A scalar-refractive theory of gravity

Density Field Dynamics

What if gravity is a refractive medium for light? In DFD one field, ψ, sets how fast light travels and how matter falls. It reproduces the classic tests of General Relativity and derives the fine-structure constant from topology.

Read the theory Start with the guide

n = e^ψlight slows near mass
a = ½c²∇ψmatter follows the same field
γ = β = 1Einstein’s weak-field tests

Gary Alcock · Independent researcher · ORCID 0009-0009-5682-6518 · garyalcock.com

The idea

One field does the work of curved spacetime.

DFD is a scalar-field reformulation of gravity and optics. A single field ψ lives on flat three-dimensional space and controls both how light moves and how matter accelerates.

01 · Optics

n = eψ

Light slows near mass

Empty space behaves like a medium whose refractive index rises near mass, so the local speed of light is c·e^−ψ. Light bends toward mass, the way starlight bends around the Sun.

02 · Dynamics

a = ½c²∇ψ

Matter follows the same field

A freely falling body accelerates along the gradient of the same field that bends light. One field replaces the geometry of curved spacetime.

03 · Tests

γ = β = 1

Einstein’s tests still pass

In the weak-field limit all ten post-Newtonian parameters match General Relativity, and gravitational waves travel at exactly the speed of light, as GW170817 requires.

Headline derivations

Numbers you can check yourself.

The framework’s strongest claims come with closed-form expressions and code. Run them, and compare them with experiment.

Fine-structure constant · closed form

α from the CP²×S³ microsector, in closed form

137.03599985α⁻¹ · 4.9 ppb from CODATA 2022

$$\alpha^{-1} = \frac{\pi^{3/2}}{24}\;\mathrm{Tr}(Y^2)\;k_{\max}\;\frac{k_{\max}+3}{k_{\max}+4}\;\left[1 + \frac{N_{\mathrm{sp}}}{g_F\;\mathrm{Tr}(Y^2)\;\bigl((k_{\max}+4)^2 - 1\bigr)}\right]$$

With $\mathrm{Tr}(Y^2)=10,\; k_{\max}=60,\; N_{\mathrm{sp}}=7,\; g_F=8$.

verify_alpha.py

import math
k, TrY2, N_sp, gF = 60, 10, 7, 8
d = k + 4  # = 64
raw = (math.pi**1.5 / 24) * TrY2 * k * (k+3)/(k+4)
boost = 1 + N_sp / (gF * TrY2) / (d**2 - 1)
alpha_inv = raw * boost  # = 137.0359998541

The integers alone give 137.03307 (21 ppm); the bracket brings the closed form to within 4.9 parts per billion of the measured value. The book calls it a closed form, not a derivation: the weight w = 7/80 is stated, and the step that identifies the hypercharge-trace coefficient with 1/e² is not yet derived.

Paper (v2.1) Software (v1.1)

Cosmology · two clocks

Both Hubble rates read as right

$$H_0^{\rm loc} = 72.09, \qquad H_0^{\rm early} = H_0^{\rm loc}/\lambda \simeq 67.79$$

One stated postulate: matter and the expanding universe keep clocks offset by one constant factor λ. The G derivation gives 72.09 km/s/Mpc on bound-matter clocks with no parameter (seven Cepheid-free local measurements give 71.87 ± 0.96), and a same-era rule predicts 67.79 for the early universe. Its costs are printed.

Read v5.0

Dark sector · CMB

The CMB third peak from a derived field

$$H_3/H_2 = 0.977, \qquad H_3/H_1 = 0.444$$

χ, the Chern–Simons transgression mode of the microsector, is a cold, collisionless field of mass 32.005 eV with Ω_χh² = 0.1193 (−0.6σ), conditional on the flux-period identification. On the measured clock it reproduces the third-peak height within 0.6σ and the peak ratio 2.20 against Planck’s 2.21, with no fitted dark-matter density.

Read v5.0

Current release · v5.0 · October 2026

Density Field Dynamics: A Complete Unified Theory

A two-volume release: the main volume with axioms, theorems and proofs, derived predictions and falsifiers, the Extended Derivations companion, and the complete LaTeX source. Every input is listed in one place, and every claim carries a tier label and a falsifier. Predictions are frozen and dated.

