The Underlying Physics
What If Gravity Reads Organization?
The whole theory in plain language — what it claims, why it might be true, what it does NOT claim, and what would prove it wrong.
A Scalar-Tensor Framework for Coherence-Dependent Gravitational Coupling: Electromagnetic Predictions and Cross-Domain Applications
Corey Silvia · v4.0 · Zenodo · April 29, 2026. Open-access preprint of the full theoretical derivation, predictions, and falsifiability criteria.
The Core Idea
Gravity Cares About How Energy Is Arranged
For 110 years, Einstein's general relativity has treated all forms of energy the same way. A joule is a joule: the heat in your coffee, the kinetic energy of a baseball, the electromagnetic energy in a charged capacitor — all of them curve spacetime by the same amount, per joule.
The coherence-dependent gravitational coupling framework proposes a single new term added to Einstein's equations that breaks this democracy. The claim: gravity feels the difference between organized energy and disorganized energy. Organized energy gravitates with enhanced strength. Disorganized (thermal) energy gravitates normally — exactly as standard general relativity says.
That is the entire theory in one sentence. Everything that follows — the device, the asymmetric-capacitor thrust observations, the neutron-star mass-radius results, the superconductor pseudogap, even why this hasn't shown up in everyday experiments — is the consequence of that one sentence.
The Math, in One Picture
Splitting a Field Into “Steady” and “Random”
Picture a river. The total water flow has two parts: the steady downstream current (the “organized” component) and the swirling eddies and turbulence riding on top of it (the “random” component). A British engineer named Osborne Reynolds invented the formal version of this split in 1895 to study turbulent flow. He wrote it as one short equation:
X = ⟨X⟩ + X′
Total field = organized average + random fluctuations.
The trick is that the same split shows up in field after field of physics, completely independently. Fluid dynamics. Quark-gluon plasma. Neutron-star interiors. Superconductors. Even gravity itself, in the way Jacobson derived Einstein's equations from thermodynamics. Five separate fields converged on the same mathematical decomposition, in different decades, by different people, for different reasons.
When that kind of convergence happens, it's usually a sign that the math is telling you something real about nature — not just a notational convenience.
The theory takes that observation seriously: if the organized/random split is fundamental to so many areas of physics, maybe gravity respects that split too. Maybe gravity reads the organized part with one strength and the random part with another.
What Changes
One New Line in Einstein's Equations
Einstein's general relativity says that mass and energy curve spacetime, and the curvature is what we feel as gravity. In equation form, it's:
Gμν = (8πG / c⁴) · [ matter + electromagnetic + ... ]
Curvature on the left. Energy on the right. They're equal.
The framework adds one term to the right-hand side:
Gμν = (8πG / c⁴) · [ matter + EM + α · Φ(φ) · EMorganized + φ ]
The new piece on the right: an extra contribution proportional to the organized part of the EM field, mediated by a scalar field φ.
Three things to notice:
- α is one number, the same in every sector. The framework predicts α = 1 — exactly unity. This is the unique value consistent with every observational constraint we have: the magnetar mass upper bound (α < ~300), the Brandes-Weise trace anomaly central estimate (α ≈ 0.5 to 1.5), and the CHANG-ES galactic null. It is also the only value that avoids introducing a new magnitude knob — it says coherent EM is gravitationally just regular stress- energy, with the structural distinction that coherence matters for which fields are sources. Anything else either requires extra theoretical justification or sits in tension with one constraint. It's the Occam's-razor answer.
- Φ(φ) is a switching function: it's zero when there's no scalar field excited (which is almost everywhere), and it saturates at one where there's lots of organized energy. It turns the new physics on and off automatically.
- EMorganized is the Reynolds-mean part of the electromagnetic field — the steady, coherent part. The random/thermal part is excluded from this term entirely.
When α = 0 or there's no organized energy, the new term vanishes and you recover Einstein's original equations exactly. Standard physics is the special case of this theory where the universe happens to be thermal — which it almost always is.
The Screening
Why Hasn't Anyone Felt This Before?
The natural objection is: if gravity reads organization, why don't we see weird gravitational effects all the time? Why doesn't a charged-up battery weigh differently than a discharged one? Why doesn't a magnet fall faster in a gravitational field?
