A Higher-Order Electromagnetism Model of Gravity (Draft v0.1)
Author: Wm. Cook
Status: Concept note
Abstract
We hypothesize that what we call “gravity” is a higher-order, coarse-grained effect of electromagnetism (EM). Neutral matter—composed of charged constituents (protons, electrons)—acts as a conduit that polarizes the electromagnetic vacuum, producing spatial gradients in EM energy density that manifest as gravitational potential. In the weak-field, static limit this reduces to a Poisson-type equation where the source is EM energy density (and charge/current fluctuations) rather than an independent “mass density.” We recover Newton’s law g=GM/r^2 with a specific coupling and outline falsifiable predictions: (i) weight shifts proportional to stored EM energy, (ii) tiny “gravity-like” accelerations from large field gradients, (iii) correlations between strong astrophysical EM environments and lensing/clock-rate anomalies beyond baryonic expectations.
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1) Motivation & Postulates
P0. Mass—via its electrons and protons—pulls on a universal EM field and thereby attracts other matter. Gravity is the name we give this higher-order EM interaction.
P1 (Microscopic neutrality, quadratic residue). Though bulk matter is net neutral
\langle \rho_q \rangle \approx 0, quadratic quantities (e.g., \langle \rho_q^2\rangle, \langle \mathbf{J}^2\rangle, \langle \mathbf{E}^2\rangle, \langle \mathbf{B}^2\rangle) do not cancel under coarse-graining and can source a macroscopic potential.
P2 (Vacuum polarizability). The EM vacuum has an effective susceptibility \chi_{\rm vac}: neutral matter polarizes the vacuum, creating a spatial profile in EM energy density u_{\rm EM} that decays outward.
P3 (Equivalence). Test-body acceleration is composition-independent (equivalence principle). Any effective force law must depend only on the field configuration of space, not on the internal makeup of the test body.
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2) Minimal Mathematical Framework
Let F_{\mu\nu} be the EM field tensor. Define the standard EM energy density
u_{\rm EM}(\mathbf{x})=\frac{\varepsilon_0}{2}\, \mathbf{E}^2(\mathbf{x})+\frac{1}{2\mu_0}\,\mathbf{B}^2(\mathbf{x}).
We posit that the Newtonian gravitational potential \Phi(\mathbf{x}) in the static, weak-field limit obeys a Poisson-type equation with an EM-sourced density:
\nabla^2 \Phi(\mathbf{x}) \;=\; 4\pi\,\gamma \,\Bigg[\frac{u_{\rm EM}(\mathbf{x})}{c^2} \;+\; \alpha_1 \,\big\langle \rho_q^2(\mathbf{x})\big\rangle_L \;+\; \alpha_2 \,\big\langle \mathbf{J}^2(\mathbf{x})\big\rangle_L\Bigg]. \tag{1}
• \gamma is a coupling constant (to be related to G).
• \langle\cdot\rangle_L denotes coarse-graining over a mesoscopic scale L (large vs. atomic, small vs. astrophysical).
• The \alpha_i weight charge/current fluctuation terms that survive neutrality. (Setting \alpha_i=0 recovers a pure energy-density model.)
Remark. In standard GR, all energy gravitates with weight 1/c^2. Equation (1) intentionally privileges EM structure as the fundamental source, treating “mass” as emergent from EM at deeper scales.
Recovering Newton’s Law (spherical case)
Assume a compact, approximately spherical source where the right-hand side integrates to a finite “EM mass”
M_{\rm EM} \;\equiv\; \frac{1}{c^2}\int u_{\rm EM}\,d^3x \;+\; \alpha_1 \int \langle\rho_q^2\rangle_L d^3x \;+\; \alpha_2 \int \langle \mathbf{J}^2\rangle_L d^3x .
Integrating (1) over all space and using Gauss’s theorem with \Phi\sim -GM/r at infinity gives
4\pi G M \;=\; 4\pi \gamma\, M_{\rm EM}
\;\;\Rightarrow\;\;
M \;=\; \frac{\gamma}{G}\, M_{\rm EM}. \tag{2}
Choosing \gamma=G yields M=M_{\rm EM}: gravitational mass equals EM-derived mass (your conduit thesis).