Main volume Extended derivations LaTeX source Zenodo

What’s inside v5.0

Gravity. Light obeys Maxwell’s equations in the field. Gravity raises the vacuum’s permittivity and permeability together, so the vacuum stays impedance-matched while light slows and bends. Light and gravitational waves share one metric (c_T = c_γ exactly); γ = β = 1 exactly, with a worst-case preferred-frame parameter ≲ 4×10⁻⁸ in the solar system. Newton’s law is an exact zero-parameter identity of the quantized ψ sector, with a laboratory discriminator, and in the rest-mass sector DFD’s gravity is general relativity’s written in absolute time: stars obey TOV, black holes have Schwarzschild’s and Kerr’s horizons, and two-body dynamics is GR’s through second post-Newtonian order.

Galaxies. μ(x) = x/(1+x) is a theorem and a₀ = 2√α cH₀ is derived (1.1966×10⁻¹⁰ m/s²); across the full 175-galaxy SPARC sample n_opt = 1.15 ± 0.12, with standard MOND’s n = 2 outside its 95% interval. The a₀(z) rise is published in MNRAS and stated as contested.

Dark sector and CMB. The early-clock CMB fit uses four continuous calibrations against ΛCDM’s six (Δχ² = +3.2 for three fewer effective parameters). The derived χ field reproduces the third peak, and clusters and the Bullet Cluster need it: the shortfall of the μ-law alone is χ at 0.84 ± 0.12 of the cosmic mix (an estimate).

Hubble tension. One stated two-clock postulate: 72.09 km/s/Mpc on bound-matter clocks from the G derivation, the early clock at H₀/λ, and a same-era rule predicting 67.79. The postulate’s form is derived; its size is the one measured input.

Particle physics. α⁻¹ = 137.03599985 in closed form (4.9 ppb); sin²θ_W = 3/13; v = 246.09 GeV (exponent derived, prefactor fitted); nine charged-fermion mass exponents derived (1.42% mean error, seven prefactors data-selected); Cabibbo λ = 31α; TM1 solar mixing sin²θ₁₂ = 0.3184; strong CP θ̄ = 0 at tree level with loop corrections bounded, no axion.

Clocks. Clocks side by side stay in step in the core theory, and the cavity–atom cancellation is supported by four data streams, including JILA’s 205-day silicon-cavity/Sr record. The sharpest clock prediction is a perihelion-locked annual modulation of the thorium-229 nuclear clock, about 350 Hz in half-amplitude; DFD’s family model also predicts the H-maser/Sr coefficient equal to Cs/Sr’s.

Decided and retired since v4.0. The supernova-lensing sign, the ISW amplitude and the Oort-cloud energy budget are decided and printed as such; the electromagnetic threshold extension, the solar-corona factor Γ = 4 and κ = α/4 are retired. The confrontation matrix lists 78 claims: 45 validated, 8 pending, 23 open and 2 contested.

433 pp
Main volume: axioms, theorems, predictions, falsifiers
77 pp
Extended derivations and frontier predictions
78
Claims, each tier-labelled with a falsifier
350 Hz
Predicted annual thorium-229 nuclear-clock modulation

Papers and preprints

The research record.

Every Density Field Dynamics paper, newest first. All of them are preprints.

22 papers

Oct 2026

Density Field Dynamics: A Complete Unified Theory (v5.0)

Unified theoryGravityParticle physicsCosmology & galaxies

The completed two-volume release: a 433-page main volume (axioms, theorems with proofs, derived predictions, falsifiers, a table of principal corrections and a list of open review items) and a 77-page Extended Derivations companion, with the complete LaTeX source. New in v5.0: the gravity completion (Newton’s law as an exact zero-parameter identity of the quantized ψ sector), the two-clock reading of the Hubble tension (72.09 on bound-matter clocks, 67.79 predicted for the early clock), the CMB third peak from the derived χ field (m_χ = 32.005 eV, Ω_χh² = 0.1193), the channel-resolved clock sector with a perihelion-locked thorium-229 prediction (about 350 Hz), the published MNRAS a₀(z) result, and an input census listing every input of the graded predictions.