The answer is built into the math, not patched on after the fact. Almost everything around you is thermal. The energy in your body, the photons from the Sun, the heat in a wire, the electromagnetic noise in a circuit — all of it is random fluctuations. By definition, random fluctuations have zero coherent average:
⟨thermal field⟩ = 0
When the coherent average is zero, the new term in the equation is exactly zero. The theory's extra coupling shuts itself off. It doesn't hide behind small numbers or fine-tuning — it identically vanishes. You recover standard gravity, exactly, for everything thermal.
The only systems where the coupling activates are the rare ones that have macroscopic organization: a DC capacitor (steady field), a superconductor (Cooper-pair condensate), a neutron-star core (deconfined quark-gluon matter). Three highly specialized physical situations. Everything else is invisible to this effect by construction.
That same screening is what makes the theory pass the most precision tests of standard gravity automatically — the MICROSCOPE Eötvös test, the Cassini Shapiro time-delay measurement, the gravitational-wave speed measurement from GW170817. The framework is invisible to all of them by design, not by parameter tuning.
Where It Should Show Up
Where the Framework Has Been Applied
The framework's primary empirical contribution is in the electromagnetic sector — the lab-capacitor regime. The neutron-star and superconductor sectors are cross-domain consistency checks, not independent confirmations: the framework is consistent with the observations, but other mechanisms also produce them.
Lab capacitors
scale ~ 10⁻² morganization: DC electric fieldObservable: Anomalous thrust
The Aurigema-Buhler / Exodus vacuum-thrust program (patent WO2020159603A2) reports millinewton-scale thrust at 30–40 kV in hard vacuum, scaling as V², persisting for days after power is removed, and vanishing for AC. The framework's primary empirical contribution is here — and specifically in the unified prediction across the asymmetric-capacitor literature: prior null results (Talley 1991; Canning et al. 2004; Bahder & Fazi 2002) all involved current flow, breakdown, or Trichel pulses that destroy the coherent component, where the framework predicts zero thrust. The Aurigema-Buhler program operates without current flow, where the framework predicts thrust. This unified prediction is the principal empirical case.
Neutron stars
scale ~ 10⁴ morganization: Deconfined quark-gluon matterObservable: Mass and radius
NICER X-ray pulsar data shows neutron stars near or above the standard maximum-mass bound, and Brandes & Weise (2025) report a negative trace-anomaly Δ<0 signature in the EOS literature. The framework remains consistent with the Δ<0 observation across the tested coupling range, but the Δ<0 sign is inherited from the underlying nuclear equation of state, not generated by the coupling. This is a cross-domain consistency check, not an independent confirmation.
Superconductors
scale ~ 10⁻⁹ morganization: Cooper-pair condensateObservable: Pseudogap phase
The pseudogap state in cuprate superconductors maps onto the boundary between organized and disordered electronic phases, and T* shows a roughly linear scaling with hole doping. The framework is consistent with this picture but does not uniquely produce it — many condensed-matter mechanisms compete to explain the pseudogap. Cross-domain consistency check, not an independent confirmation.
Development chronology (matters for the curve-fitting question): the framework was originally developed in late March 2026 to try to explain galactic rotation curves through electromagnetic coupling. Applying the Reynolds decomposition to the SPARC rotation-curve data and CHANG-ES magnetic-field data revealed that galactic-scale magnetic fields are predominantly turbulent — the Reynolds mean is small after coarse-graining. The framework therefore predicts no observable galactic effect. That was a null result, not a success. It also revealed the framework's predictive structure: the same machinery that gave a null for turbulent galactic fields predicts thrust for coherent capacitor fields. The capacitor predictions were formulated first; the encounter with the Aurigema-Buhler experimental program followed, in early April 2026, prior to manuscript drafting on April 8–9. The v1 manuscript was published April 9, 2026 (Zenodo).
The Lab Prediction
One Equation, Five Things to Measure
For an asymmetric capacitor in a steady DC electric field, the theory predicts a force given by:
F = α · (ε₀ V² / d²) · (κ−1)/κ · A · η
α: the coupling constant · V: applied voltage · d: electrode gap · κ: dielectric constant · A: electrode area · η: geometric asymmetry factor
Each piece of that equation is testable:
- V² (voltage squared): double the voltage, quadruple the force. The published asymmetric-capacitor vacuum data shows this. A clean V² curve from 1 kV to 10 kV is the first discriminator any test article should produce.
