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. On
this account, 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. The model yields
the full light deflection, and three conditions for empirical
distinguishability 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 [1]. This law
describes what gravity does with extraordinary precision but says nothing about
why it does it. Newton himself acknowledged this explicitly in the General
Scholium added to the second edition (1713): “I have not yet been able to
discover the cause of those properties of gravity from phenomena, and I frame
no hypotheses” [2].
Two centuries later, Einstein's general theory of relativity
(1915) reframed the question [3]. 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 [4].
The geometric account contains a closure that requires exact
statement. Wheeler’s summary, that spacetime tells matter how to move and
matter tells spacetime how to curve, describes a coupled system in which each
side is specified through the other. Mass enters the field equations through
T_uv as the source of curvature, and the same mass enters the geodesic equation
as a body whose motion that curvature governs. The identity of these two roles
is the equivalence principle, which general relativity adopts as its founding
postulate rather than derives. The field equations are not a tautology: given
T_uv and boundary conditions, they yield the perihelion shift, light deflection
and gravitational waves, none of which is contained in the definitions. What
the closure leaves unaccounted for is the capacity itself. General relativity
states nowhere what property of matter makes it a source of curvature; T_uv is
supplied from outside the theory and inserted on the right-hand side of the
equations. A body at rest on a table makes the point concrete. Its rest mass,
its weight and the gravitational field it produces are three distinct
quantities: the weight is the force the body experiences in the Earth’s field,
and is therefore a consequence of gravitation, not its source. The theory
computes the body’s own field from its rest mass and energy content, and says
nothing about why rest mass should produce a field at all. This is the same
vacancy that Newton declared. Einstein acknowledged it in his own terms,
comparing the left side of his equations to fine marble and the right side, the
matter tensor, to low-grade wood, a provisional phenomenological placeholder
awaiting a theory of matter [5]. That theory of matter was never supplied, and
the geometric description has since been treated as the explanation of gravity
itself. The radiation-field model addresses precisely the vacancy that
Einstein’s wood stands for.
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
[6,7]. This programme rests on an unstated assumption: that because the
electromagnetic field admits quantisation, 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 [8].
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 [9]. Verlinde (2011) proposed that gravity arises as
an emergent force associated with information on holographic screens [10]. Padmanabhan
has independently developed a systematic case that the Einstein equations have
the character of emergent thermodynamic relations rather than fundamental field
equations [11]. 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, formulated on the ground that the maximal
information capacity of a black hole scales with its horizon area rather than
its volume [12,13,14], states that the information content of a spatial region
is bounded 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 [15,16].
The SxD model, formalised in Ripple-Instantiation
Cosmogenesis [15], 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. On this account, 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 ontology 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 on this account. 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 [17], 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 [18]. 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 [19,20].
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 [21]. 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 dimensional
cascade, that the radiation field is the fundamental substrate from which mass
condenses. The full relativistic energy-momentum relation makes the continuity
between the two cases explicit:
E² = p²c² + m²c⁴
(1)
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.
In the SxD dimensional cascade, 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, in the field of
a nucleus that absorbs the recoil momentum, 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.
On this account, 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 [15], denotes
six stratified layers of cosmological structure defined not by spatial axes but
by their function within the projection cascade. S⁶D is the primordial nucleus,
which has a centre and no boundary and is the source of all radiation. 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.
The projection is atemporal:
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 ontology 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, defined as the magnitude
of the ambient flux deficit created by its condensation, is proportional to M:
L_R(M) = alpha x M
(2)
where L_R is the effective intensity of the flux deficit,
the radiation shadow, produced by the body, 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 linear regime is defined quantitatively, in terms of
the potential U_R and constant G_eff of Eqs. (8) and (6), by |U_R| / c² = G_eff
M / (c² r) ≪ 1: this ratio is about 2 × 10^−6
at the solar surface, about 0.2 at the surface of a neutron star, and 0.5 at a
black-hole horizon, where the weak-field linear scaling no longer holds. 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
(3)
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. On the present account, 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 flux deficit 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 flux deficit at distance r from the body 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)
(4)
This is not a physical assumption but a geometric identity:
any isotropic quantity spreading from a point 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 is
the net momentum flux imbalance between the unshadowed ambient flux arriving
from the far side of m and the depleted flux arriving from the direction of
M—radiation flux divided by c yields momentum flux, the classical mechanism of
radiation pressure [22]—and this imbalance is directed toward M:
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 (5)
Defining the effective gravitational constant as:
G_eff = alpha x beta
/ (4 pi c) (6)
we obtain:
F_R = G_eff x Mm / r² (7)
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. Identifying
G_eff with the measured Newtonian constant G fixes the product of the two
coupling constants, alpha x beta = 4 pi c G ≈ 0.25 W m² kg⁻², while leaving
their separate values to be determined by the projection structure.