PDF (Main)PDF (Extended Derivations)LaTeX source (zip)Zenodo
Apr 2026

General Relativity as the Padé Approximant of Density Field Dynamics

Gravity

An exact mathematical identity: GR’s isotropic-coordinate Schwarzschild lapse-squared L_GR(u) = [(1+u/2)/(1−u/2)]² equals [P_1,1(exp(u))]², while DFD’s exterior solution gives L_DFD(u) = exp(2u). GR is the m=1 slot in a Padé hierarchy; DFD is the entire-function limit. The Schwarzschild horizon at r=2GM/c² is the Padé pole of the m=1 truncation, while the exponential itself has no finite pole. The two lapses agree through O(u²) by construction (consistent with all gravitational-redshift, clock, and PPN-β observations to date) and first differ at O(u³). In v5.0, DFD’s strong-field gravity in the rest-mass sector is general relativity’s written in absolute time, with Schwarzschild’s and Kerr’s horizons (Kerr beyond first order in the spin argued), and the paper’s larger-shadow prediction is retired.

PDF
Apr 2026

Epoch Evolution of the MOND Crossover Scale: a_⋆(z) = 2√α·cH(z)

Cosmology & galaxies

Within DFD the galactic transition acceleration tracks cosmic expansion epoch-by-epoch: a_⋆(z) = 2√α·cH(z), not a frozen present-day value. Derived from two topological invariants (k_a=3/(8α) from CP²×S³ gauge emergence, q_S³=3/2 from the Chern–Simons partition function on S³) and a conditional uniqueness proposition for the cosmic IR scale, under the same epoch-consistency rule that promotes G·ℏ·H²/c⁵=α⁵⁷ to an all-epoch statement. Prediction: the MOND transition scale should appear enhanced by H(1)/H₀≈1.79 at z∼1 relative to the local-universe value — directly comparable to JWST rotation-curve measurements after standard kinematic and inclination reductions. Observation of a frozen a_⋆ at high redshift falsifies the proposition. In v5.0, a₀(z) = 2√α·cH(z) is published in MNRAS and stated as contested, since massive discs at z ≈ 2 with molecular gas counted do not show the rise.

PDF
Apr 2026

Tree-Level No-Drive Theorem for the Minimal Optical-Metric EM Sector: λ_bare = 1

ExperimentsFoundations

Proves λ_bare=1 in the minimal tree-level optical-metric EM sector of DFD. The linear-in-ψ EM source produced by the gauge-invariant action is proportional to the energy density (E²/c²+B²)/(2μ₀), not the stress invariant (E²/c²−B²)/(2μ₀). For ideal standing-wave cavity modes with energy equipartition, the energy-density source carries no 2ω component after volume integration, so EM fields cannot pump ψ through this channel. Reinterprets Appendix R’s |λ−1|<3×10⁻⁵ accidental bound as a constraint on beyond-minimal channels (finite-Q mimic, geometry restoration for asymmetric/TE+TM superposition, dim-5 operators ξψF_μνF^μν), not on the minimal-sector baseline. In v5.0, the electromagnetic threshold extension and κ = α/4 are retired, so neither is listed as a channel here.

PDF
Apr 2026

Mach’s Principle in Density Field Dynamics: An Interpretive and Phenomenological Consolidation

Cosmology & galaxiesFoundations

Situates DFD against the Bondi–Samuel Mach taxonomy and consolidates its Machian phenomenology. The structural identity a_⋆=2√α·cH₀ ties the galactic transition scale to cosmic expansion through S³ topology — the long-noted a₀∼cH₀ coincidence is no longer a coincidence. The epoch-extended form a_⋆(z)=2√α·cH(z) predicts a drift in the radial-acceleration-relation normalisation that follows H(z)/H₀, ≈1.79× at z ∼ 1, falsifiable by JWST and DESI. In v5.0, the ψ-screen cosmology is retired, and a₀(z) is published in MNRAS and stated as contested. Against the ten Mach criteria of Bondi–Samuel: DFD satisfies Mach 3, Mach 10, and effectively Mach 8; partially satisfies Mach 1, 2, 6; fails Mach 4, 5, 7, 9. The ψ rest frame is dynamically determined by cosmic matter (operational preferred frame), while the flat R³ kinematic substrate remains absolute.

