
the least explained. In Newtonian gravity, it is an unexplained coincidence. In
general relativity, it is elevated to a postulate: the equivalence principle is
assumed, not derived, and the entire geometric structure of the theory is built
upon it.
In the radiation-field model, the equivalence principle is
neither a coincidence nor a postulate. It is a structural consequence of the
single ontological identification of mass with radiative condensation (Section
III.2). A body's gravitational mass—its capacity to produce a radiation-field
perturbation—is proportional to its radiative condensation. Its inertial mass—its
resistance to acceleration—is also proportional to its radiative condensation,
because acceleration of a condensed radiation structure requires work against
the binding energy of that condensation. Both quantities are manifestations of
the same underlying physical property. Their equality is not remarkable; their
inequality would be.
This constitutes a genuine explanatory gain over both
Newtonian gravity (where the equivalence is unexplained) and general relativity
(where it is assumed). The radiation-field model provides a structural
ontological basis for the equivalence principle from a single commitment,
rather than requiring it as an independent foundational postulate.
IV.6 Comparison: Newton, Einstein, and the Radiation-Field Model
Newton described the phenomenon of gravity: masses attract
with a force proportional to Mm/r². He did not explain why.
Einstein described the geometry of gravity: mass curves
spacetime, and bodies follow geodesics through the curved manifold. He
explained how the phenomenon arises geometrically but did not explain why mass
curves spacetime.
The radiation-field model proposes the source: mass is
condensed radiation; condensed radiation perturbs the ambient radiation field;
the perturbation, propagating through three-dimensional space, creates an
anisotropic flux that produces a directional force. The phenomenon that Newton
described and the geometry that Einstein formalised are both consequences of
this underlying radiative process.
The three accounts do not contradict one another. They
describe the same physical reality at three levels of depth:
Level 1—Phenomenon (Newton): Masses attract with a
force F = GMm/r². The inverse-square law is established empirically and
mathematically, but no mechanism is proposed. The question "why do masses
attract?" is explicitly set aside.
Level 2—Geometry (Einstein): Mass curves spacetime;
bodies follow geodesics through the curved manifold. The phenomenon is
explained geometrically, and the geometric description generates new
predictions (gravitational lensing, frame-dragging, gravitational waves) that
have been confirmed with extraordinary precision. But the question "why
does mass curve spacetime?" receives no answer. The Einstein field
equations assert the correspondence between mass-energy and curvature; they do
not explain it.
Level 3—Source (SxD model): Mass is condensed
radiation. Condensed radiation perturbs the ambient radiation field. The
perturbation creates an anisotropic flux that pushes nearby bodies toward the
shadow. In S³D, this is observed as attraction (Level 1). When the radiation
field is sufficiently smooth and slowly varying, the trajectories of bodies
through the perturbed field can be equivalently described as geodesics of an
effective metric (Level 2). The three levels are not competing theories but
nested descriptions of the same process, each complete at its own level of
analysis.
Newton's inverse-square law is a consequence of spherical
flux geometry in three dimensions. Einstein's metric curvature is the effective
geometric encoding of the radiation-field configuration. The present model
proposes the physical process from which both descriptions emerge.
V. Relationship to General Relativity: From Radiation Field to Effective
Geometry
V.1 Mass-Energy as a Radiative Quantity in Einstein's Equations
The right-hand side of the Einstein field equations, G_uv =
8 pi G T_uv, is the stress-energy tensor T_uv, which encodes the energy
density, momentum density, pressure, and stress at each point in spacetime [Einstein,
1916; Misner, Thorne, & Wheeler, 1973]. In standard general relativity,
T_uv is treated as a given—the matter-energy content of spacetime is specified,
and the field equations determine the resulting geometry.