Thus outside the source, \Phi(r)=-GM/r and g(r)=GM/r^2 follow if the EM-sourced mass scales linearly with the bulk you call “matter.”
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3) Field-Gradient View (your “conduit” intuition)
An equivalent, more electrician-friendly picture: suppose neutral matter produces a radial profile in EM energy density relative to background, \Delta u_{\rm EM}(r). Define the potential as
\Phi(\mathbf{x}) \;=\; \beta \,\Delta u_{\rm EM}(\mathbf{x}), \quad
\Rightarrow\quad
\mathbf{g}=-\nabla \Phi \;=\; -\beta \,\nabla \Delta u_{\rm EM}. \tag{3}
For a spherical source, taking \Delta u_{\rm EM}(r)\propto 1/r gives g\propto 1/r^2. Matching to Newton fixes \beta. This realizes your idea that matter acts like a coil/transformer shaping the surrounding “cosmic current,” and objects fall down the energy-density gradient.
Note on units & equivalence. To keep acceleration independent of the test body, \beta must be a universal constant (built from G, c, and vacuum parameters), not material properties.
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4) Relativistic Packaging (for physicist readers)
Let T^{\mu\nu}{\rm EM}=\frac{1}{\mu_0}\!\left(F^{\mu\alpha}F^\nu{}\alpha-\frac{1}{4}\eta^{\mu\nu}F^{\alpha\beta}F_{\alpha\beta}\right) be the EM stress-energy.
Our claim is that the entire effective stress-energy sourcing curvature is EM-constructed after coarse-graining:
G_{\mu\nu} \;=\; \kappa\, \Big\langle T^{\rm EM}_{\mu\nu}\Big\rangle_L \;+\; \text{(quadratic fluctuation terms in }\rho_q,\;J\text{)}, \tag{4}
with \kappa=8\pi G/c^4. In standard GR this is one contributor; here we conjecture all matter stress-energy reduces to EM structure at some deeper level (historically related to “electromagnetic mass” programs, but extended with vacuum polarization and coarse-grained fluctuations).
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5) Worked toy estimates (lab-testable)
5.1 Stored EM energy should increase weight
Any stored EM energy U should add gravitational mass \Delta m \approx U/c^2 (here it’s not just allowed by GR; it’s the mechanism).
• Example: A super-capacitor storing U=10^6\ \mathrm{J} (0.28 kWh) should gain
\Delta m = U/c^2 \approx 10^6 / (9\times10^{16}) \approx 1.1\times10^{-11}\ \mathrm{kg}
(weight change \sim 10^{-10}\ \mathrm{N}).
This is tiny but, in principle, measurable with ultra-sensitive balances. A null result at this level would strongly constrain \gamma, \alpha_i.
5.2 Field-gradient “push”
From (3), intense field gradients should produce tiny accelerations.
Magnetic energy density u_B=\tfrac{B^2}{2\mu_0}. A large-bore magnet with B\sim 30~\mathrm{T} and \nabla B\sim 10~\mathrm{T/m} has \nabla u_B \approx \frac{B}{\mu_0}\nabla B \sim \frac{30}{1.26\times10^{-6}}\times10 \approx 2.4\times10^8\ \mathrm{J\,m^{-4}}.
If g = -\beta \nabla u_{\rm EM} and \beta is fixed by matching planetary gravity, the resulting lab g would be minuscule, but this sets an upper bound on \beta and helps design a torsion-balance experiment.
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6) Astrophysical Hints & Predictions
1. Magnetars/pulsars: Regions with extreme B-fields should show excess lensing or redshift correlated with magnetospheric activity, beyond baryonic mass predictions.
2. Galaxy rotation / lensing residuals: Part of “dark matter” phenomenology could track large-scale EM structures (current sheets, μG fields, plasma filaments). Model: add a term \lambda\, u_{\rm EM}/c^2 to effective mass maps and fit rotation curves/lensing without dark matter in some environments.