PDF
Apr 2026

Constitutive Derivation of Tensor Gravitational Radiation from CP²×S³ Spectral Geometry in Density Field Dynamics

Gravity

Closes the gravitational-wave seam in DFD. The scalar field ψ and the transverse-traceless tensor h_ij^TT are derived as irreducible components of a single zero-mode parent tensor on CP²×S³, eliminating the need to postulate the TT sector independently. Lichnerowicz rigidity (CP² gap = 8/R₁², S³ gap = 12/R₂², b₁=0) guarantees no unwanted scalar or vector graviton modes propagate. The Einstein product condition τ*=1/√3 is derived as the unique minimum of the internal constraint function Φ(τ), fixing the squashing modulus at Planck mass. Constitutive interpretation via generalized Tamm–Plebanski relations identifies K₀=c⁴/(8πG) as compression stiffness and K₀/4 as shear stiffness, consistent with the vacuum loading framework. Result: c_T=c exactly, satisfying the GW170817 constraint, with both sectors emerging from a single topological origin.

PDF Zenodo
Mar 2026

Uniqueness of the Internal Manifold: Deriving CP²×S³ from Vacuum Axioms in Density Field Dynamics

Particle physicsFoundations

Proves that CP²×S³ is the unique internal manifold for DFD’s spectral completion, under six physically motivated axioms on the ψ-vacuum encoding chirality (empirical), multiplicative vacuum composition (from postulate P1), ground-state stability, and minimality. The product structure K=K_C×K_G is not assumed but forced by the logical incompatibility of the chirality requirement (w₂≠0) with Lie-group parallelizability (w₂=0) on a single connected manifold. The Matsushima–Lichnerowicz obstruction kills CP²#CP² (the only non-trivial competitor), and the Cartan classification fixes S³≅SU(2) as the unique minimal Lie group factor. Dimensional arithmetic (4+3=7) leaves no room for additional factors. The paper then traces the gauge group SU(3)×SU(2)×U(1), three generations, and the value of α⁻¹ to this manifold. In v5.0, three generations is a stated input and α is a closed form whose identification step is not derived.

PDF Zenodo
Dec 2025

Ab Initio Derivation of the Fine-Structure Constant from Density Field Dynamics (v2.1)

Particle physics

A closed form for α from Chern–Simons quantization on CP²×S³. The closed form reaches 137.03599985, 4.9 parts per billion from the CODATA 2022 value. In v5.0, it is called a closed form rather than a derivation: its bracket weight is stated and its identification step is not derived (the lattice runs check the alpha-free inputs, not α itself). Companion software package provided.

Paper (v2.1)Software (v1.1)
Mar 2026

Ab Initio Derivation of the Charged Fermion Mass Spectrum from Density Field Dynamics

Particle physics

Nine charged fermion masses from topology, with a 1.42% mean error. Builds all nine charged fermion masses (e, μ, τ, u, d, s, c, b, t) from CP²×S³ topology, using Spin^c bundle degrees for the power-law exponents and A₅ class geometry for the amplitude factors. In v5.0, the nine exponents are derived, the leading-order mean error is 1.42%, and seven prefactors are data-selected and labelled as such.

PDF
Mar 2026

Alpha Rosetta Stone: The DFD Prediction Web

Particle physics

A dependency graph tracing particle masses, cosmological observables, and galactic dynamics back to α, the Planck mass, and CP²×S³ topology. In v5.0, every input of the graded predictions is listed in one place (App. FK).

PDF
Mar 2026

The Physical Origin of the Refractive Field in Density Field Dynamics: Gravity as Electromagnetic Vacuum Loading

FoundationsGravity

Why does mass create a refractive field? Because mass is energy, and energy loads the electromagnetic vacuum. The exponential n = e^ψ is proved unique via Cauchy's functional equation, under the stated premise that successive loadings compose multiplicatively. Newton's constant G = c⁴/(8πK₀) is identified as inverse vacuum force scale, with K₀ ≈ 4.82×10⁴² N. The nonlinear field equation is reinterpreted as the constitutive response of a vacuum medium exhibiting reduced gravitational permittivity at low gradients, the mechanism behind flat galaxy rotation curves. The paper also proposed a constitutive split κ = α/4 with TE/TM cavity splitting. In v5.0, κ = α/4 is retired, since no derivation survives and the Gordon optical metric gives κ = 0 at tree level; the vacuum stiffness K₀ = c⁴/(8πG) stays.