Within the present framework, T_uv acquires a physical
interpretation that standard general relativity does not provide. If mass is
condensed radiation and energy is radiation (Section II), then the
stress-energy tensor is not a description of some ontologically fundamental
"matter-energy" that happens to curve spacetime. It is the S³D
effective representation of the projected radiation field:
T_uv = T_uv[R]
where R denotes the full state of the projected radiation
field. Energy density in T_uv corresponds to the local radiation condensation
density. Momentum density corresponds to the directional flux of the radiation
field. Pressure and stress correspond to the field's self-interaction at that
location.
Consider the components of T_uv individually. The T_00
component is the energy density—in the radiation-field model, this is the local
density of radiative condensation. The T_0i components are the momentum density—the
directional flux of the radiation field. The T_ij components encode pressure
and shear stress—the self-interaction of the radiation field at that location.
Each component of T_uv, which in standard general relativity is simply posited
as the matter-energy content of spacetime, acquires in the present framework a
specific physical interpretation as a property of the projected radiation
field. The stress-energy tensor is not filled in by hand; it is determined by
the state of R.
This reinterpretation does not alter any calculation within
general relativity. Every prediction of the Einstein field equations remains
unchanged, because the mathematical structure of T_uv is untouched. What
changes is the ontological reading: T_uv is no longer an unexplained primitive
but a representation of the underlying radiation field from which matter,
energy, and gravity all emerge.
V.2 The Weak-Field Metric Correspondence
In the weak-field limit, general relativity reduces to the
linearised approximation in which the metric is written as:
g_uv = eta_uv + h_uv
where eta_uv is the flat Minkowski metric and h_uv is a
small perturbation. For a static, spherically symmetric mass, the dominant
perturbation is h_00 = -2 Phi / c², where Phi is the Newtonian gravitational
potential [Misner, Thorne, & Wheeler, 1973].
In the radiation-field model, the Newtonian potential is
identified with the radiation potential U_R = -G_eff M / r (Section IV.3). The
weak-field metric perturbation therefore becomes:
h_00 = -2 U_R / c² = 2 G_eff M / (c² r)
This is identical to the standard linearised result. The
radiation-field model therefore reproduces general relativity's weak-field
predictions by construction.
V.3 The Non-Linear Regime and the Effective Metric
When the projected radiation density becomes large—in the
vicinity of very massive bodies or in cosmological contexts—the linear
relationship L_R = alpha x M ceases to be adequate. The radiation field
perturbation produced by M is no longer small relative to the background, and
the radiation field's own structure contributes to the effective source. This
is a non-linear regime in which a scalar potential Phi_R is insufficient to
describe the full dynamics.
In S³D, an observer embedded within this non-linear
radiation environment requires a more general description of local spacetime
relations. The standard tool for this description is the metric tensor g_uv.
The present model proposes that the metric perturbation h_uv is a functional of
the local radiation-field configuration:
h_uv = F_uv[R]
In the weak-field limit, this functional reduces to the
scalar case h_00 = -2 U_R / c², recovering the Newtonian regime. In the
non-linear regime, the full tensorial structure of h_uv encodes the non-linear
self-interaction of the radiation field—its coupling to its own condensations,
the back-reaction of the condensed regions on the ambient field, and the
resulting modifications to the local spacetime geometry experienced by S³D
observers.
This proposal does not claim to derive the Einstein field
equations G_uv = 8 pi G T_uv from the radiation-field model. Such a derivation
would require specifying the complete non-linear dynamics of the projected
radiation field, including the field equations governing R and the explicit
form of the functional F_uv. This lies beyond the scope of the present paper
and constitutes the principal limitation of the current formulation (Section
VII). What is claimed is more modest and more fundamental: the geometric
curvature described by general relativity is not the cause of gravity but an
effective description of the radiation-field asymmetry that produces
gravitational phenomena. Einstein's equations accurately describe the geometry
of the projected shadows on the S³D screen; the SxD model identifies the
projector.
V.4 Why the Effective Geometric Description Works
A natural question arises: if gravity is fundamentally a
radiation-field effect, why does a purely geometric theory (general relativity)
describe it so accurately?