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 (8)
Then the gravitational acceleration field is:
g_R(r) = -nabla U_R =
-G_eff x M / r² x r-hat (9)
and the force on a test body m is:
F_R = m x g_R =
-G_eff x Mm / r² x r-hat (10)
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. For an extended body of projected mass density ρ, the flux
deficits of its elements superpose linearly in the weak-field regime, and the
potential satisfies the Poisson equation
∇²U_R = 4 pi G_eff ρ
(11)
so in the weak-field regime the account applies to extended
bodies and planetary interiors, not only to point masses.
IV.4 The Mechanism of Attraction: Radiation Shadowing
A natural objection arises against the force law of Sections
IV.1-IV.3: 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. On this account, 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 on an
isolated body, because there is no ontological boundary between
"body" and "field"; the coupling cross-section sigma_R of
Postulate 2 is not a mechanical surface but the measure of how much of the
ambient field a condensation restructures, and it acts only on the flux
imbalance created by another condensation.
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: m remains enveloped by the ambient field from every direction, and
the shadow of M is not a region emptied of radiation but a partial depletion of
the flux arriving from the direction of M, 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 [23]. 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 objection is
removed by a definite condition on the ambient field. An isotropic radiation
field in general defines a rest frame, as the dipole of the cosmic microwave
background shows, and a body moving through such a field experiences drag. The
single exception is a field whose spectral intensity scales as the cube of the
frequency: this spectrum is Lorentz invariant, it is identical in every
inertial frame, and uniform motion through it produces no drag [24]. The
ambient field of the present model must therefore carry this spectrum, which
excludes its identification with the cosmic microwave background and fixes it
as a Lorentz-invariant background of the zero-point type. The heating objection
is answered by the interpretation adopted here: the shadow is a restructuring
of the field by its own condensation, in which flux is redistributed within the
field rather than absorbed by a foreign body, so no net energy is deposited.
These objections 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 [25] and the
MICROSCOPE space mission to parts in 10^15 [26]) 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 equal to its total energy content divided by
c² [18], and that energy content is the radiative condensation itself. 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 [4,27].
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 this analysis, 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]
(12)
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 on this account 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 (13)
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 [4].
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)
(14)
This is identical to the standard linearised result. The
metric perturbation produced by the radiation field is taken to act
isotropically on the spatial sector in the weak-field limit, h_ij = -2 U_R δ_ij
/ c², on the same ground as Postulates 1 and 2: the shadow deficit depletes the
spatial stress components of the field equally with its energy density, not the
energy density alone. With this definition the weak-field line element takes
the isotropic form of general relativity, and the model yields the full light
deflection 4G_eff M / (c² b) and the Shapiro time delay rather than the
half-value of a purely scalar theory; the derivation of this spatial structure
from the explicit governing laws of the radiation field belongs to the
programme stated in Section VII.2.
The weak-field line element then reads
ds² = −(1 + 2U_R /
c²) c² dt² + (1 − 2U_R / c²)(dx² + dy² + dz²) (15)
In the parametrised post-Newtonian description this spatial
coefficient fixes γ = 1. A light ray passing the mass M at impact parameter b
is deflected through the angle
δφ = (1 + γ) × 2G_eff
M / (c² b) = 4G_eff M / (c² b) (16)
and a signal passing the same mass acquires the Shapiro
delay
Δt = (1 + γ) × (G_eff
M / c³) × ln(4r₁r₂ / b²)
(17)
where r₁ and r₂ are the distances of emitter and receiver
from M. With G_eff = G, both expressions coincide with the general-relativistic
values, and the Cassini measurement γ − 1 = (2.1 ± 2.3) × 10^−5 [28] constrains
any departure of the radiation-field functional from this isotropic spatial
form to the same precision.
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 U_R is insufficient to describe
the full field configuration.