PDF
Mar 2026

Pairing-Symmetry Selection Rules for the Cooper-Pair Mass Anomaly from A₅ Microsector Representation Theory

ExperimentsParticle physics

Addresses the 36-year-old Tate et al. Cooper-pair mass anomaly (δ=92±21 ppm in niobium). Working within the DFD A₅ microsector, establishes two pairing-symmetry selection rules: (a) the quintet exchange channel in S²(V*) couples maximally to s-wave condensates but vanishes for d-wave (angular cancellation of sign-changing gap), and (b) spin-triplet pairs live in Λ²(V*)=3, orthogonal to the quintet by representation theory alone. Numerical conjecture: δ=√3 α²=92.23 ppm (0.01σ match to Tate). Unlike the BCS-exchange correction of Lipavský (2016), this framework predicts universality for conventional s-wave superconductors—a material-independent distinction testable with existing SQUID magnetometry.

PDF Zenodo
Mar 2026

Composition-Dependent Bounds on Scalar-Field Coupling to Nuclear Decay Rates

Experiments

Applies the Flambaum nuclear sensitivity formalism to compute isotope-specific sensitivity coefficients κ_q for eight nuclides central to the decade-long Jenkins–Fischbach debate on solar-modulated decay rates. Sensitivity is driven by Q-value (κ_q∝n/Q), placing ³²Si (κ_q=308) and ¹⁸⁷Re (κ_q≈19,000) at the top of the hierarchy. Existing null results constrain different regions of the (k_q^eff, κ_q) parameter space but do not exclude composition-dependent signals in untested low-Q isotopes. The original positive datasets (³²Si at BNL, ²²⁶Ra at PTB) are now attributed to environmental systematics. Identifies ¹⁸⁷Re and the ²²⁹Th nuclear clock isomer (K∼10⁴) as the most sensitive future targets, and proposes a multi-isotope ratio test that eliminates systematics by design.

PDF Zenodo
Dec 2025

Two Numerical Relations Linking the Fine-Structure Constant to Gravitational Phenomenology

Cosmology & galaxiesExperiments

Two relations connecting α to gravitational observables: the MOND acceleration scale a₀=2√α·cH₀ and the gravitational clock coupling k_α=α²/(2π)≈8.5×10⁻⁶. In v5.0, a₀=2√α·cH₀ stays a derived result, while the unscreened clock coupling at the 10⁻⁵ level is excluded at Earth by the same-ion Yb⁺ E3/E2 null. Co-located clocks stay in step in the core theory, and the extended channel’s sharpest number is the thorium-229 annual modulation, about 350 Hz.

PDF Zenodo
Dec 2025

k_α and the a² Invariant: A Unified Acceleration Scale from Galaxies to Atomic Clocks

Experiments

Derives the α-relations from scalar self-coupling structure. Extends predictions to strong-field regimes and proposes clock comparison signatures at the 10⁻⁵ level across multiple atomic species. In v5.0, that unscreened 10⁻⁵ clock coupling is excluded at Earth by the same-ion Yb⁺ E3/E2 null; co-located clocks stay in step in the core theory, the extended channel’s sharpest number is the thorium-229 annual modulation (about 350 Hz), and a₀=2√α·cH₀ stays derived.

PDF
Oct 2025

Solar-Locked Differential in Ion–Neutral Optical Frequency Ratios

Experiments

Analysis of published ROCIT frequency ratio data (Yb⁺/Sr) revealing perihelion-locked modulation: amplitude A=(−1.045±0.078)×10⁻¹⁷ with period matching Earth's orbital eccentricity. The paper reads it as a sector-differential ψ coupling. In v5.0, the signal is called suggestive rather than definitive: neither the minimal action nor the screened extended channel predicts it, and independent replication is needed.

PDF Zenodo
Sep 2025

Parametrized Post-Newtonian Analysis of Density Field Dynamics

Gravity

Complete PPN expansion in the weak-field, slow-motion limit. All ten PPN parameters match General Relativity at 1PN order: γ=β=1, ξ=α₁=α₂=α₃=ζ₁=ζ₂=ζ₃=ζ₄=0. DFD is observationally indistinguishable from GR for all current solar system tests.