- 1/d² (gap): halve the electrode gap, quadruple the force. The framework uses a single electromagnetic coupling here. Earlier alternative parameterizations (gradient, threshold) are not pursued because available data does not distinguish among them.
- (κ−1)/κ (dielectric): stronger insulators give bigger force, but with diminishing returns. Past κ ≈ 50 the curve flattens. A specific, falsifiable quantitative prediction.
- A (area): bigger plates, more force, exactly linear.
- η (asymmetry): without geometric asymmetry, the per-conductor forces cancel and you get nothing. Symmetric capacitors are predicted to produce zero thrust. That's also testable.
On top of those five, three more predicted behaviors: DC only (AC averages to zero coherent field, so no force at any frequency — the framework predicts EmDrive-style nulls); multi-day persistence (force continues for hours-to-days after power is removed, decaying on the scalar-field timescale rather than vanishing instantly — this is the strongest single signature, since classical electrostatics on a discharged capacitor predicts zero residual force); and current-flow nulls (any configuration with current flow, breakdown, or Trichel pulses destroys the coherent component and the coupling vanishes — the framework predicts zero thrust in those configurations, consistent with the prior null literature: Talley 1991, Canning et al. STAIF-2004, Bahder & Fazi 2002).
The principal empirical case is the unified prediction across the asymmetric-capacitor literature — both signs (null and positive) come from a single mechanism (decoherence destroys coupling), and the data divides along the framework's predicted boundary.
How to Prove It Wrong
Predictions, classified honestly
v4.0 reorganized the prediction list by discrimination class: which predictions are confirmed and discriminating, which are untested but would discriminate, which are observed but also consistent with classical mechanisms, and which are cross-domain consistency checks rather than independent confirmations. The honest accounting: one discriminating-and-confirmed prediction (multi-day persistence), one discriminating-but-untested-at-publishable-resolution prediction (AC null), three predictions consistent with but not unique to the framework (V², polarity, magnitude), three cross-domain consistency checks, and one open universality question.
Force continues for hours-to-days after power is removed, decaying on the scalar-field timescale rather than vanishing instantly. Classical electrostatics on a discharged capacitor predicts zero residual force. This is the strongest discriminating signature — the load-bearing observation in the Aurigema-Buhler dataset. Test: continuous-force-vs-time measurements after disconnecting the supply, at publishable resolution.
Time-averaged AC fields produce zero thrust at any frequency from 1 Hz to 1 MHz. Predicted by the framework (the Reynolds-mean of an AC field vanishes). No publishable-resolution measurement exists yet across the relevant frequency range. Test: replace DC supply with AC at the same RMS voltage; thrust must vanish identically.
Force scales as voltage squared. Consistent with the framework, also consistent with classical Maxwell-stress mechanisms in some configurations. Not by itself discriminating. Test: V² fit across a voltage range.
Reversing the supply polarity does not flip the thrust direction. Consistent with the framework. Also consistent with several classical mechanisms (e.g. electrostatic pressure on asymmetric geometry). Not by itself discriminating.
The 237 mN blade thrust reported at 40 kV is reproduced by classical Maxwell electrostatic pressure on the blade-tip area to within ~15%. Magnitude alone does not discriminate between classical electrostatics and the framework. The discriminator is persistence + the current-flow boundary across the prior literature.
Prior null results (Talley 1991; Canning et al. STAIF-2004; Bahder & Fazi 2002) all involved current flow, breakdown, or Trichel pulses that destroy the coherent component. The framework predicts no thrust in those configurations. The Aurigema-Buhler program operates without current flow, where the framework predicts thrust. This unified prediction across six independent experimental programs split along the framework's predicted boundary is the principal structural argument.
Brandes & Weise (2025) report a negative trace-anomaly Δ<0 in the neutron-star EOS literature. The framework's modified TOV equations remain consistent with that observation across the tested coupling range. The Δ<0 sign is inherited from the underlying nuclear equation of state, not generated by the framework. A genuine framework-level prediction of Δ<0 would require pressure-modification work deferred to a later paper.