The answer is that geometry is the natural language for
describing the macroscopic effects of a pervasive field on the motion of
objects embedded within it. When a radiation field is sufficiently smooth and
slowly varying, the trajectories of bodies through that field can be
equivalently described as geodesics of an effective metric. This is not unique
to gravity; analogous effective-metric descriptions arise in condensed matter
physics (acoustic metrics in superfluids), optics (gradient-index media), and analogue
gravity models [Barcelo, Liberati, & Visser, 2005]. In each case, the
effective geometry is real in the sense that it accurately predicts
trajectories, but it is not fundamental—it emerges from the underlying field
dynamics.
General relativity, on this reading, is the supremely
successful effective theory of gravitational geometry. Its accuracy in
predicting perihelion precession, gravitational lensing, frame-dragging, and
gravitational wave propagation reflects the fact that the effective-metric
description captures the macroscopic behaviour of the radiation field with
extraordinary fidelity. The question the present paper raises is not whether
general relativity is correct—it is—but whether it is complete. The claim is
that it describes the geometry without identifying the physical process that
generates it.
V.5 Gravitational Waves as Radiation-Field Perturbations
The detection of gravitational waves by LIGO and Virgo
[Abbott et al., 2016] confirmed one of general relativity's most striking
predictions: that perturbations in the spacetime metric propagate as waves at
the speed of light. Any viable alternative to general relativity must account
for this observation.
Within the radiation-field model, gravitational waves are
not perturbations of spacetime geometry per se; they are propagating
perturbations of the radiation field itself. When a massive system undergoes
rapid acceleration—binary neutron stars spiralling inward, black holes merging—the
radiation-field configuration changes dynamically. These changes propagate
outward through the ambient radiation field at the speed of light, because the
radiation field's characteristic propagation speed is c. An S³D observer
equipped with an interferometer detects these propagating perturbations as
oscillations in the effective metric—precisely what LIGO measures.
The formal correspondence is straightforward in the
linearised regime: if h_uv = F_uv[R], then a time-varying R produces a
time-varying h_uv—a gravitational wave. The wave equation satisfied by h_uv in
linearised general relativity (the transverse-traceless wave equation) would,
on this account, be the S³D effective description of the underlying
radiation-field wave equation. The detailed derivation of this correspondence—demonstrating
that the radiation-field wave equation reduces to the linearised Einstein wave
equation in the appropriate limit—is identified as a key objective for future
work (Section VII.3).
What is important at this stage is the conceptual point: the
existence of gravitational waves does not require that spacetime itself be a
dynamical entity capable of oscillation. It requires only that the underlying
physical medium—the radiation field—be capable of propagating perturbations.
The effective-metric description translates these radiation-field perturbations
into the language of spacetime geometry, producing the gravitational wave
phenomenology that LIGO detects. The waves are real; their interpretation as
oscillations of spacetime is, on the present account, an effective description
rather than a fundamental one.
VI. The Status of Quantum Gravity
The failure of quantum gravity programmes acquires a natural
explanation within this framework. If gravity is not a fundamental field
interaction but an emergent macroscopic effect of radiation-field asymmetry, then
attempting to quantise the gravitational field would constitute a category
error—analogous to attempting to quantise the pressure in a fluid rather than
the molecules that compose it. Pressure is real, measurable, and obeys precise
laws; but it is a statistical, emergent property of the underlying molecular
dynamics, not a fundamental field admitting independent quantisation. Gravity,
on the present account, occupies an analogous status [Padmanabhan, 2010].
The radiation field itself may admit a quantum description
at S⁴D—the quantum-field conversion interface in the SxD cascade [Zhong,
2026a]. The emergent gravitational effect observed in S³D, however, is a
macroscopic consequence of radiation-field geometry, not a quantum interaction
between individual quanta. If this is correct, then the fundamental quantum
degrees of freedom underlying gravity are not gravitational quanta (gravitons)
but the quantum excitations of the radiation field at the S⁴D level. The
graviton, rather than being a missing particle awaiting detection, would not
represent an independent fundamental degree of freedom but a macroscopic
radiation-field effect misidentified as a fundamental quantum.