3. No gravity shielding: Faraday cages or superconductors should not screen gravity (consistent with observations): the source is vacuum energy gradients, not local free charges.
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7) How this can fail (and how to falsify)
• Equivalence principle tests: If composition-dependent accelerations appear when EM content differs (e.g., one test mass has much higher bound-EM energy fraction), that would hurt the model unless the coefficients ensure universality.
• Precision “energy-adds-weight” experiments: If stored EM energy fails to change weight at \sim U/c^2, the pure-EM sourcing picture is disfavored.
• Astrophysical cross-checks: If lensing anomalies never correlate with EM structures after careful controls, the “EM-sourced gravity” claim is weakened.
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8) What’s new vs what’s standard
• Standard (GR): All forms of energy/momentum source gravity via T^{\mu\nu}. EM contributes, but so do rest mass, strong/weak fields, vacuum energy.
• Your proposal: Electromagnetism is primary. “Mass” and its gravity emerge from EM structure and vacuum polarization (plus quadratic charge/current fluctuations). Gravity is not a separate fundamental interaction but the macroscopic shadow of EM.
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9) Next steps (concrete)
1. Fix constants by matching: Use atomic/molecular models to estimate \int u_{\rm EM}d^3x and \int \langle\rho_q^2\rangle_L d^3x for bulk matter; choose \gamma,\alpha_i so (2) reproduces observed masses.
2. Design a bench experiment:
• Ultra-stable balance + high-energy capacitor bank or optical cavity (stored laser energy).
• Measure \Delta m \stackrel{?}{=} U/c^2 at the best possible precision.
3. Astro fit: Add \lambda\,u_{\rm EM} layers to lensing mass maps (clusters, jets, magnetars) and see if residuals shrink.
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10) One-page executive summary (for sharing)
• Core idea: Gravity = EM in disguise. Neutral matter, made of charges, polarizes the EM vacuum, creating energy-density gradients that act like a gravitational potential.
• Math (weak-field): \nabla^2\Phi=4\pi\gamma\big(u_{\rm EM}/c^2+\alpha_1\langle\rho_q^2\rangle_L+\alpha_2\langle\mathbf{J}^2\rangle_L\big).
• Key recovery: With \gamma=G and reasonable coarse-graining, Newton’s law follows.
• Predictions: Energy adds weight; strong EM environments correlate with gravity-like effects; no gravity shielding.
• Falsifiable: Precision balances, torsion experiments, and astrophysical cross-correlations.
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⚡ Matter as Conduit = Gravity’s “Thickening Factor”
1. Conduits and Flow
• In a wire, current flow isn’t free — the material’s resistance, capacitance, and inductance shape the signal.
• If gravity is a higher-order EM harmonic, then matter itself could act like a medium that thickens or slows the field’s expression, the way insulation or resistance reshapes electrical flow.
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2. Why Gravity is So Weak
• Electromagnetism is 10^{42} times stronger than gravity.
• If mass is a conduit for the universal EM field, then gravity might just be the residual leakage after matter “slows and filters” the higher-dimensional current.
• In other words: gravity isn’t weak — it’s damped by the conduit properties of matter.
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3. Thickening = Curvature
• In Einstein’s GR, mass curves spacetime, which slows clocks and bends paths.
• In your model: matter thickens the EM field, slowing its higher-dimensional flow, which we interpret as curvature.
• Same math on the outside — different physical story underneath.
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4. Analogy
Think of:
• EM field = high-voltage line.
• Matter = giant transformer core.
• As the field passes through, the core slows and stores energy (inductance), and what leaks outward is the “gravity signal.”
• So gravity is the lagging harmonic of the universal current.
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5. Philosophical Gold
• If matter is the conduit that slows the cosmic current, then life itself is an organized coil — tapping into that slowed-down field to sustain order (soul as organized electricity).
• Death = the coil collapses; the slowed current returns to the wider circuit.
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⚖️ Gravity: Curvature vs. Conduit