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]
(18)
In the weak-field limit, this functional reduces to h_00 =
-2 U_R / c² together with h_ij = -2 U_R δ_ij / c², recovering the Newtonian
regime and the line element of Eq. (15). 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 governing laws 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 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 [29]. 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 structure.
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 [30]
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 rapidly. These changes propagate outward
through the ambient radiation field at the speed of light, because the
radiation field's characteristic propagation speed is c, in agreement with the
joint gravitational-wave and gamma-ray observation of GW170817, which
constrains the fractional speed difference to −3 × 10^−15 < (v_gw − c)/c
< +7 × 10^−16 [31]. 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 on this account. 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 [32], and whether gravity
must be quantised at all remains an open question in the literature [33].
The radiation field itself may admit a quantum description
at S⁴D—the quantum-field conversion interface in the SxD cascade [15]. 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. On the radiation-field account, the gravitational "field" is
effective, and the fundamental degrees of freedom to be quantised are those of
the radiation field at S⁴D, not those of the effective metric. The ninety-year
absence of an empirically confirmed quantum gravity, on this reading, follows
from quantising the effective description instead of the radiation field that
underlies it.
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.
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 a non-vanishing correlation floor at super-horizon scales and a
cross-redshift coherence floor in galaxy distributions, both invariant under
LCDM parameter re-fitting, as predicted in [15].
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 governing laws 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 distribution and is
proposed as a programme for future work.
These conditions define the empirical boundary of the model:
where no deviation from standard gravity is observed, the radiation-field model
and general relativity agree in every prediction, and the radiation-field model
retains what general relativity lacks, a physical source for the curvature it
describes.
VII.2 Principal Limitations
The present formulation has four principal limitations that
must be acknowledged.
First, the non-linear governing laws 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 [15].
Third, the correspondence between the wave propagation of
the radiation field 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 [30].
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 radiation-field ontology opens four lines of
investigation.
The first direction concerns whether a macroscopic
correspondence can be established between the governing laws of the projected
radiation field 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 governing laws of the radiation field 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 process 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
governing laws of the radiation field; disagreement would either challenge the
model or point to new physics beyond general relativity.
The fourth direction, drawing on the analysis in [17],
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 the hypothesis stated in
that paper together with its three falsification conditions, then the
relationship between mass, binding energy, and the radiation field becomes a
question that the present ontology 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 distribution of the projected radiation
field.
The present theory nevertheless has a clearly defined
limitation. The nonlinear field 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 establishes the structural connection
between gravitational phenomenology and its radiative source; the explicit
non-linear field equations are the next stage of that connection.
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.
Declarations
Funding: This research received no external funding.
Conflicts of interest: The author declares no conflicts of interest.
Data availability: No new data were generated or analysed in this study.
Author contributions: Juliet Zhong: conceptualisation, methodology, formal
analysis, investigation, writing, review, editing.
Declaration of generative AI and AI-assisted technologies in the manuscript
preparation process:
During the preparation of this
work, the author used Claude (Anthropic), ChatGPT (OpenAI), and Gemini (Google)
for assistance with drafting text, formulating mathematical expressions,
searching and formatting references, and language editing. The author reviewed
and edited the output as needed and takes full responsibility for the content
of the published article.
References
[1] I. Newton, Philosophiae Naturalis Principia Mathematica
(Royal Society, London, 1687).
[2] I. Newton, The Mathematical Principles of Natural
Philosophy, trans. A. Motte, General Scholium (Benjamin Motte, London, 1729).
[3] A. Einstein, Die Feldgleichungen der Gravitation,
Sitzungsber. Preuss. Akad. Wiss. 1915, 844 (1915).
[4] C. W. Misner, K. S. Thorne, and J. A. Wheeler,
Gravitation (Freeman, San Francisco, 1973).
[5] A. Einstein, Physics and reality, J. Franklin Inst. 221,
349 (1936).
[6] L. Rosenfeld, Zur Quantelung der Wellenfelder, Ann.
Phys. 397, 113 (1930).
[7] M. P. Bronstein, Quantentheorie schwacher
Gravitationsfelder, Phys. Z. Sowjetunion 9, 140 (1936).
[8] L. Smolin, The Trouble with Physics: The Rise of String
Theory, the Fall of a Science, and What Comes Next (Houghton Mifflin, Boston,
2006).