It is instructive to note the historical parallel. The
programme of quantising gravity assumed, from its inception in the 1930s, that
because electromagnetism—a fundamental field interaction—admits quantisation,
gravity—also apparently a fundamental field interaction—must admit it too. But
the analogy is only valid if gravity is, in fact, a fundamental field
interaction. If it is instead an emergent macroscopic effect, the analogy fails
at the root. The electromagnetic field is fundamental; its quantisation yields
photons. The gravitational "field" may be effective; its quantisation
yields nothing, because there is no fundamental field to quantise. The
ninety-year null result of quantum gravity, on this reading, is not a failure
of ingenuity but a correct consequence of a false premise.
This does not mean that gravitational phenomena are entirely
classical. At the interface between the quantum regime (S⁴D) and the
macroscopic regime (S³D), the radiation field's quantum structure may produce
subtle corrections to the effective gravitational geometry—corrections that
would manifest as departures from the predictions of classical general
relativity in extreme environments (near black hole horizons, at very early
cosmological epochs, or at the Planck scale). These corrections, if they exist,
would constitute the empirical signature of the radiation field's quantum
nature, without requiring the existence of a graviton.
VII. Conditions for Empirical Distinguishability, Limitations, and Future
Directions
VII.1 Empirical Distinguishability
The force law derived in Section IV is formally identical to
Newton's law, and the weak-field metric correspondence in Section V reproduces
the linearised general-relativistic result. In the domain where these theories
have been tested, the SxD radiation-field model therefore reproduces general
relativity's weak-field predictions by construction [Carlip, 2019].
The question is whether the model predicts any deviations
from standard gravitational theory that could, in principle, be observed. Three
conditions are identified.
Condition 1: Radiation-field anisotropy at cosmological
scales.
If gravity arises from a background radiation field, then
large-scale anisotropies in this field—arising from the geometry of the
dimensional projection itself—should produce correlated deviations in
gravitational dynamics at super-galactic scales. These deviations would
manifest as residual correlations in galaxy distributions not accounted for by
LCDM transfer functions, consistent with the non-vanishing correlation floor
predicted in [Zhong, 2026a].
Condition 2: Mass-dependent coupling anomalies in the
strong-field regime.
Postulates 1 and 2 assert strict proportionality between
mass and radiative coupling in the weak-field limit. At extreme mass densities
(neutron stars, black hole accretion environments), deviations from linearity
may produce measurable departures from general-relativistic predictions—particularly
in orbital precession rates or gravitational wave signatures that probe the
strong-field regime. If the non-linear dynamics of the radiation field differ
from those encoded in the Einstein field equations, these differences would
appear precisely where the weak-field approximation breaks down.
Condition 3: Non-geometric gravitational effects.
If gravity is a radiation-field effect rather than a
geometric property of spacetime, then in principle there exist configurations
where the radiation-field asymmetry and the metric curvature diverge. Such
configurations would produce gravitational effects not predicted by the
Einstein equations alone. The identification of such configurations requires
detailed modelling of the non-linear radiation-field dynamics and is proposed
as a programme for future work.
These conditions do not constitute immediate falsification
tests but define the empirical boundary of the model: if no deviation from
standard gravity is ever observed under any of these conditions, the SxD
radiation-field model remains empirically indistinguishable from general
relativity, and its additional ontological commitments become a matter of
philosophical preference rather than physical necessity.
VII.2 Principal Limitations
The present formulation has four principal limitations that
must be acknowledged.
First, the non-linear dynamics of the projected radiation
field have not been specified. The functional F_uv[R] mapping the
radiation-field configuration to the effective metric perturbation is posited
but not derived. A complete theory would require radiation-field equations from
which the Einstein field equations can be recovered as the macroscopic limit,
analogous to the way in which the Navier-Stokes equations emerge from molecular
dynamics. This derivation is the central open problem of the research programme.