The cuprate pseudogap maps onto the boundary between organized (Cooper-pair) and disordered (quasiparticle) electronic phases — the framework is consistent with this picture but does not uniquely produce it. Test: existing ARPES / neutron-scattering datasets; cross-check, not a unique prediction.
Whether the coupling α is genuinely the same across the EM, QCD, and electronic sectors is an open theoretical question this paper does not settle. Currently the EM-sector and NS-sector coupling ranges overlap at order-of-magnitude level, which is suggestive but not confirmatory. A genuine universality test requires tightening both ranges with future data.
Setting Expectations
What This Theory Does Not Claim
Propellantless propulsion has a long history of overclaiming. The framework is more careful than that. Here's what it explicitly does NOT say.
It does NOT explain galactic dark matter
Galactic-scale magnetic fields are turbulent at the relevant coarse-graining scales, so the Reynolds-mean component is small and the framework predicts no observable galactic effect. This null prediction was tested against SPARC rotation-curve data and CHANG-ES magnetic-field data and confirmed. The galactic application produced a null result and was honestly reported. The framework does not explain dark matter at galactic scales.
It does NOT generate the Δ<0 trace anomaly in neutron stars
The framework's modified TOV equations remain consistent with the Brandes-Weise Δ<0 observation across the tested coupling range, but the Δ<0 sign is inherited from the underlying nuclear equation of state, not generated by the coupling. A genuine framework-level prediction of Δ<0 would require pressure-modification work deferred to future work.
It does NOT unify electromagnetism and gravity
The framework is a scalar-tensor extension of general relativity with a specific coupling to the coherent (Reynolds-mean) electromagnetic stress-energy. This is a coupling, comparable in structure to Brans-Dicke theory's coupling to a scalar field, not Kaluza-Klein-style geometric unification of EM and gravity in the deep theoretical sense.
It does NOT predict an EmDrive
EmDrive concepts use microwave (AC) fields. The framework predicts zero thrust for AC at any frequency, because the time-averaged coherent field is zero. EmDrive null results in careful experiments are correctly predicted.
It does NOT modify Newtonian gravity in everyday situations
Bulk thermal matter — your body, the Earth's mantle, the Sun's photosphere — has no coherent macroscopic field. The coupling vanishes exactly in thermal equilibrium. Standard general relativity is recovered everywhere except in the special systems listed above.
It is NOT derived from string theory or loop quantum gravity
The framework is proposed phenomenologically on physical grounds (gravity should care about organization) and tested by what it predicts. It is not derived from a more fundamental theory. Its credibility rests on empirical performance — specifically on independent replication of the Aurigema-Buhler vacuum-thrust persistence observations, which has not yet happened.
Where Things Stand
The Honest Status
The framework is compelling. It's also not yet confirmed. Both of those are true at the same time, and overclaiming or underclaiming would be wrong.
α = 1 — Occam's-razor coupling, anchored on multiple constraints
α = 1 fits the data best because it's the only value that's simultaneously consistent with every observational constraint AND theoretically parsimonious. It satisfies the magnetar mass upper bound (α < ~300), aligns with the tentative trace-anomaly central estimate (α ≈ 0.5 to 1.5) from Brandes-Weise, doesn't violate the CHANG-ES galactic null result, and represents the simplest non-trivial theoretical commitment: coherent EM stress-energy contributes to gravitational coupling with the same strength as ordinary stress-energy, with no new free parameter introduced. Any other value either requires extra theoretical justification (why would α be 0.3 or 2.7 specifically?) or sits in tension with one of the constraints. α = 0 means the theory adds nothing; α ≫ 1 demands an explanation for why coherent EM gravitates more strongly than ordinary matter; α = 1 is the unique value that says 'coherent EM is just regular stress-energy gravitationally, but with the structural distinction that coherence matters for which fields are sources' — adding one structural feature without adding a magnitude knob. Earlier drafts used a Buhler-anchored estimate (≈ 1.4×10⁻²) from paper-internal modeling choices for gap / area / dielectric; the current framework abandons that calibration in favor of the unity target.
