emergent-gravity.com · account of a research program · 2025–2026

General relativity is what a self-auditing
vacuum looks like.

In one year, a human–AI program derived gravity's attraction from the vacuum's information geometry with nothing put in by hand, built inertia from the same object — the equivalence principle as an identity — and reduced Einstein's γ to a single exponent, with GR as the exact limit. The result survived two hostile referees. The twenty-two ideas it killed along the way are buried below, in public: they are why you can believe the one that stands.

γPPN  =  1 − 2a1 + 2a
γ — the parameter the solar system measures: 1 ± 2.3×10⁻⁵ (Cassini) a — how the vacuum's audit rate scales with local stiffness a = 0 — the ledger's clock doesn't care what it prices → general relativity

one formula standing · valid in the strong-monitoring regime γ·F ≳ 7 · five named assumptions · two hostile referees · every number has a public script

physics
no metaphor

The theory in standard physics: six equations, four mechanisms.

A lattice scalar field whose stiffnesses deform under a Gauss law, (A·δk)ᵢ = −cᵢ, priced by the vacuum's Fubini–Study metric — defects share deformation clouds, and the shared state-displacement is a force: emergent electrostatics, with gauge invariance as a theorem. The constraint sector is continuously measured (Lindblad); constraint-satisfying states are dark states — zero decoherence at rest, and a Lorentzian knee Γ ∝ (dT₀₀/dt)²/(γ²+ω²) for modulated masses. The measuring bath's back-action induces the second force: repulsive for every passive bath (KMS), attractive for the non-equilibrium vacuum a working measurement requires — gravity as a Casimir force of information flow. And redshift follows from ω = E/ħ alone: only quantum phases read the potential as time; classical rates see tides (exact theorem). One dimensionless lock ties it together: γ_knee/G = κ/|Δ| — gravity is weak because the measurement is overdamped. And the newest closure: with γ pinned, Mercury measures the substrate's anharmonicity to four digits, and that same coefficient makes the vacuum's idle bill positive — dark energy's sign, from the perihelion's coefficient. The full page: equations, mechanisms, and what each one measured →

the wager
2025

Existing is expensive.

A mass is not a thing placed in the vacuum; it is a pattern the vacuum maintains, and maintaining it consumes entanglement — the links a mass uses to exist are links the vacuum no longer has. Entanglement is monogamous: every region has a budget, and what is consumed must be drained from elsewhere under a strict local sum rule. A conserved drainage is a Gauss law; Newton's 1/r² is dilution over spheres; the potential is the depression of the water table. One year, fifty-six numbered experiments, and every gate pre-registered before its code existed.

n46–n46c
measured

The vacuum prices in information — and information attracts.

Who sets the price of a rearrangement? Not energy: the vacuum's zero-point energy is concave in its couplings — a theorem (n45) — so it can only destabilize. The one functional left is the vacuum's geometry of states: the quantum information metric, positive by construction, nobody's choice. Price the drainage with it and like masses attract — in one, two and three dimensions, machine-exact Coulomb, with nothing declared anywhere. Falling is the vacuum discovering that two dents in its self-knowledge overlap.

n51a
theorem

The obstacle was worth a theorem of its own.

Gravity is a metric: deeper in a potential, every clock slows. Getting clocks out of the vacuum produced the dichotomy theorem — in any flux-conservation theory with a positive quadratic cost, the architecture that attracts has no linear clock response for substrate observables, and the architecture with linear clocks repels. The theorem identified the assumption that secretly carries the metric in every emergent-gravity program: GR's potential is a local field a clock can touch. Knowing exactly which wall stood in the way is what made the breakthrough findable.

n54–n55
measured

The referees reopened the case: inertia was never built.

An adversarial review found what we had missed: every clock we tested was a substrate observable or a ledger entry — the theory's own matter was never asked the time, and the theory had never constructed inertia. Built honestly — second-order adiabatic response — inertia is the gap-weighted fidelity metric, scaling as k−5/2 (verified to seven digits, independently re-derived by a hostile second referee). Charge, potential and inertia now descend from one geometric object: the equivalence principle as an identity of scaling dimensions, not a coincidence.

n55–n56
standing

Everything collapsed into one exponent.

With inertia from the unitary sector and maintenance priced at the monitor's rate, the theory's post-Newtonian γ closes into the formula above. a is the scaling dimension of the vacuum's monitoring rate: a = 0 gives γ = +0.9999 measured — general relativity; a = ½ gives Nordström's dead scalar. The minimality argument for a = 0 (n56): the monitored violations are dimensionless bookkeeping sitting at exactly zero frequency, protected by the conservation law itself. On this reading, Cassini's six-digit γ is a measurement of the statement that the ledger's clock does not care what it prices — and general relativity is what a self-auditing vacuum looks like in the strong-monitoring limit.

n55b
audited

Then we paid two referees to kill it, and published their knives.

The first review re-carved a headstone we had cut wrongly. The second — fully hostile — found a discarded term 685× larger than the kept one, a registered gate that had silently gone unrun, and a cross-prediction off by eleven orders of magnitude. Every finding was verified, conceded or bounded the same day: the discarded term turned out to define the regime (γ·F ≳ 7, a clean measured scaling law), the dropped gate was run late and passed, the first wave ever propagated through a well confirmed the optics at 10%, and the claim now carries its five assumptions in public. The prior-art sweep says the central claim — a PPN parameter as the scaling dimension of a decoherence rate — is unoccupied territory.

n48
for the lab

One prediction is waiting for an apparatus.

A drainage vacuum reads only violations of its sum rule, so a mass superposition at rest decoheres not at all — and one modulated faster than the vacuum rearranges decoheres along an exact Lorentzian with a knee at the drainage rate. General relativity predicts nothing at any frequency. Collapse models predict a floor already present at rest. Drainage predicts the knee. A frequency-swept levitated-mass interferometer — hardware this decade — reads which universe we live in. The experiment page →

balance

The balance sheet: what one year bought.

ItemStandingRecord
Attraction from the vacuum's information metric, 1D/2D/3Dmeasuredn46
The dichotomy theorem (scope narrowed by review, as proven)theoremn51a
Inertia = gap-weighted fidelity metric, k−5/2measured ×2n55
γ = (1−2a)/(1+2a); GR at a = 0, strong-monitoring regimestandingn55b
Motion-gated decoherence kneeawaits a labn48
Twenty-seven of our own ideasburiedgraveyard