Second, the coupling constants alpha and beta (and therefore
G_eff) are introduced as parameters of the model but are not derived from the
SxD dimensional cascade. A complete account would derive these constants from
the properties of the projection functional Pi introduced in [Zhong, 2026a].
Third, the correspondence between radiation-field wave
dynamics and the linearised Einstein wave equation, proposed conceptually in
Section V.5, has not yet been formally derived. General relativity predicts
gravitational waves as propagating perturbations of the spacetime metric; the
LIGO/Virgo detections have confirmed their existence [Abbott et al., 2016]. The
radiation-field model must account for these observations as propagating
perturbations of the radiation field itself—radiation-field waves whose S³D
effective description corresponds to the metric perturbations detected by
interferometers. This correspondence has not yet been formally established.
Fourth, the model has not yet addressed the behaviour of
gravity at cosmological scales—specifically, the phenomena attributed to dark
matter and dark energy. If gravity is a radiation-field effect, then anomalous
gravitational dynamics at galactic and cosmological scales (flat rotation
curves, accelerated expansion) may reflect properties of the radiation field
that are not captured by the Newtonian or weak-field general-relativistic
approximations. Whether the radiation-field model can account for these phenomena
without invoking dark matter or dark energy is an open question with
potentially transformative implications, but it lies beyond the scope of the
present paper.
VII.3 Future Research Directions
The following directions identify areas where the present
model motivates further investigation. They are not framed as objectives to be
completed but as open questions that the radiation-field ontology makes it
possible to pose.
The first direction concerns whether a macroscopic
correspondence can be established between the projected radiation-field
dynamics and the Einstein field equations. If T_uv = T_uv[R] and h_uv =
F_uv[R], then the structure of the radiation field and the effective spacetime
geometry are not independent. However, a complete derivation of the Einstein
equations from the underlying radiation-field dynamics may not be a tractable
objective within any current theoretical framework. As an analogy: biology knows
the initial state of a fertilised egg and the outcome of a fully formed
organism, yet cannot derive in full, from first principles, how a fertilised
egg develops into a chick. The obstacle is not ignorance of the endpoint but
the irreducible complexity of the generative dynamics between known boundaries.
The value of this correspondence lies in establishing that the macroscopic
gravitational laws and the underlying radiative ontology are structurally
connected, not in the expectation that the former can be generated from the
latter in closed form. Derivability is not the measure of ontological truth;
structural connection is.
The second direction concerns cosmological parameters. If
the ambient radiation field is the residual projection medium of the SxD
cascade, then its large-scale structure is not arbitrary but is determined by
the geometry of the projection. This raises the question of whether
cosmological parameters currently obtained by fitting observational data—the
Hubble constant, the matter-radiation ratio, the cosmological constant—may
instead reflect structural properties of the projection geometry. The present
model motivates this question but does not yet possess the theoretical tools to
resolve it.
The third direction concerns gravitational waves. Section
V.5 proposed that gravitational waves are propagating perturbations of the
radiation field whose S³D effective description corresponds to metric
oscillations. The prediction that gravitational wave speed equals c is
automatically satisfied, since the radiation field propagates at c. Whether the
radiation-field wave equation can reproduce the polarisation structure, energy
loss rate, and waveform morphology predicted by general relativity for binary inspirals
and mergers remains an open question. Agreement would constrain the form of the
radiation-field dynamics; disagreement would either challenge the model or
point to new physics beyond general relativity.
The fourth direction, drawing on the analysis in [Zhong,
2026c], concerns the nature of invariant mass. If the electron's invariant mass
represents the effective behaviour of a more fundamental massless field
structure in a bound configuration—as proposed in that paper's concluding
hypothesis—then the relationship between mass, binding energy, and the
radiation field becomes a question that the present ontological framework makes
formally addressable.