PDF
Sep 2025

Strong Fields and Gravitational Waves in Density Field Dynamics

Gravity

Extension to the strong-field regime: photon sphere locations, black hole shadows, and gravitational wave propagation. Tensor wave speed c_T=c exactly, satisfying the GW170817 constraint. All parameterized post-Einsteinian (ppE) bounds satisfied. In v5.0, the paper’s shadow predictions are retired: in the rest-mass sector DFD has general relativity’s horizons and shadows, and c_T=c stays.

PDF Zenodo
Sep 2025

Well-Posedness and Boundary Value Problems for the ψ Equation

Foundations

Rigorous PDE analysis of the DFD field equation. Establishes existence, uniqueness, and regularity of weak solutions in appropriate Sobolev spaces. Proves energy conservation and derives asymptotic boundary conditions.

PDF
Sep 2025

Accidental and Intentional Constraints on EM→ψ Back-Reaction

Experiments

Laboratory bounds on electromagnetic coupling to ψ from cavity stability measurements. Constrains back-reaction parameter |λ−1|≲3×10⁻⁵, demonstrating consistency with precision metrology and identifying future experimental sensitivity targets.

PDF Zenodo
Sep 2025

Matter-Wave Interferometry Tests of Density Field Dynamics

Experiments

Proposed signatures in atom interferometers: a T³ phase scaling (versus T² for Newtonian gravity) in long-baseline configurations, with designs for the Stanford 10m tower and proposed satellite experiments. In v5.0, the T³ signature is withdrawn as a null: DFD’s matter-wave phase equals general relativity’s through first post-Newtonian order, and the static metric is GR’s at second order as well.

PDF Zenodo
Aug 2025

Density Field Dynamics and the c-Field

FoundationsGravity

Foundational paper establishing the core framework: field equations for ψ, energy-momentum conservation, recovery of Newtonian limit, and classical test predictions. Introduces the optical-refractive interpretation of gravitational phenomenology. Note: Superseded by Unified v3.2 for clock predictions; foundational framework remains current.

PDF Zenodo

Related work by the author

This paper is Gary Alcock’s astrophysics research, published in MNRAS. It is not a Density Field Dynamics paper and does not assume DFD. It tests, directly against galaxy data, how the acceleration scale of galaxies changes with cosmic time. The DFD papers above are preprints.

Peer-reviewed Open access · CC BY 4.0 Published 7 Sept 2026

Monthly Notices of the Royal Astronomical Society

G. T. Alcock · Vol. 551, Issue 4 · stag1485 · doi:10.1093/mnras/stag1485

Is the acceleration scale of the radial acceleration relation tracking the cosmic expansion rate?

Below a tiny acceleration called a₀, stars in galaxies stop following Newton’s law. For decades a₀ has sat suspiciously close to the speed of light times the Hubble rate. If that link is physical, a₀ should have been larger in the past, when the universe expanded faster.

This paper tests the idea with the MUSE-DARK survey’s binned measurements out to redshift 1.44. Using the published bin errors, a constant a₀ is excluded at 5.3σ and matter-density scaling at 4.8σ, while tracking the expansion rate, a₀ ∝ H(z), is consistent within 2.1σ.

5.3σ

Constant a₀ excluded, using the published bin errors

2.1σ

Consistent with a₀ tracking the expansion rate H(z)

0.78 ± 0.15

Growth exponent γ in a₀ ∝ (1+z)^γ

Read the paper PDF

The acceleration scale a₀ rises with redshift

MUSE-DARK bins compared with three scalings. Model amplitudes are fitted to the four bins.

MUSE-DARK bins
SPARC, today
a₀ ∝ H(z)
Constant a₀
a₀ ∝ (1+z)^1.5

Data table

Acceleration scale a0 by redshift, in units of 10^-10 m s^-2
Sample	z	a₀	Error
SPARC (local)	0	1.20	±0.02 stat, ±0.24 sys
MUSE-DARK bin 1	0.503	1.990	−0.085 / +0.086
MUSE-DARK bin 2	0.825	2.200	±0.105
MUSE-DARK bin 3	1.047	2.571	−0.114 / +0.110
MUSE-DARK bin 4	1.276	2.710	−0.134 / +0.138

Units of 10⁻¹⁰ m s⁻². Bins from Ciocan et al. (2026) as analysed in the paper; SPARC value from McGaugh, Lelli & Schombert (2016).

Open data and code

Everything needed to check the work.