[9] T. Jacobson, Thermodynamics of spacetime: The Einstein
equation of state, Phys. Rev. Lett. 75, 1260 (1995).
[10] E. P. Verlinde, On the origin of gravity and the laws
of Newton, J. High Energy Phys. 2011(4), 29 (2011).
[11] T. Padmanabhan, Gravity as an emergent phenomenon, Int.
J. Mod. Phys. D 17, 591 (2008).
[12] J. D. Bekenstein, Black holes and entropy, Phys. Rev. D
7, 2333 (1973).
[13] G. ’t Hooft, Dimensional reduction in quantum gravity,
in Salamfestschrift (World Scientific, Singapore, 1993), pp. 284–296.
[14] L. Susskind, The world as a hologram, J. Math. Phys.
36, 6377 (1995).
[15] J. Zhong, Ripple-Instantiation Cosmogenesis [Part I]:
The Six-Dimensional Spherical Cascade as an Alternative to Temporal Assembly,
SSRN (2026). https://doi.org/10.2139/ssrn.6753518.
[16] J. Zhong, Six-Dimensional Mirror Multi-Universe: An
Operator-Based Ontology, SSRN (2026). https://doi.org/10.2139/ssrn.6850199.
[17] J. Zhong, The Boundary Between Matter and Radiation: An
Unresolved Classificatory Inconsistency in Modern Physics, SSRN (2026).
https://doi.org/10.2139/ssrn.7186058.
[18] A. Einstein, Ist die Trägheit eines Körpers von seinem
Energieinhalt abhängig?, Ann. Phys. 18, 639 (1905).
[19] M. Planck, Zur Theorie des Gesetzes der
Energieverteilung im Normalspektrum, Verh. Dtsch. Phys. Ges. 2, 237 (1900).
[20] A. Einstein, Über einen die Erzeugung und Verwandlung
des Lichtes betreffenden heuristischen Gesichtspunkt, Ann. Phys. 17, 132
(1905).
[21] F. Wilczek, Mass without mass I: Most of matter, Phys.
Today 52(11), 11 (1999).
[22] J. H. Poynting, Radiation in the solar system: Its
effect on temperature and its pressure on small bodies, Phil. Trans. R. Soc. A
202, 525 (1904).
[23] M. R. Edwards (ed.), Pushing Gravity: New Perspectives
on Le Sage’s Theory of Gravitation (Apeiron, Montreal, 2002).
[24] T. H. Boyer, Random electrodynamics: The theory of
classical electrodynamics with classical electromagnetic zero-point radiation,
Phys. Rev. D 11, 790 (1975).
[25] S. Schlamminger, K.-Y. Choi, T. A. Wagner, J. H.
Gundlach, and E. G. Adelberger, Test of the equivalence principle using a
rotating torsion balance, Phys. Rev. Lett. 100, 041101 (2008).
[26] P. Touboul et al., MICROSCOPE mission: Final results of
the test of the equivalence principle, Phys. Rev. Lett. 129, 121102 (2022).
[27] A. Einstein, Die Grundlage der allgemeinen
Relativitätstheorie, Ann. Phys. 49, 769 (1916).
[28] B. Bertotti, L. Iess, and P. Tortora, A test of general
relativity using radio links with the Cassini spacecraft, Nature 425, 374
(2003).
[29] C. Barceló, S. Liberati, and M. Visser, Analogue
gravity, Living Rev. Relativity 8, 12 (2005).
[30] B. P. Abbott et al. (LIGO Scientific Collaboration and
Virgo Collaboration), Observation of gravitational waves from a binary black
hole merger, Phys. Rev. Lett. 116, 061102 (2016).
[31] B. P. Abbott et al. (LIGO Scientific Collaboration,
Virgo Collaboration, Fermi GBM, INTEGRAL), Gravitational waves and gamma-rays
from a binary neutron star merger: GW170817 and GRB 170817A, Astrophys. J.
Lett. 848, L13 (2017).
[32] T. Padmanabhan, Gravitation: Foundations and Frontiers
(Cambridge University Press, Cambridge, 2010), Ch. 16, pp. 670–688.
[33] S. Carlip, Is quantum gravity necessary? Class. Quantum
Grav. 25, 154010 (2008).
Comments
Post a Comment