VIII. Conclusion: From Shadow to Source
Newton described what gravity does. Einstein described how
gravity geometrically manifests. Neither theory, however, identifies a physical
mechanism underlying gravitational attraction. This paper has proposed that
gravity is an emergent radiative phenomenon: matter is a high-density
condensation of a projected radiation field, and the gravitational interaction
arises from the asymmetric radiation pressure produced when massive bodies
shadow one another within an ambient radiation field. On this account, gravity
is not a fundamental attractive interaction between masses, but a macroscopic
consequence of the spatial redistribution of radiation.
The model develops this proposal from the dimensional
structure of the SxD cascade and the mass-energy equivalence of special
relativity. Matter is treated not as an ontologically independent substance,
but as a condensed configuration of projected radiation. From this
identification, the radiative source strength of a body and the coupling
cross-section of a test body can be related to their projected masses in the
weak-field limit without introducing independent mass-dependent interaction
assumptions. The inverse-square gravitational law then follows from the
spherical dilution of radiation flux in three-dimensional space, yielding an
effective force of the form F = G_eff Mm/r² and recovering the Newtonian
potential. The resulting physical interpretation is radiation shadowing: a
massive body reduces the incident ambient radiation flux in the direction it
obstructs, creating a pressure imbalance that drives neighbouring bodies toward
the region of reduced flux. The apparent attraction of gravity is therefore
reinterpreted as the net result of an anisotropic radiative pressure field.
This reinterpretation extends beyond the Newtonian limit.
Within the proposed ontology, the stress-energy tensor appearing in Einstein's
field equations is interpreted as the S³D effective representation of the
projected radiation field, while spacetime curvature is regarded as an
effective geometric description of the underlying radiative configuration
rather than its fundamental cause. In this sense, general relativity may
describe the macroscopic geometry generated by a deeper radiative structure. The
model therefore provides an ontological re-anchoring of gravitational physics:
the familiar geometric description is retained at the macroscopic level while
its physical origin is relocated to the dynamics of the projected radiation
field.
The present theory nevertheless has a clearly defined
limitation. The nonlinear dynamical equations governing the underlying
radiation field have not yet been explicitly formulated, and consequently the
full Einstein field equations have not been derived from first principles. Such
a derivation may not constitute a tractable objective for any current
theoretical framework, given the complexity of reconstructing a macroscopic
spacetime description from a deeper generative structure. The appropriate future
question is therefore not whether every macroscopic gravitational quantity can
be calculated in closed form from the underlying radiation field, but whether a
mathematically consistent correspondence can be established between the two
levels of description. The present model should consequently be understood as a
proposed structural connection between gravitational phenomenology and a deeper
radiative ontology, rather than as a completed fundamental field theory.
If this interpretation is correct, the conceptual status of
gravity changes fundamentally. Gravity does not require a hypothetical
attractive substance or an independently existing gravitational field acting
between masses. It is the macroscopic consequence of radiation pressure
becoming spatially asymmetric through shadowing. What appears locally as
attraction is therefore the directional result of an ambient field: an
unshielded radiative flux pushes matter away from the illuminated side and
toward the region of reduced flux.
Gravity is not a pull. It is a push—from the unshielded
radiation behind you, toward the shadow in front of you.
Acknowledgements
The author acknowledges the use of AI tools in the
preparation of this manuscript. These tools were employed as supportive
instruments for language refinement, structural organisation, and clarity
improvement of the technical exposition. All scientific ideas, modelling
choices, and interpretations presented in this work are the sole responsibility
of the author. The use of AI did not involve any generation of experimental
data or alteration of underlying physical assumptions, and all content was
reviewed and validated by the author prior to submission.
Declarations
Funding: This research received no external funding.
Conflicts of interest: The author declares no conflicts of interest.
Data availability: No new observational data were generated or analysed in this
study. All referenced datasets are publicly available from the sources cited.
Author contributions: Juliet Zhong: conceptualisation, formal analysis, writing.
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