Discriminating evidence rests on persistence, not magnitude
The 237 mN blade-thrust magnitude is reproduced by classical Maxwell electrostatic pressure on the blade-tip area to within ~15% — magnitude alone does not discriminate between classical electrostatics and the framework. The discriminator is multi-day persistence after power-off (which classical electrostatics cannot explain on a discharged capacitor) and the framework's prediction of current-flow null results across the prior literature.
Cross-domain results are consistency checks
The neutron-star and superconductor applications are cross-domain consistency checks on whether the framework's structural assumptions and coupling constants remain internally consistent across regimes — they are not independent confirmations of the EM-sector predictions. The framework's primary empirical contribution is in the electromagnetic sector.
Load-bearing test: independent replication
The framework's primary empirical anchor (the Aurigema-Buhler persistence reports) has not yet been independently replicated. The load-bearing falsification test is independent replication of the Buhler-geometry vacuum thrust by a group with no financial or reputational stake in the Exodus program, conducted inside an independently-constructed and verified Faraday enclosure. If the persistence and current-flow boundary observations do not replicate, the framework's primary empirical claim is falsified.
The Strongest Evidence
What is the single most discriminating observation?
Multi-day thrust persistence after power-off. The Aurigema-Buhler / Exodus dataset reports thrust continuing for hours-to-days after the high-voltage supply is disconnected, decaying gradually rather than vanishing instantly.
Classical electrostatics on a discharged capacitor predicts zero residual force. There is no charged region left to produce Maxwell stress. The framework predicts a slow decay on the scalar-field timescale, because the scalar field that mediates the coupling has a finite mass and therefore a finite lifetime. This is the load-bearing observation — the one that cannot be reproduced by any classical mechanism on a discharged device.
Two further structural features support the case but do not by themselves discriminate: zero current flow during operation (the framework requires this; the prior null literature operated with current flow, where the framework also predicts no thrust), and the ~2,370× DIY-to-optimized geometric enhancement scale (Aurigema's DIY single-thruster reports ~0.1 mN at 40 kV vs. the optimized 9-blade ~237 mN at the same voltage). Reproducing the persistence independently is the priority test.
Note: the 237 mN blade magnitude is reproduced by classical Maxwell electrostatic pressure on the blade-tip area to within ~15%. Magnitude alone does not discriminate between classical electrostatics and the framework. Persistence does.
How to Falsify the Framework
The load-bearing test
Independent replication of the Buhler-geometry vacuum thrust. By a group with no financial or reputational stake in the Exodus program. Inside an independently-constructed and verified Faraday enclosure with documented grounding integrity. Under a continuous force-vs-time measurement that runs through power-down so the persistence decay is captured directly.
Buhler's ITO-PET grounded enclosure is accepted as adequate Faraday shielding for the original measurements — the falsification test is not about adding shielding Buhler lacked, it's about independent reproduction by a non-aligned group under their own controls.
If the persistence and current-flow boundary observations do not replicate, the framework's primary empirical claim is falsified. The framework does not have escape hatches: there is no parameter that can be retuned to keep the prediction alive if the central observations don't reproduce.
Historical context
The asymmetric-capacitor literature did not start in 2010
The same device geometry the Aurigema-Buhler program is testing today was first patented by Thomas Townsend Brown in 1928, and the “persistence after power-off” observation that anchors the framework's discriminating prediction has been in his notebooks since the 1920s. Six decades of one experiment, most of it ignored.
T. T. Brown · 1905 — 1985
Read about the original program
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Visit the about pageReference: Silvia, C. (2026). “A Scalar-Tensor Framework for Coherence-Dependent Gravitational Coupling: Electromagnetic Predictions and Cross-Domain Applications,” v4.0 (Zenodo, April 29, 2026, 10.5281/zenodo.19547728). v4.0 reflects an independent audit of v3.x; the prediction count, the discriminating-vs-consistent classification of individual predictions, the cross-domain framing as consistency-checks rather than confirmations, and the attribution of the Δ<0 trace anomaly to the underlying equation of state (rather than to the framework) all reflect that audit. The full paper covers the action principle, scalar-field equation, weak-field force-law derivation, and consistency checks against MICROSCOPE, Cassini, GW170817, and tidal-deformability constraints.