Zenodo · DOI 10.5281/zenodo.19173548

Fine-structure constant: code and data (v1.1)

Lattice Monte Carlo code, the spectral pipeline, and reproducibility scripts for the α derivation.

Open record

v5.0 · zip

LaTeX source

The complete source of both volumes, with figures and bibliography; both PDFs rebuild from it.

Download

Zenodo · DOI 10.5281/zenodo.17272596

ROCIT frequency-ratio analysis

Full methods, figures, and scripts for the ion–neutral optical frequency-ratio analysis.

Open record

Explore

Go deeper, your way.

Interactive guide

Gravity is Light

A plain-English, interactive journey through the theory, from the problem with dark matter to the numbers DFD derives.

Start the guide

Reference

Topics index

Every named result, formula, and theorem, with a link to the paper that derives it.

History

Historical lineage

From Fermat and Einstein’s 1911–12 variable-c program to scalar–tensor theories and DFD.

Context

Framework comparison

How DFD compares with General Relativity, MOND, and scalar–tensor alternatives.

Machine-readable

Plain-text corpus

Markdown and plain-text versions of every paper, with an llms.txt index and an RSS feed of releases.

Run an experiment?

DFD is an independent research program open to experimental collaboration: ²²⁹Th nuclear clocks, cross-species atomic comparisons, cavity–atom residuals, and galaxy kinematics at high redshift. Send your setup and get a concrete prediction back.

Or email gary@gtacompanies.com

Density Field Dynamics

Light slows near mass

Matter follows the same field

Einstein’s tests still pass

α from the CP²×S³ microsector, in closed form

Both Hubble rates read as right

The CMB third peak from a derived field

Density Field Dynamics: A Complete Unified Theory

Density Field Dynamics: A Complete Unified Theory (v5.0)

General Relativity as the Padé Approximant of Density Field Dynamics

Epoch Evolution of the MOND Crossover Scale: a⋆(z) = 2√α·cH(z)

Tree-Level No-Drive Theorem for the Minimal Optical-Metric EM Sector: λbare = 1

Mach’s Principle in Density Field Dynamics: An Interpretive and Phenomenological Consolidation

Constitutive Derivation of Tensor Gravitational Radiation from CP²×S³ Spectral Geometry in Density Field Dynamics

Uniqueness of the Internal Manifold: Deriving CP²×S³ from Vacuum Axioms in Density Field Dynamics

Ab Initio Derivation of the Fine-Structure Constant from Density Field Dynamics (v2.1)

Ab Initio Derivation of the Charged Fermion Mass Spectrum from Density Field Dynamics

Alpha Rosetta Stone: The DFD Prediction Web

The Physical Origin of the Refractive Field in Density Field Dynamics: Gravity as Electromagnetic Vacuum Loading

Pairing-Symmetry Selection Rules for the Cooper-Pair Mass Anomaly from A5 Microsector Representation Theory

Composition-Dependent Bounds on Scalar-Field Coupling to Nuclear Decay Rates

Two Numerical Relations Linking the Fine-Structure Constant to Gravitational Phenomenology

kα and the a² Invariant: A Unified Acceleration Scale from Galaxies to Atomic Clocks

Solar-Locked Differential in Ion–Neutral Optical Frequency Ratios

Parametrized Post-Newtonian Analysis of Density Field Dynamics

Strong Fields and Gravitational Waves in Density Field Dynamics

Well-Posedness and Boundary Value Problems for the ψ Equation

Accidental and Intentional Constraints on EM→ψ Back-Reaction

Matter-Wave Interferometry Tests of Density Field Dynamics

Density Field Dynamics and the c-Field

Fine-structure constant: code and data (v1.1)

LaTeX source

ROCIT frequency-ratio analysis

Gravity is Light

Topics index

Historical lineage

Framework comparison

Plain-text corpus

Run an experiment?

Epoch Evolution of the MOND Crossover Scale: a_⋆(z) = 2√α·cH(z)

Tree-Level No-Drive Theorem for the Minimal Optical-Metric EM Sector: λ_bare = 1

Pairing-Symmetry Selection Rules for the Cooper-Pair Mass Anomaly from A₅ Microsector Representation Theory

k_α and the a² Invariant: A Unified Acceleration Scale from Galaxies to Atomic Clocks